NCERT Solutions for Class 11 Chemistry Chapter 7
Q.1. A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.
a) What is the initial effect of the change on vapour pressure?
b) How do rates of evaporation and condensation change initially?
c) What happens when equilibrium is restored finally and what will be the final vapour pressure?
Ans.
(a) On increasing the volume of the container, the vapour pressure will initially decrease because the same amount of vapours is now distributed over a large space.
(b) On increasing the volume of the container, the rates of evaporation will increase initially because now more space is available. Since the amount of vapours per unit volume decrease on increasing the volume, the rate of condensation will decrease initially.
(c) Finally, equilibrium will be restored when the rates of the forward and backward processes become equal. However, the vapour pressure will remain unchanged because it depends upon the temperature and not upon the volume of the container.
Q.2.What is Kc for the following equilibrium when the equilibrium concentration of each substance is: [SO2]= 0.60M, [O2] = 0.82M and [SO3] = 1.90M?
\(\begin{array}{l}2SO_{2}(g)+O_{2}(g) ⇌ 2SO_{3}(g)\end{array} \)
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Ans.
As per the question,
\(\begin{array}{l}2SO_{2}(g)+O_{2}(g) ⇌ 2SO_{3}(g)\end{array} \)
(Given)
\(\begin{array}{l}K_{c}=\frac{[SO_{3}]^{2}}{[SO_{2}]^{2}[O_{2}]}\\ \\ =\frac{(1.9)^{2}M^{2}}{(0.6)^{2}(0.82)M^{3}}\\ \\ =12.229M^{-1}\end{array} \)
(approximately)
Hence, K for the equilibrium is 12.229 M–1.
Q.3. At a certain temperature and total pressure of 105 Pa, iodine vapour contains 40% by volume of I atoms
I2(g) ⇌ 2I (g) Calculate Kp for the equilibrium
Ans.
The partial pressure of Iodine atoms (I)
\(\begin{array}{l}p_{I}=\frac{40}{100}\times p_{total}\\ \\ =\frac{40}{100}\times 10^{5}\\ \\ =4\times 10^{4}Pa\end{array} \)
The partial pressure of I2 molecules,
\(\begin{array}{l}p_{I}=\frac{60}{100}\times p_{total}\\ \\ =\frac{60}{100}\times 10^{5}\\ \\ =6\times 10^{4}Pa\end{array} \)
Now, for the given reaction,
\(\begin{array}{l}K_{p}=\frac{(p_{I})^{2}}{p_{I_{2}}} =\frac{(4\times 10^{4})^{2}Pa^{2}}{6\times 10^{4}Pa}\\ \\ =2.67\times 10^{4}Pa\end{array} \)
Q.4.Write the expression for the equilibrium constant, Kc, for each of the following reactions:
(i)
\(\begin{array}{l}2NOCl(g)\leftrightarrow 2NO(g)+Cl_{2}(g)\end{array} \)
(ii)
\(\begin{array}{l}2Cu(NO_{3})_{2}(s)\leftrightarrow 2CuO(s)+4NO_{2}(g)+O_{2}(g)\end{array} \)
(iii)
\(\begin{array}{l}CH_{3}COOC_{2}H_{5}(aq)+H_{2}O(1)\leftrightarrow CH_{3}COOH(aq)+C_{2}H_{5}OH(aq)\end{array} \)
(iv)
\(\begin{array}{l}Fe^{3+}(aq)+3OH^{-}(aq)\leftrightarrow Fe(OH)_{3}(s)\end{array} \)
(v)
\(\begin{array}{l}I_{2}(s)+5F_{2}\leftrightarrow 2IF_{5}\end{array} \)
Ans.
(i)
\(\begin{array}{l}K_{C}=\frac{[NO_{g}]^{2}[Cl_{2_{(g)}}]}{[NOCl_{(g)}]^{2}}\end{array} \)
(ii)
\(\begin{array}{l}K_{C}=\frac{[CuO_{(s)}]^{2}[NO_{2_{(g)}}]^{4}[O_{2_{(g)}}]}{[Cu(NO_{3})_{2(g)}]^{2}}\\ \\ =[NO_{2(g)}]^{4}[O_{2(g)}]\end{array} \)
(iii)
\(\begin{array}{l}K_{C}=\frac{[CH_{3}COOH_{(aq)}][C_{2}H_{5}OH_{(aq)}]}{[CH_{3}COOC_{2}H_{5(aq)}][H_{2}O_{(l)}]}\\ \\ =\frac{[CH_{3}COOH_{(aq)}][C_{2}H_{5}OH_{(aq)}]}{[CH_{3}COOC_{2}H_{5(aq)}]}\end{array} \)
(iv)
\(\begin{array}{l}K_{C}=\frac{[Fe(OH)_{3(s)}]}{[Fe^{3+}_{(aq)}][OH^{-}_{(aq)}]^{3}}\\ \\ =\frac{1}{[Fe^{3+}_{(aq)}][OH^{-}_{(aq)}]^{3}}\end{array} \)
(v)
\(\begin{array}{l}K_{C}=\frac{[IF_{5}]^{2}}{[I_{2(s)}][F_{2}]^{5}}\\ \\ =\frac{[IF_{5}]^{2}}{[F_{2}]^{5}}\end{array} \)
Q.5.Find out the value of Kc for each of the following equilibria from the value of Kp:
(i)
\(\begin{array}{l}2NOCl(g) ⇌ 2NO(g)+Cl_{2}(g);\: \: \: K_{p}=1.8\times 10^{-2}\: \: at\: 500K\end{array} \)
(ii)
\(\begin{array}{l}CaCO_{3}(s) ⇌ CaO(s)+CO_{2}(g);\: \: \: K_{p}=167\: \: at\: 1073K\end{array} \)
Ans.
The relation between Kp and Kc is given as follows:
\(\begin{array}{l}K_{p}=K_{c}(RT)^{\Delta n}\end{array} \)
(i) Given,
R = 0.0831 barLmol–1K–1
\(\begin{array}{l}\Delta n = 3-2 =1\end{array} \)
T = 500 K
Kp=
\(\begin{array}{l}1.8\times 10^{-2}\end{array} \)
Now,
Kp = Kc (RT) ∆n
\(\begin{array}{l}\Rightarrow 1.8\times 10^{-2}=K_{c}(0.0831\times 500)^{1}\\ \\ \Rightarrow K_{c}=\frac{1.8\times 10^{-2}}{0.0831\times 500}\\ \\ =4.33\times 10^{-4}(approximately)\end{array} \)
(ii) Here,
∆n =2 – 1 = 1
R = 0.0831 barLmol–1K–1
T = 1073 K
Kp= 167
Now,
Kp = Kc (RT) ∆n
\(\begin{array}{l}\Rightarrow 167=K_{c}{(0.0831\times 1073)^{\Delta n}}\\ \\ \Rightarrow K_{c}=\frac{167}{0.0831\times 1073}\\ \\ =1.87(approximately)\end{array} \)
.
Q.6. For the following equilibrium,
\(\begin{array}{l}K_{c}=6.3\times 10^{14}\: \: \: at\: 1000K\\ \\ NO(g)+O_{3(g)} ⇌ NO_{2(g)}+O_{2(g)}\end{array} \)
Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is Kc for the reverse reaction?
Ans.
For the reverse reaction,
\(\begin{array}{l}K_{c}=\frac{1}{K_{c }}\\ \\ =\frac{1}{6.3\times 10^{14}}\\ \\ =1.59\times 10^{-15}\end{array} \)
Q.7. Explain why solids and pure liquids can be ignored while writing the equilibrium constant expression.
Ans.
Solids and pure liquids can be ignored while writing the equilibrium constant expression because the molar concentration of a pure solid or liquid is independent of the amount present.
Mole concentration=
\(\begin{array}{l}\frac{Number\: of\: moles}{Volume}\\ \\ \frac{Mass/molecular\:mass}{Volume}\\ \\ =\frac{Mass}{Volume\,\times\, Molecular \:mass}\\ \\ =\frac{Density}{Molecular\: mass}\end{array} \)
As the density of the solid and pure liquid is fixed, the molar mass is also fixed.
\(\begin{array}{l}∴\end{array} \)
Molar concentration is constant.
Q.8. The reaction between N2 and O2 takes place as follows:
\(\begin{array}{l}2N_{2}(g)+O_{2} ⇌ 2N_{2}O(g)\end{array} \)
If a solution of 0.933 mol of oxygen and 0.482 mol of nitrogen is placed in a 10 L reaction vessel and allowed to form N2O at a temperature for which Kc =
\(\begin{array}{l}2.0\times 10^{-37}\end{array} \)
, determine the composition of the equilibrium solution.
Ans.
Let the concentration of N2O at equilibrium be x.
The given reaction is:
2N2(g) + O2(g) ⇌ 2N2O(g)
Initial conc. 0.482 mol 0.933 mol 0
At equilibrium(0.482-x)mol (1.933-x)mol x mol
\(\begin{array}{l}[N_{2}]=\frac{0.482-x}{10}\cdot [O_{2}]=\frac{0.933-\frac{x}{2}}{10},[N_{2}O]=\frac{x}{10}\end{array} \)
The value of the equilibrium constant is extremely small. This means that only small amounts. Then,
\(\begin{array}{l}[N_{2}]=\frac{0.482}{10}=0.0482molL^{-1} \: \:and\:\: [O_{2}]=\frac{0.933}{10}=0.0933molL^{-1}\end{array} \)
Now,
\(\begin{array}{l}K_{c}=\frac{[N_{2}O_{(g)}]^{2}}{[N_{2(g)}][O_{2(g)}]}\\ \\ \Rightarrow 2.0\times 10^{-37}=\frac{(\frac{x}{10})^{2}}{(0.0482)^{2}(0.0933)}\\ \\ \Rightarrow \frac{x^{2}}{100}=2.0 \times 10^{-37}\times (0.0482)^{2}\times (0.0933)\\ \\ \Rightarrow x^{2}=43.35\times 10^{-40}\\ \\ \Rightarrow x=6.6\times 10^{-20}\end{array} \)
\(\begin{array}{l}[N_{2}O]=\frac{x}{10}=\frac{6.6\times 10^{-20}}{10}\\ \\ =6.6\times 10^{-21}\end{array} \)
.
Q.9. Nitric oxide reacts with Br2 and gives nitrosyl bromide as per the reaction given below:
2NO(g)+Br2(g) ⇌ 2NOBr(g)
When 0.087 mol of NO and 0.0437 mol of Br2 are mixed in a closed container at a constant temperature, 0.0518 mol of NOBr is obtained at equilibrium. Calculate the equilibrium amount of NO and Br2.
Ans.
The given reaction is:
2NO(g)+Br2(g) ⇌ 2NOBr(g)
2mol 1mol 2mol
Now, 2 mol of NOBr is formed from 2 mol of NO. Therefore, 0.0518 mol of NOBr is formed from 0.0518 mol of NO.
Again, 2 mol of NOBr is formed from 1 mol of Br.
Therefore, 0.0518 mol of NOBr is formed from
\(\begin{array}{l}\frac{0.0518}{2}\end{array} \)
mol or Br, or 0.0259 mol of NO.
The amount of NO and Br present initially is as follows:
[NO] = 0.087 mol [Br2] = 0.0437 mol
Therefore, the amount of NO present at equilibrium is:
[NO] = 0.087 – 0.0518 = 0.0352 mol.
And the amount of Br present at equilibrium is:
[Br2] = 0.0437 – 0.0259 = 0.0178 mol.
Q.10. At 450 K, Kp=
\(\begin{array}{l}2.0 \times 10^{10}\end{array} \)
/bar for the given reaction at equilibrium.
2SO2(g)+O2(g) ⇌ 2SO3(g) What is Kc at this temperature?
Ans.
For the given reaction,
∆n = 2 – 3 = – 1
T = 450 K
R = 0.0831 bar L bar K–1 mol–1
Kp=
\(\begin{array}{l}2.0 \times 10^{10}bar^{-1}\end{array} \)
We know that,
\(\begin{array}{l}K_{p}=K_{c}(RT)\Delta n\\ \\ \Rightarrow 2.0\times 10^{10}bar^{-1}=K_{c}(0.0831L\, bar\, K^{-1}mol^{-1}\times 450K)^{-1}\\ \\ \Rightarrow K_{c}=\frac{2.0\times 10^{10}bar^{-1}}{(0.0831L\, bar\, K^{-1}mol^{-1}\times 450K)^{-1}}\\ \\ =(2.0\times 10^{10}bar^{-1})(0.0831L\, bar\, K^{-1}mol^{-1}\times 450K)\\ \\ =74.79\times 10^{10}L\, mol^{-1}\\ \\ =7.48\times 10^{11}L\, mol^{-1}\\ \\ =7.48\times 10^{11}\, M^{-1}\end{array} \)
.
Q.11. A sample of HI(g) is placed in a flask at a pressure of 0.2 atm. At equilibrium, the partial pressure of HI(g) is 0.04 atm. What is Kp for the given equilibrium?
2HI(g) ⇌ H2(g)+I2(g)
Ans.
The initial concentration of HI is 0.2 atm. At equilibrium, it has a partial pressure of 0.04 atm.
Therefore, a decrease in the pressure of HI is 0.2 – 0.04 = 0.16. The given reaction is:
2HI(g) ⇌ H2(g) + I2(g)
Initial conc. 0.2 atm 0 0
At equilibrium 0.4 atm 0.16/2 0.16/2
= 0.08atm = 0.08atm
Therefore,
\(\begin{array}{l}K_{p=}\frac{p_{H_{2}}\times p_{I_{2}}}{p^{2}_{HI}}\\ \\ =\frac{0.08\times 0.08}{(0.04)^{2}}\\ \\ =\frac{0.0064}{0.0016}\\ \\ =4.0\end{array} \)
Hence, the value of Kp for the given equilibrium is 4.0.
Q.12. A mixture of 1.57 mol of N2, 1.92 mol of H2 and 8.13 mol of NH3 is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, Kc, for the reaction is
N2(g)+3H2(g) ⇌ 2NH3(g) is
\(\begin{array}{l}1.7\times 10^{2}\end{array} \)
.
Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?
Ans.
The given reaction is:
N2(g)+3H2(g) ⇌ 2NH3(g)
The given concentration of various species is
[N2]=
\(\begin{array}{l}\frac{1.57}{20}mol\, L^{-1}\end{array} \)
[H2]=
\(\begin{array}{l}\frac{1.92}{20}mol\, L^{-1}\end{array} \)
[NH3]=
\(\begin{array}{l}\frac{8.31}{20}mol\, L^{-1}\end{array} \)
Now, the reaction quotient Qc is:
\(\begin{array}{l}Q=\frac{[NH_{3}]^{2}}{[N_{2}][H_{2}]^{3}}\\ \\ =\frac{(\frac{(8.13)}{20})^{2}}{(\frac{1.57}{20})(\frac{1.92}{20})^{3}}\\ \\ =2.4\times 10^{3}\end{array} \)
Since Qc ≠ Kc, the reaction mixture is not at equilibrium.
Again, Qc > Kc. Hence, the reaction will proceed in the reverse direction.
Q.13. The equilibrium constant expression for a gas reaction is,
\(\begin{array}{l}K_{c}=\frac{[NH_{3}]^{4}[O_{2}]^{5}}{[NO]^{4}[H_{2}O]^{6}}\end{array} \)
.
Write the balanced chemical equation corresponding to this expression.
Ans.
The balanced chemical equation corresponding to the given expression can be written as:
4NO(g)+6H2o(g) ⇌ 4NH3(g)+5O2(g).
Q.14. One mole of H2O and one mole of CO are taken in a 10 L vessel and heated to 725 K. At equilibrium, 60% of water (by mass) reacts with CO according to the equation,
H2O(g) + CO(g) ⇌ H2(g) + CO2(g)
Calculate the equilibrium constant for the reaction.
Ans.
The given reaction is:
H2O(g) + CO(g) ⇌ H2(g) + CO2(g)
Compound | H20 | CO | H2 | CO2 |
Initial Conc. | 0.1M | 0.1M | 0 | 0 |
Equilibrium Conc. | 0.06M | 0.06M | 0.04M | 0.04M |
Therefore, the equilibrium constant for the reaction,
Kc = ([H2][CO2])/([H2O][CO]) = (0.4*0.4)/(0.6*0.6) = 0.444.
Q.15. At 700 K, the equilibrium constant for the reaction H2(g)+I2(g) ⇌ 2HI(g) is 54.8. If 0.5 molL–1 of HI(g) is present at equilibrium at 700 K, what is the concentration of H2(g) and I2(g), assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700 K?
Ans.
It is given that equilibrium constant Kc for the reaction
H2(g)+I2(g) ⇌ 2HI(g) is 54.8.
Therefore, at equilibrium, the equilibrium constant K’c for the reaction
2HI(g) ⇌ H2(g)+I2(g)
[HI]=0.5 molL-1 will be 1/54.8.
Let the concentrations of hydrogen and iodine at equilibrium be x molL–1
[H2]=[I2]=x mol L-1
Therefore,
\(\begin{array}{l}\frac{[H_{2}][I_{2}]}{[HI]^{2}}=K^{‘}_{c}\\ \\ \Rightarrow \frac{x\times x}{(0.5)^{2}}=\frac{1}{54.8}\\ \\ \Rightarrow x^{2}=\frac{0.25}{54.8}\\ \\ \Rightarrow x=0.06754\\ \\ x=0.068molL^{-1}(approximately)\end{array} \)
Hence, at equilibrium, [H2]=[I2]=0.068 mol L-1.
Q.16. What is the equilibrium concentration of each of the substances in the equilibrium when the initial concentration of ICl was 0.78 M?
2ICl(g) ⇌ I2(g)+Cl2(g) ; Kc =0.14
Ans.
The given reaction is:
2ICl(g) ⇌ I2(g) + Cl2(g)
Initial conc. 0.78 M 0 0
At equilibrium (0.78-2x) M x M x M
Now, we can write,
\(\begin{array}{l}\frac{[I_{2}][Cl_{2}]}{[IC]^{2}}=K_{c}\\ \\ \Rightarrow \frac{x\times x}{(0.78-2x)^{2}}=0.14\\ \\ \Rightarrow \frac{x^{2}}{(0.78-2x)^{2}}=0.14\\ \\ \Rightarrow \frac{x}{0.78-2x}=0.374\\ \\ \Rightarrow x=0.292-0.748x\\ \\ \Rightarrow 1.748x=0.292\\ \\ \Rightarrow x=0.167\end{array} \)
Hence, at equilibrium,
[H2]=[I2]=0.167 M
[HI]=
\(\begin{array}{l}(0.78-2\times 0.167)M\\ \\ =0.446M\end{array} \)
.
Q.17. Kp = 0.04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C2H6 when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?
C2H6(g) ⇌ C2H4(g) +H2(g)
Ans.
Let p be the pressure exerted by ethene and hydrogen gas (each) at equilibrium. Now, according to the reaction,
C2H6(g) ⇌ C2H4(g) + H2(g)
Initial conc. 4.0 M 0 0
At equilibrium (4.0-p) p p
We can write,
\(\begin{array}{l}\frac{p_{c_{2}H_{4}}\times p_{H_{2}}}{p_{c_{2}H_{6}}}=K_{P}\\ \\ \Rightarrow \frac{p\times p}{40-p}=0.04\\ \\ \Rightarrow p^{2}=0.16-0.04p\\ \\ \Rightarrow p^{2}+0.04p-0.16=0\end{array} \)
Now,
\(\begin{array}{l}p=\frac{-0.04\pm \sqrt{(0.04)^{2}-4\times 1\times (-0.16)}}{2\times 1}\\ \\ =\frac{-0.04\pm 0.80}{2}\\ \\ =\frac{0.76}{2}\: \: \: \: \: \: \: \: \: (Taking \:positive\: value)\\ \\ =0.38\end{array} \)
Hence, at equilibrium, [C2H6] = 4 – p = 4 – 0.38
= 3.62 atm.
Q.18. Ethyl acetate is formed by the reaction between ethanol and acetic acid, and the equilibrium is represented as:
CH3COOH(l) + C2H5OH(l) ⇌ CH3COOC2H5(l) + H2O(l)
(i) Write the concentration ratio (reaction quotient) Qc for this reaction (note: water is not in excess and is not a solvent in this reaction).
(ii) At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.
(iii) Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after some time. Has equilibrium been reached?
Ans.
(i)Reaction quotient,
\(\begin{array}{l}Q_{c}=\frac{[CH_{3}COOC_{2}H_{5}][H_{2}O]}{[CH_{3}COOH][C_{2}H_{5}OH]}\end{array} \)
(ii) Let the volume of the reaction mixture be V. Also, here we will consider that water is a solvent and is present in excess.
The given reaction is:
CH3COOH(l) + C2H5OH(l) ⇌ CH3COOC2H5(l) + H2O(l)
Initial conc. 1/V M 0.18/V M 0 0
At equilibrium (1-0.171)/V (0.18 – 0.171)/V 0.171/V M 0.171/V M
= 0.829/V M = 0.009/V M
Therefore, the equilibrium constant for the given reaction is:
\(\begin{array}{l}K_{c}=\frac{[CH_{3}COOC_{2}H_{5}][H_{2}O]}{[CH_{3}COOH][C_{2}H_{5}OH]}\\ \\ =\frac{\frac{0.171}{V}\times \frac{0.171}{V}}{\frac{0.829}{V}\times \frac{0.009}{V}}=3.919\\ \\ =3.92(approximately)\end{array} \)
(iii) Let the volume of the reaction mixture be V.
CH3COOH(l)+C2H5OH(l) ⇌ CH3COOC2H5(l)+H2O(l)
Initial conc. 1.0/V M 0.5/V M 0 0
At equilibrium (10-0.214)/V (0.5-0.214)/V 0.214/V M 0.214/V M
= 0.786/V M = 0.286/V M
Therefore, the reaction quotient is,
\(\begin{array}{l}K_{c}=\frac{[CH_{3}COOC_{2}H_{5}][H_{2}O]}{[CH_{3}COOH][C_{2}H_{5}OH]}\\ \\ =\frac{\frac{0.214}{V}\times \frac{0.214}{V}}{\frac{0.786}{V}\times \frac{0.286}{V}}=0.2037\\ \\ =0.204(approximately)\end{array} \)
Since Qcc, equilibrium has not been reached.
Q.19. A sample of pure PCl5 was introduced into an evacuated vessel at 473 K. After equilibrium was attained, the concentration of PCl5 was found to be
\(\begin{array}{l}0.5\times 10^{-1}\end{array} \)
mol L–1. If the value of Kc is
\(\begin{array}{l}8.3\times 10^{-3}\end{array} \)
, what are the concentrations of PCl3 and Cl2 at equilibrium?
PCl5(g) ⇌ PCl3(g) + Cl2(g)
Ans.
Consider the concentration of both PCl3 and Cl2 at equilibrium to be x molL–1. The given reaction is:
PCl5(g) ⇌ PCl3(g) + Cl2(g)
At equilibrium
\(\begin{array}{l}0.5\times 10^{-10}molL^{-1}\end{array} \)
x mol L-1 x mol L-1
It is given that the value of the equilibrium constant, Kc, is
\(\begin{array}{l}8.3\times 10^{-10}molL^{-3}\end{array} \)
Now, we can write the expression for equilibrium as:
\(\begin{array}{l}\frac{[PCl_{2}][Cl_{2}]}{[PCl_{3}]}=K_{c}\\ \\ \Rightarrow \frac{x\times x}{0.5\times 10^{-10}}=8.3\times 10^{-3}\\ \\ \Rightarrow x^{2}=4.15\times 10^{-4}\\ \\ \Rightarrow x=2.04\times 10^{-2}\\ \\ =0.0204\\ \\ =0.02(approximately)\end{array} \)
Therefore, at equilibrium,
[PCl3]=[Cl2]=0.02mol L-1.
Q.20. One of the reactions that take place in producing steel from iron ore is the reduction of iron (II) oxide by carbon monoxide to give iron metal and CO2.
FeO (s) + CO (g) ⇌ Fe (s) + CO2 (g); Kp= 0.265 at 1050 K.
What is the equilibrium partial pressures of CO and CO2 at 1050 K if the initial partial pressures are: pCO = 1.4 atm and pCO2= 0.80 atm?
Ans.
For the given reaction,
FeO(g) + CO(g) ⇌ Fe(s)+CO2(g)
Initially, pCO = 1.4 atm and pCO2= 0.80 atm
Qp=
\(\begin{array}{l}\frac{p_{CO_{2}}}{p_{CO}}\\ \\ =\frac{0.80}{1.4}\\ \\ =0.571\end{array} \)
Since Qp > Kp, the reaction will proceed in the backward direction.
Therefore, we can say that the pressure of CO will increase while the pressure of CO2 will decrease.
Now, let the increase in pressure of CO = decrease in pressure of CO2 be p. Then, we can write,
\(\begin{array}{l}K_{p}=\frac{p_{CO_{2}}}{p_{CO}}\\ \\ \Rightarrow 0.265=\frac{0.80-p}{1.4+p}\\ \\ \Rightarrow 0.371+0.265p=0.80-p\\ \\ \Rightarrow 1.265p=0.429\\ \\ \Rightarrow p=0.339 atm\end{array} \)
Therefore, the equilibrium partial of CO2,pCO=0.80-0.339 = 0.461 atm.
And, equilibrium partial pressure of CO,pCO=1.4+0.339 = 1.739 atm.
Q.21. The equilibrium constant, Kc, for the reaction
N2(g)+3H2(g) ⇌ 2NH3 at 500 K is 0.061
At a specific time, from the analysis, we can conclude that the composition of the reaction mixture is 3.0 mol L –1 N2, 2.0 mol L–1 H2 and 0.5 mol L–1 NH3. Find out whether the reaction is at equilibrium or not. Find in which direction the reaction proceeds to reach equilibrium.
Ans.
N2(g) + 3H2(g) ⇌ 2NH3
At a particular time: 3.0 mol L-1 2.0mol L-1 0.5 mol L-1
So,
Qc=
\(\begin{array}{l}\frac{[NH_{3}]^{2}}{[N_{2}][H_{2}]^{3}}\\ \\ =\frac{(0.5)^{2}}{(3.0)(2.0)^{3}}\\ \\ =0.0104\end{array} \)
It is given that Kc=0.061
\(\begin{array}{l}∵\end{array} \)
\(\begin{array}{l}Qc \neq K_{c}\end{array} \)
, the reaction is not at equilibrium.
\(\begin{array}{l}∵\end{array} \)
\(\begin{array}{l}Qc < K_{c}\end{array} \)
,
The reaction proceeds in the forward direction to reach at equilibrium.
Q.22.Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:
2BrCl(g) ⇌ Br2(g) + Cl2(g)
For which Kc= 32 at 500 K.
If initially pure BrCl is present at a concentration of
\(\begin{array}{l}3.3 \times 10^{-3}\end{array} \)
molL-1, what is its molar concentration in the mixture at equilibrium?
Ans.
Let the amount of bromine and chlorine formed at equilibrium be x. The given reaction is:
2BrCl(g) ⇌ Br2(g) + Cl2(g)
Initial conc.
\(\begin{array}{l}3.3\times 10^{-3}\end{array} \)
0 0
At equilibrium
\(\begin{array}{l}3.3\times 10^{-3}-2x\end{array} \)
x x
Now, we can write,
\(\begin{array}{l}\frac{[Br_{2}][Cl_{2}]}{[BrCl]^{2}}=K_{c}\\ \\ \Rightarrow \frac{x\times x}{(3.3\times 10^{-3}-2x)^{2}}=32\\ \\ \Rightarrow \frac{x}{3.3\times 10^{-3}-2x}=5.66\\ \\ \Rightarrow x=18.678\times 10^{-3}-11.32x\\ \\ \Rightarrow 12.32x=18.678\times 10^{-3}\\ \\ \Rightarrow x=1.5\times 10^{-3}\end{array} \)
So
\(\begin{array}{l},\end{array} \)
at equilibrium
\(\begin{array}{l}[BrCl]=3.3\times 10^{-3}-(2\times 1.5\times 10^{-3})\\ \\ =3.3\times 10^{-3}-3.0\times 10^{-3}\\ \\ =0.3\times 10^{-3}\\ \\ =3.0\times 10^{-4}molL^{-1}\end{array} \)
Q.23.At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO2 in equilibrium with solid carbon has 90.55% CO by mass
C(s) + CO2 (g) ⇌ 2CO (g)
Calculate Kc for this reaction at the above temperature.
Ans.
Let us assume that the solution is 100g in total.
Given, the mass of CO = 90.55 g
Now, the mass of CO2 = (100 – 90.55) = 9.45 g
Now, the number of moles of CO,
\(\begin{array}{l}n_{CO}=\frac{90.5}{28}=3.234\: mol\end{array} \)
The number of moles of CO2,
\(\begin{array}{l}n_{CO_{2}}=\frac{9.45}{44}=0.215\: mol\end{array} \)
The partial pressure of CO,
PCO=
\(\begin{array}{l}\frac{n_{CO}}{n_{CO}+n_{CO_{2}}}\times p_{total}=\frac{3.234}{3.234+0.215}\times 1=0.938\, atm\end{array} \)
Partial pressure of CO2,
\(\begin{array}{l}P_{CO_{2}}=\frac{n_{CO_{2}}}{n_{CO}+n_{CO_{2}}}\times p_{total}=\frac{0.215}{3.234+0.215}\times 1=0.062, atm\end{array} \)
Therefore, Kp=
\(\begin{array}{l}\frac{[CO]^{2}}{[CO_{2}]}\\ \\ =\frac{(0.938)^{2}}{0.062}\\ \\ =14.19\end{array} \)
For the given reaction,
∆n = 2 – 1 = 1
We know that,
Kp = Kc(RT)
\(\begin{array}{l}\Delta n\end{array} \)
\(\begin{array}{l}\Rightarrow 14.19 = K_{c}(0.082\times 1127)^{1}\\ \\ \Rightarrow K_{c}=\frac{14.19}{0.082\times 1127}\\ \\ =0.154(approximately)\end{array} \)
.
Q.24. Calculate a) ∆G0 and b) the equilibrium constant for the formation of NO2 from NO and O2 at 298K
\(\begin{array}{l}NO(g)+\frac{1}{2}O_{2}(g) ⇌ NO_{2}(g)\end{array} \)
Where;
∆fG° (NO2) = 52.0 kJ/mol
∆fG° (NO) = 87.0 kJ/mol
∆fG° (O2) = 0 kJ/mol
Ans.
(a) For the given reaction, we have
∆G° = ∆G°(Products) – ∆G°(Reactants)
∆G° = 52.0 – (87.0 + 0)
= -35.0 KJ mol-1
(b) We know that,
∆G° = RT log Kc
∆G° = 2.303 RT log Kc
\(\begin{array}{l}K_{c}=\frac{-35.0\times 10^{-3}}{-2.303\times 8.314\times 298}\\ \\ =6.134\\ \\ ∴ K_{c}=antilog(6.134)\\ \\ =1.36\times 10^{6}\end{array} \)
Therefore, the equilibrium constant for the given reaction Kc is
\(\begin{array}{l}1.36\times 10^{6}\end{array} \)
.
Q.25. Does the number of moles of reaction products increase, decrease or remain the same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?
(a) PCl5(g) ⇌ PCl3 +Cl2 (g)
(b) CaO(s) + CO2 (g) ⇌ CaCO3(s)
(c) 3Fe (s) + 4H2O (g) ⇌ Fe3O4 (s) +4H2 (g)
Ans.
(a) The number of moles of reaction products will increase. According to Le Chatelier’s principle, if pressure is decreased, then the equilibrium shifts in the direction in which the number of moles of gases is more. In the given reaction, the number of moles of gaseous products is more than that of gaseous reactants. Thus, the reaction will proceed in the forward direction. As a result, the number of moles of reaction products will increase.
(b) The number of moles of reaction products will decrease.
(c) The number of moles of reaction products remains the same.
Q.26. Which of the following reactions will get affected by increasing the pressure? Also, mention whether the change will cause the reaction to go in a forward or backward direction.
(I) COCl2 (g) ⇌ CO (g) +Cl2 (g)
(II) CH4 (g) +2S2 (g) ⇌ CS2 (g) + 2H2S (g)
(III) CO2 (g) +C (s) ⇌ 2CO (g)
(IV) 2H2 (g) +CO (g) ⇌ CH3OH(g)
(V) CaCO3 (s) ⇌ CaO (s) + CO2 (g)
(VI) 4NH3 (g) + 5O2 (g) ⇌ 4NO (g) + 6H2O (g)
Ans.
When pressure is increased:
The reactions given in (i), (iii), (iv), (v), and (vi) will get affected.
Since the number of moles of gaseous reactants is more than that of gaseous products, the reaction given in (iv) will proceed in the forward direction
Since the number of moles of gaseous reactants is less than that of gaseous products, the reactions given in (i), (iii), (v), and (vi) will shift in the backward direction.
Q.27. The equilibrium constant for the following reaction is
\(\begin{array}{l}1.6 \times 10^{5}\end{array} \)
at 1024 K.
H2 (g) + Br2 (g) ⇌ 2HBr (g)
Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024 K.
Ans.
Given, Kp for the reaction, i.e., H2 (g) + Br2 (g) ⇒ 2HBr (g) is
\(\begin{array}{l}1.6 \times 10^{5}\end{array} \)
.
Therefore, for the reaction 2HBr (g) ⇒ H2 (g) + Br2 (g), the equilibrium constant will be,
K’p=
\(\begin{array}{l}\frac{1}{K_{p}}\\ \\ =\frac{1}{1.6\times 10^{5}}\\ \\ =6.25\times 10^{-6}\end{array} \)
Now, let p be the pressure of both H2 and Br2 at equilibrium.
2HBr (g) ⇌ H2 (g) + Br2 (g)
Initial conc. 10 0 0
At equilibrium 10-2p p p
Now, we can write,
\(\begin{array}{l}\frac{p_{HBr}\times p_{2}}{p^{2}_{HBr}}=K^{‘}_{p}\\ \\ \frac{p\times p}{(10-2p)^{2}}=6.25\times 10^{-6}\\ \\ \frac{p}{10-2p}=2.5\times 10^{-3}\\ \\ p=2.5\times 10^{-2}-(5.0\times 10^{-3})p\\ \\ p+(5.0\times 10^{-3})p=2.5\times 10^{-2}\\ \\ (1005\times 10^{-3})=2.5\times 10^{-2}\\ \\ p=2.49\times 10^{-2}bar=2.5\times 10^{-2}bar (approximately)\end{array} \)
Therefore, at equilibrium,
[H2]=[Br2]=
\(\begin{array}{l}2.49\times 10^{-2}bar\end{array} \)
[HBr]=
\(\begin{array}{l}10-2\times (2.49\times 10^{-2})bar\\ \\ =9.95 bar=10 bar(approximately)\end{array} \)
.
Q.28. Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per the following endothermic reaction:
\(\begin{array}{l}CH_{4}(g)+H_{2}O(g) ⇌ CO(g)+3H_{2}(g)\end{array} \)
(a) Write as an expression for Kp for the above reaction
(b) How will the values of Kp and composition of the equilibrium mixture be affected by
(i) Increasing the pressure
(ii) Increasing the temperature
(iii) Using a catalyst
Ans.
(a) For the given reaction,
Kp=
\(\begin{array}{l}\frac{p_{CO}\times p_{H_{2}}^{3}}{p_{CH_{4}}\times p_{H_{2}O}}\end{array} \)
(b) (i) According to Le Chatelier’s principle, the equilibrium will shift in the backward direction.
(ii) According to Le Chatelier’s principle, as the reaction is endothermic, the equilibrium will shift in the forward direction.
(iii) The equilibrium of the reaction is not affected by the presence of a catalyst. A catalyst only increases the rate of a reaction. Thus, equilibrium will be attained quickly.
Q.29. Describe the effect of:
a) Addition of H2
b) Addition of CH3OH
c) Removal of CO
d) Removal of CH3OH on the equilibrium of the reaction:
2H2 (g)+CO (g) ⇌ CH3OH (g)
Ans.
(a) According to Le Chatelier’s principle, on the addition of H2, the equilibrium of the given reaction will shift in the forward direction.
(b) On addition of CH3OH, the equilibrium will shift in the backward direction.
(c) On removing CO, the equilibrium will shift in the backward direction.
(d) On removing CH3OH, the equilibrium will shift in the forward direction.
Q.30. At 473 K, equilibrium constant Kc for decomposition of phosphorus pentachloride, PCl5 is
\(\begin{array}{l} 8.3 \times 10^{-3} \end{array} \)
. If decomposition is depicted as,
\(\begin{array}{l}PCl_{5}(g) ⇌ PCl_{3}(g)+Cl_{2}(g)\end{array} \)
∆rH° = 124.0 kJmol–1
a) Write an expression for Kc for the reaction.
b) What is the value of Kc for the reverse reaction at the same temperature?
c) What would be the effect on Kc if
(i) more PCl5 is added?
(ii) pressure is increased?
(iii) The temperature is increased?
Ans.
(a)
\(\begin{array}{l}K_{c}=\frac{[PCl_{3}(g)][Cl_{2}(g)]}{[PCl_{3}(g)]}\end{array} \)
(b) Value of Kc for the reverse reaction at the same temperature is:
\(\begin{array}{l}K_{c}^{‘} = \frac{1}{K_{c}}\\ \\ =\frac{1}{8.3 \times 10^{-3}} = 1.2048 \times 10^{2}\\ \\ =120.48\end{array} \)
(c) (i) Kc would remain the same because, in this case, the temperature remains the same.
(ii) Kc is constant at a constant temperature. Thus, in this case, Kc would not change.
(iii) In an endothermic reaction, the value of Kc increases with an increase in temperature. Since the given reaction is an endothermic reaction, the value of Kc will increase if the temperature is increased.
Q.31. Dihydrogen gas used in Haber’s process is produced by reacting methane from natural gas with high-temperature steam. The first stage of the two-stage reaction involves the formation of CO and H2. In the second stage, CO formed in the first stage is reacted with more steam in the water gas shift reaction,
\(\begin{array}{l}CO(g)+H_{2}O(g) ⇌ CO_{2}(g)+H_{2}(g)\end{array} \)
If a reaction vessel at 400°C is charged with an equimolar mixture of CO and steam such that Pco=PH2O = 4.0 bar, what will be the partial pressure of H2 at equilibrium? Kp= 10.1 at 400°C
Ans.
Let the partial pressure of both carbon dioxide and hydrogen gas be p. The given reaction is:
CO(g) + H2O ⇌ CO2(g) + H2(g)
Initial conc. 4.0 bar 4.0 bar 0 0
At equilibrium 4.0-p 4.0-p p p
Given Kp = 10.1
\(\begin{array}{l}\frac{P_{CO_{2}}\times P_{H_{2}}}{P_{CO}\times P_{H_{2}O}} = K_{P}\\ \\ \Rightarrow \frac{p\times p}{(4.0-p)(4.0-p)}=10.1\\ \\ \Rightarrow \frac{p}{4.0-p} =3.178\\ \\ \Rightarrow p =12.712-3.178p\\ \\ 4.178p = 12.712\\ \\ p =\frac{12.712}{4.178}\\ \\ p=3.04\end{array} \)
So, the partial pressure of H2 is 3.04 bar at equilibrium.
Q.32. Predict which of the following reaction will have an appreciable concentration of reactants and products:
(a)
\(\begin{array}{l}Cl_{2}(g)\leftrightarrow 2Cl(g);K_{c}=5 \times 10^{-39}\end{array} \)
(b)
\(\begin{array}{l}Cl_{2}(g)+2NO(g)\leftrightarrow 2NOCl(g);K_{c}=3.7 \times 10^{8}\end{array} \)
(c)
\(\begin{array}{l}Cl_{2}(g)+2NO_{2}(g)\leftrightarrow 2NO_{2}Cl(g);K_{c}=1.8\end{array} \)
Ans.
If the value of Kc lies between 10–3 and 103, a reaction has an appreciable concentration of reactants and products. Thus, the reaction given in (c) will have an appreciable concentration of reactants and products.
Q.33. The value of Kc for the reaction 3O2 (g) ⇌ 2O3 (g) is
\(\begin{array}{l}2.0\times 10^{-50} \end{array} \)
at 25°C. If the equilibrium concentration of O2 in the air at 25°C is
\(\begin{array}{l} 1.6 \times 10^{-2} \end{array} \)
, what is the concentration of O3?
Ans.
Given,
3O2 (g) ⇌ 2O3 (g)
Then, Kc =
\(\begin{array}{l} \frac{ [O_{3}(g)]^{2}}{[O_{2}(g)]^{3}}\end{array} \)
Given that Kc =
\(\begin{array}{l} 2.0 \times 10^{-50}\end{array} \)
and [O2(g)] =
\(\begin{array}{l}1.6 \times 10^{-2}\end{array} \)
Then,
\(\begin{array}{l} 2.0 \times 10^{-50} = \frac { [O_{3}(g)]^{2} }{ [1.6 \times 10^{ -2 }]^{3}}\\ \\ \Rightarrow [O_{3} (g)]^{2} = 2.0 \times 10^{-50} \times (1.6 \times 10^{-2})^{3}\\ \\ \Rightarrow [O_{3} (g)]^{2} = 8.192 \times 10^{-56}\\ \\ \Rightarrow [O_{3} (g)]^{2} = 2.86 \times 10^{-28} M\end{array} \)
So, the concentration of O3 is
\(\begin{array}{l}2.86 \times 10^{-28}M\end{array} \)
.
Q.34. The reaction,
\(\begin{array}{l}CO_{(g)} \; + \; 3H_{2(g)} \; ⇌ \; CH_{4(g)} \; + \; H_{2}O_{(g)}\end{array} \)
at 1300 K is at equilibrium in a 1 L container. It has 0.30 mol of CO, 0.10 mol of
\(\begin{array}{l}H_{2}\end{array} \)
and 0.02 mol of
\(\begin{array}{l}H_{2}O\end{array} \)
and an unknown amount of
\(\begin{array}{l}CH_{4}\end{array} \)
in the flask. Determine the concentration of
\(\begin{array}{l}CH_{4}\end{array} \)
in the mixture. The equilibrium constant,
\(\begin{array}{l}K_{c}\end{array} \)
, for the reaction at the given temperature, is 3.90.
Ans.
Let the concentration of
\(\begin{array}{l}CH_{4}\end{array} \)
at equilibrium be y.
\(\begin{array}{l}CO_{(g)} \; + \; 3H_{2(g)} \; ⇌ \; CH_{4(g)} \; + \; H_{2}O_{(g)}\end{array} \)
At equilibrium,
For CO –
\(\begin{array}{l}\frac{0.3}{1} \; = \; 0.3M\end{array} \)
For
\(\begin{array}{l}H_{2}\end{array} \)
–
\(\begin{array}{l}\frac{0.1}{1} \; = \; 0.1M\end{array} \)
For
\(\begin{array}{l}H_{2}O\end{array} \)
–
\(\begin{array}{l}\frac{0.02}{1} \; = \; 0.02M\end{array} \)
\(\begin{array}{l}K_{c}\end{array} \)
= 3.90
Therefore,
\(\begin{array}{l}\frac{[CH_{4(g)}][H_{2}O_{(g)}]}{[CO_{(g)}][H_{2(g)}]^{3}} \; = \; K_{c}\end{array} \)
\(\begin{array}{l}\frac{y \times 0.02}{0.3 \times (0.1)^{3}} \; = \; 3.9\end{array} \)
\(\begin{array}{l}y \; = \; \frac{3.9 \times 0.3 \times (0.1)^{3}}{0.02}\end{array} \)
\(\begin{array}{l}y \; = \; \frac{0.00117}{0.02}\end{array} \)
\(\begin{array}{l}y \; = \; 0.0585M\end{array} \)
\(\begin{array}{l}y \; = \; 5.85 \times 10^{-2}M\end{array} \)
Therefore, the concentration of
\(\begin{array}{l}CH_{4}\end{array} \)
at equilibrium is
\(\begin{array}{l}5.85 \times 10^{-2}M\end{array} \)
.
Q.35. What is conjugate acid-base pair? Find the conjugate acid/base of the given species:
\(\begin{array}{l}HNO_{2}\end{array} \)
,
\(\begin{array}{l}CN^{-}\end{array} \)
,
\(\begin{array}{l}HClO_{4}\end{array} \)
,
\(\begin{array}{l}F^{-}\end{array} \)
,
\(\begin{array}{l}OH^{-}\end{array} \)
,
\(\begin{array}{l}CO_{3}^{2-}\end{array} \)
and
\(\begin{array}{l}S^{-}\end{array} \)
Ans.
A conjugate acid-base pair is a pair that has a difference of only one proton.
The conjugate acid-base pair of the following are as follows:
\(\begin{array}{l}HNO_{2}\end{array} \)
–
\(\begin{array}{l}NO_{2}^{-}\end{array} \)
(Base)
\(\begin{array}{l}CN^{-}\end{array} \)
– HCN (Acid)
\(\begin{array}{l}HClO_{4}\end{array} \)
–
\(\begin{array}{l}ClO_{4}^{-}\end{array} \)
(Base)
\(\begin{array}{l}F^{-}\end{array} \)
– HF (Acid)
\(\begin{array}{l}OH^{-}\end{array} \)
–
\(\begin{array}{l}H_{2}O\end{array} \)
(Acid)/
\(\begin{array}{l}O^{2-}\end{array} \)
(Base)
\(\begin{array}{l}CO_{3}^{2-}\end{array} \)
–
\(\begin{array}{l}HCO_{3}^{-}\end{array} \)
(Acid)
\(\begin{array}{l}S^{2-}\end{array} \)
–
\(\begin{array}{l}HS^{-}\end{array} \)
(Acid).
Q.36. Which of the followings are Lewis acids?
\(\begin{array}{l}H_{2}O\end{array} \)
,
\(\begin{array}{l}BF_{3}\end{array} \)
,
\(\begin{array}{l}H^{+}\end{array} \)
and
\(\begin{array}{l}NH_{4}^{+}\end{array} \)
Ans.
Lewis acids are acids which can accept a pair of electrons.
\(\begin{array}{l}H_{2}O\end{array} \)
– Lewis base
\(\begin{array}{l}BF_{3}\end{array} \)
– Lewis acid
\(\begin{array}{l}H^{+}\end{array} \)
– Lewis acid
\(\begin{array}{l}NH_{4}^{+}\end{array} \)
– Lewis acid
Q.37. What will be the conjugate bases for the Brönsted acids: HF,
\(\begin{array}{l}H_{2}SO_{4}\end{array} \)
and
\(\begin{array}{l}HCO_{3}\end{array} \)
?
Ans.
The following shows the conjugate bases for the Bronsted acids:
HF –
\(\begin{array}{l}F^{-}\end{array} \)
\(\begin{array}{l}H_{2}SO_{4}\end{array} \)
–
\(\begin{array}{l}HSO_{4}^{-}\end{array} \)
\(\begin{array}{l}HCO_{3}\end{array} \)
–
\(\begin{array}{l}CO_{3}^{2-}\end{array} \)
.
Q.38. Write the conjugate acids for the following Brönsted bases:
\(\begin{array}{l}NH_{2}^{-}\end{array} \)
, NH3 and
\(\begin{array}{l}HCOO^{-}\end{array} \)
Ans.
The conjugate acids for the given Bronsted bases are:
NH2– → NH3
NH3 → NH4+
HCOO– → HCOOH
Q.39. The species: H2O, HCO3–, HSO4– and NH3 can act both as Brönsted acids and bases. For each case, give the corresponding conjugate acid and base.
Ans.
The conjugate acids and conjugate bases for the given species are listed below:
Species Conjugate Acid Conjugate Bases
H2O H3O+ OH–
HCO3– H2CO3 CO32-
HSO4– H2SO4 SO42-
NH3 NH4+ NH2–
Q.40. Classify the following species into Lewis acids and Lewis bases and show that these species act as Lewis base/acid:
(a)
\(\begin{array}{l}OH^{-}\end{array} \)
(b)
\(\begin{array}{l}F^{-}\end{array} \)
(c)
\(\begin{array}{l}H^{+}\end{array} \)
(d) BCl3
Ans.
(a)
\(\begin{array}{l}OH^{-}\end{array} \)
It is a Lewis base as it has a tendency to lose a pair of electrons.
(b)
\(\begin{array}{l}F^{-}\end{array} \)
It is a Lewis base as it has a tendency to lose its lone pair of electrons.
(c)
\(\begin{array}{l}H^{+}\end{array} \)
It is a Lewis acid as it has a tendency to accept a pair of electrons.
(d) BCl3:
It is a Lewis acid as it has a tendency to accept a pair of electrons.
Q.41.The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10–3 M. what is its pH?
Ans.
\(\begin{array}{l}pH=-log[H^{+}]\\ \\ =-log(3.8\times 10^{-3})\\ \\ =-log\: 3.8\, -\, log\: 10^{-3}\\ \\ =-log\, 3.8+3\\ \\ =−0.5798+3\\ \\ =2.423\end{array} \)
Q.42. The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.
Ans.
\(\begin{array}{l}pH = -log [H^{+}]\\ \\ \Rightarrow log[H^{+}]=-pH\\ \\ \Rightarrow [H^{+}]=antilog(-pH)\\ \\ =antilog(-3.76)\\ \\ =0.000178\\ \\ =1.78\times 10^{-4}\end{array} \)
\(\begin{array}{l} ∴\end{array} \)
\(\begin{array}{l}1.78\times 10^{-4}\end{array} \)
is the concentration of white vinegar sample.
Q.43. The ionisation constant of HF, HCOOH and HCN at 298K are 6.8 × 10–4, 1.8 × 10–4 and 4.8 × 10–9, respectively. Calculate the ionisation constants of the corresponding conjugate base.
Ans.
For F–,
\(\begin{array}{l}K_{b} = \frac{K_{w}}{K_{a}}=\frac{10^{-14}}{(6.8\times 10^{-4})}=1.47\times 10^{-11}\end{array} \)
For HCOO–,
\(\begin{array}{l}K_{b}=\frac{10^{-14}}{(1.8\times 10^{-4})}=5.6\times 10^{-11}\end{array} \)
For CN– =
\(\begin{array}{l}K_{b}=\frac{10^{-14}}{(4.8\times 10^{-9})}=2.08\times 10^{-6}\end{array} \)
Q.44. The ionisation constant of phenol is 1.0 × 10–10. What is the concentration of phenolate ion in a 0.05 M solution of phenol? What will be its degree of ionisation if the solution is also 0.01 M in sodium phenolate?
Ans.
C6H5OH ⇌ C6H5O– + H+
Initial 0.05M 0 0
After dissociation 0.05-x x x
∴
\(\begin{array}{l}K_{}\alpha = \frac{x^{2}}{0.05-x}\end{array} \)
Because the value of the ionisation constant is very small, the value of x is very small. Accordingly, we may ignore x in the denominator.
\(\begin{array}{l}x = \sqrt{1\times 10^{-10}\times 0.05}\end{array} \)
\(\begin{array}{l}x = \sqrt{5\times 10^{-12}}\end{array} \)
∴ x = 2.2×10-6M
In the presence of 0.01 sodium phenolate(C6H5Na), suppose y is the amount of phenol dissociated, then at equilibrium,
[C6H5OH] = 0.05 -y
[C6H5OH] ≈ 0.05
[C6H5O–] = 0.01 + y ≈ 0.01M,
[H+]=y M
∴
\(\begin{array}{l}K_{\alpha }=\frac{(0.01)(y)}{0.05}=1.0\times 10^{-10}\end{array} \)
y = 5 × 10-10
\(\begin{array}{l}\alpha = \frac{y}{c}\end{array} \)
\(\begin{array}{l}\alpha = \frac{5\times 10^{-10}}{5\times 10^{-2}}\end{array} \)
α = 10-8.
Q.45. The first ionisation constant of H2S is 9.1 × 10–8. Calculate the concentration of HS– ion in its 0.1 M solution. How will this concentration be affected if the solution is 0.1 M in HCl also? If the second dissociation constant of H2S is 1.2 × 10–13, calculate the concentration of S2– under both conditions.
Ans.
To calculate [HS–]
To find [HS–]:
Case 1 – HCl is absent.
Now
Ka = ([H+][HS–])/[H2S] = 9.1×10-8 (given)
∴ x2/(0.1-x) = 9.1×10-8
But 0.1-x is approximately equal to 0.1. Substituting this value in the equation,
x2/0.1 = 9.1×10-8
x2 = 9.1×10-9
x = 9.54× 10-5 M
∴ The concentration of HS– is 9.54×10-5 M.
Case 2 – HCl is present
Now,
Ka = ([H+][HS–])/[H2S] = (y× (0.1+y))/(0.1-y) = 9.1×10-8 (given)
But (0.1 + y) and (0.1 – y) can be approximated to 0.1.
9.1× 10-8 = (0.1*y)/0.1
∴ y = [HS–] = 9.1× 10-8 M
To calculate [S2-]:
Case 1 – HCl is absent.
The dissociation of HS– is given by the equation:
HS– ⇌ H+ + S2-[HS–] = 9.1×10-5 M
[H+] = 9.54×10-5 M
Ka = ([H+][S2-])/[HS–] = 1.2×10-13 (given)
Ka = (9.1× 10-5 × [S2-])/9.1×10-5
∴ [S2-] = 1.2×10-13 M
Case 2 – HCl is present
[HS–] = 9.1×10-8 M
[H+] = 0.1 M
Ka = 1.2×10-13 M
= (0.1×[S2-])/ 9.1×10-8
Therefore, [S2-] = 1.092×10-19 M.
Q.46. The ionisation constant of acetic acid is 1.74 × 10–5. Calculate the degree of dissociation of acetic acid in its 0.05 M solution. Calculate the concentration of acetate ion in the solution and its pH.
Ans.
CH3COOH ⇒ CH3COO– + H+
\(\begin{array}{l}K_{a}=\frac{[CH_{3}COO^{-}][H^{+}]}{[CH_{3}COOH]}=\frac{[H^{+}]^{2}}{[CH_{3}COOH]}\\ \\ \Rightarrow [H^{+}]=\sqrt{K_{a}[CH_{3}COOH]}=\sqrt{(1.74\times 10^{-5})(5\times 10^{-2})}=9.33\times 10^{-4}M\\ \\ [CH_{3}COO^{-}]=[H^{+}]=9.33\times 10^{-4}M\\ \\ pH=-log(9.33\times 1.0^{-4})=4-0.9699=4-0.97=3.03\end{array} \)
.
Q.47. It has been found that the pH of a 0.01M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionisation constant of the acid and its pKa.
Ans.
HA ⇌ H+ + A–
pH = -log[H+]
log[H+] = -4.15
[H+] =
\(\begin{array}{l}7.08\times 10^{-5}\, M
\end{array} \)
[A–] = [H+] =
\(\begin{array}{l}7.08\times 10^{-5}\, M\end{array} \)
\(\begin{array}{l}K_{a}=\frac{[H^{+}][A^{-}]}{[HA]}=\frac{(7.08\times 10^{-5})(7.08\times 10^{-5})}{10^{-2}}=5.0\times 10^{-7}\\ \\ p_{K_{a}}=-log\, K_{a} = -log\, (5.0\times 10^{-7})=7-0.699=6.301\end{array} \)
.
Q.48. Assuming complete dissociation, calculate the pH of the following solutions: (a) 0.003 M HCl, (b) 0.005 M NaOH, (c) 0.002 M HBr, (d) 0.002 M KOH.
Ans.
(a) HCl + aq → H+ + Cl–
\(\begin{array}{l}∴ [H^{+}]=[HCl]=3\times 10^{-3}M\\ \\ pH=-log(3\times 10^{-3})=2.52\end{array} \)
(b) NaOH + aq → Na+ + OH–
[OH–] = 5 × 10-3
[H+] = 10-14/5 × 10-3
[H+] = 2 × 10-12M
pH = -log (2 × 10-12)
pH = 11.70
(c) HBr + aq → H+ + Br–
[H+] = 2 × 10-3M
pH = -log (2 × 10-3)
pH = 2.70
(d) KOH + aq → K+ + OH–
[OH–] = 2 × 10-3
[H+] = 10-14/2 × 10-3
[H+] = 5 × 10-12M
pH = -log (5 × 10-12)
pH = 11.30
Q.49. Calculate the pH of the following solutions: (I) 2 g of TIOH dissolved in water to give 2 litres of the solution, (II) 0.3 g of Ca(OH)2 dissolved in water to give 500 mL of the solution, (III) 0.3 g of NaOH dissolved in water to give 200 mL of the solution, (IV) 1 mL of 13.6 M HCl is diluted with water to given 1 litre of the solution.
Ans.
(I) Molar conc. Of TlOH =
\(\begin{array}{l}\frac{2g}{(204+16+1)g\: mol^{-1}}\times \frac{1}{2L}=4.52\times 10^{-3}M\\ \\ [OH_{-}]=[TlOH]=4.52\times 10^{-3}M\\ \\ [H^{+}]=\frac{10^{-14}}{(4.52\times 10^{-3})}=2.21\times 10^{-12}M\\ \\ ∴ pH=-log(2.21\times 10^{-12})=12-(0.3424)=11.66\end{array} \)
(II) Molar conc. Of Ca(OH)2=
\(\begin{array}{l}\frac{0.3g}{(40+34)g\: mol^{-1}}\times \frac{1}{0.5L}=8.11\times 10^{-3}M\\ \\ [OH_{-}]=2[Ca(OH)_{2}]=2\times (8.11\times 10^{-3})M=16.22\times 10^{-3}M\\ \\ pOH=-log(16.22\times 10^{-3})=3-1.2101=1.79\\ \\ pH=14-1.79=12.21\end{array} \)
(III) Molar conc. of NaOH =
\(\begin{array}{l}\frac{0.3g}{(40+34)g\: mol^{-1}}\times \frac{1}{0.2L}=3.75\times 10^{-2}M\\ \\ [OH_{-}]=3.75\times 10^{-2}M\\ \\ pOH=-log(3.75\times 10^{-2})=2-0.0574=1.43\\ \\ pH=14-1.43=12.57\end{array} \)
(IV) M1V1 = M2V2
\(\begin{array}{l}∴ 13.6M\times \times 1mL=M_{2}\times 1000mL\\ \\ ∴ M_{2}=1.36\times 10^{-2}M\\ \\ [H^{+}]=[HCl]=1.36\times 10^{-2}M\\ \\ pH=-log(1.36\times 10^{-2})=2-0.1335\simeq 1.87\end{array} \)
.
Q.50. The degree of ionisation of a 0.1 M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pKa of bromoacetic acid.
Ans.
CH2(Br)COOH CH2(Br)COO– + H+
Initial conc. C 0 0
Conc. at eqm. C – Cα Cα Cα
\(\begin{array}{l}K_{a}=\frac{C\alpha \cdot C\alpha }{C(1-\alpha )}=\frac{C\alpha ^{2}}{1-\alpha }\simeq C\alpha ^{2}=0.1\times (0.132)^{2}=1.74\times 10^{-3}\\ \\ p_{K_{a}}=-log(1.74\times 10^{-3})=3-0.2405=2.76\\ \\ [H^{+}]=C\alpha =0.1\times 0.132=1.32\times 10^{-2}M\\ \\ pH=-log(1.32\times 10^{-2})=2-0.1206=1.88\end{array} \)
.
Q.51. What is the pH of 0.001 M aniline solution? The ionisation constant of aniline can be taken from Table 7.7. Calculate the degree of ionisation of aniline in the solution. Also, calculate the ionisation constant of the conjugate acid of aniline.
Ans.
Kb =
\(\begin{array}{l}4.27 \times 10^{-10}\end{array} \)
c = 0.001MpH =?α =?
\(\begin{array}{l}K_{b}=c\alpha ^{2}\\ \\ 4.27 \times 10^{-10}=0.001\times \alpha ^{2}\\ \\ 4270\times 10^{-10}=\alpha ^{2}\\ \\ 65.34\times 10^{-5}=\alpha =6.53\times 10^{-4}\\ \\ Then,[anion]=c\alpha =0.001\times 65.34\times10^{-5}=0.065\times10^{-5}\end{array} \)
\(\begin{array}{l}pOH=-log(0.065\times 10^{-5})\\ \\ =6.187\\ \\ pH=7.813\\ \\ Now,\\ \\ K_{a}\times K_{b}=K_{w}\\ \\ K_{a}=\frac{10^{-14}}{4.27\times 10^{-10}}\\ \\ =2.34\times 10^{-5}\end{array} \)
\(\begin{array}{l}∴ 2.34\times 10^{-5}\end{array} \)
is the ionisation constant.
Q.52. Calculate the degree of ionisation of 0.05 M acetic acid if its pKa value is 4.74. How is the degree of dissociation affected when its solution also contains (I) 0.01 M and (II) 0.1 M in HCl?
Ans.
c=0.05M pKa=4.74 pKa=-log(Ka)
\(\begin{array}{l}K_{a}=1.82\times 10^{-5}\\ \\ K_{a}=c\alpha ^{2}\\ \\ \alpha =\sqrt{\frac{K_{a}}{c}}\\ \\ \alpha =\sqrt{\frac{1.82\times 10^{-5}}{5\times 10^{-2}}}=1.908\times 10^{-2}\end{array} \)
When HCl is added to the solution, the concentration of H+ ions will increase.
Therefore, the equilibrium will shift in the backward direction, i.e. the dissociation of acetic acid will decrease.
Case 1: When 0.01 M HCl is taken, let x be the amount of acetic acid dissociated after the addition of HCl.
CH3COOH ↔ H+ + CH3COO–
Initial conc. 0.05M 0 0
After dissociation 0.05-x 0.01+x x
As the dissociation of a very small amount of acetic acid will take place, the values, i.e., 0.05 – x and 0.01 + x, can be taken as 0.05 and 0.01, respectively.
\(\begin{array}{l}K_{a}=\frac{[CH_{3}COO^{-}][H^{+}]}{[CH_{3}COOH]}\\ \\ ∴ =\frac{(0.01)x}{0.05}\\ \\ x=\frac{1.82\times 10^{-5}\times 0.05}{0.01}\\ \\ x=1.82\times 10^{-3}\times 0.05M\end{array} \)
Now,
\(\begin{array}{l}\alpha =\frac{Amount \: of \: acid\:dissociation}{Amount\:of\:acid\:taken}\\ \\ =\frac{1.82\times 10^{-3}\times 0.05}{0.05}\\ \\ =1.82\times 10^{-3}\end{array} \)
Case 2: When 0.1 M HCl is taken, let the amount of acetic acid dissociated, in this case, be X.
As we have done in the first case, the concentrations of various species involved in the reaction are:
[CH3COOH]=0.05 – X: 0.05 M
[CH3COO–]=X[H+]=0.1+X ; 0.1M
\(\begin{array}{l}K_{a}=\frac{[CH_{3}COO^{-}][H^{+}]}{[CH_{3}COOH]}\\ \\∴K_{a}=\frac{(0.1)X}{0.05}\\ \\ x=\frac{1.82\times 10^{-5}\times 0.05}{0.1}\\ \\ x=1.82\times 10^{-4}\times 0.05M\end{array} \)
Now,
\(\begin{array}{l}\alpha =\frac{Amount \: of \: acid\:dissociation}{Amount\:of\:acid\:taken}\\ \\ =\frac{1.82\times 10^{-4}\times 0.05}{0.05}\\ \\ =1.82\times 10^{-4}\end{array} \)
.
Q.53. The ionisation constant of dimethylamine is
\(\begin{array}{l}5.4 \times × 10^{-4}\end{array} \)
. Calculate its degree of ionisation in its 0.02 M solution. What percentage of dimethylamine is ionised if the solution is also 0.1 M in NaOH?
Ans.
\(\begin{array}{l}K_{b}=5.4\times 10^{-4}\\ \\ c=0.02M\\ \\ Then,\alpha =\sqrt{\frac{K_{b}}{c}}\\ \\ =\sqrt{\frac{5.4\times 10^{-4}}{0.02}}=0.1643\end{array} \)
Now, if 0.1 M of NaOH is added to the solution, then NaOH (being a strong base) undergoes complete ionisation.
NaOH(aq) ↔ Na+(aq) + OH–(aq)
0.1M 0.1M
And,
(CH3)2 NH + H2O ↔ (CH3)2 NH2+ + OH
(0.02-x) x x
0.02M 0.1M
Then,[ (CH3)2 NH+2]=x
[OH– ]=x+0.1;0.1
\(\begin{array}{l}\Rightarrow K_{b}=\frac{[(CH_{3})_{2}NH_{2}^{+}][OH^{-}]}{[(CH_{3})_{2}NH]}\\ \\ 5.4\times 10^{-4}=\frac{x\times 0.1}{0.02}\\ \\ x=0.0054\end{array} \)
It means that in the presence of 0.1 M NaOH, 0.54% of dimethylamine will get dissociated.
Q.54. Calculate the hydrogen ion concentration in the following biological fluids whose pH values are given below: (I) Human saliva, 6.4 (II) Human stomach fluid, 1.2 (III) Human muscle-fluid, 6.83 and (IV) Human blood, 7.38.
Ans.
(I) Human saliva, 6.4
pH = 6.4
6.4 = – log [H+]
[H+] = 3.98 x 10-7
(II) Human stomach fluid, 1.2
pH =1.2
1.2 = – log [H+]
∴ [H+] = 0.063
(III) Human muscle fluid 6.83
pH = 6.83
pH = – log [H+]
∴ 6.83 = – log [H+]
[H+] =1.48 x 10-7 M
(IV) Human blood, 7.38
pH = 7.38 = – log [H+]
∴ [H+] = 4.17 x 10-8 M.
Q.55. The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8, respectively. Calculate the corresponding hydrogen ion concentration in each.
Ans.
The hydrogen ion concentration in the given substances can be calculated by using the given relation: pH = –log [H+].
(I) pH of milk = 6.8
Since, pH = –log [H+]
6.8 = –log [H+]
log[H+] = –6.8
[H+] = anitlog(–6.8)=
\(\begin{array}{l}1.5\times 10^{-7} M\end{array} \)
(II) pH of black coffee = 5.0
Since pH = –log [H+]
5.0 = –log [H+]
log[H+] = –5.0
[H+] = anitlog(–5.0)=
\(\begin{array}{l} 10^{-5} M\end{array} \)
(III) pH of tomato= 4.2
Since, pH = –log [H+]
4.2 = –log [H+]
log[H+] = –4.2
[H+] = anitlog(–4.2)=
\(\begin{array}{l}6.31\times 10^{-5} M\end{array} \)
(IV) pH of lemon juice = 2.2
Since, pH = –log [H+]
2.2 = –log [H+]
log[H+] = –2.2
[H+] = anitlog(–2.2)=
\(\begin{array}{l}6.31\times 10^{-3} M\end{array} \)
(V) pH of egg white = 7.8
Since, pH = –log [H+]
7.8 = –log [H+]
log[H+] = –7.8
[H+] = anitlog(–7.8)=
\(\begin{array}{l}1.58\times 10^{-8} M\end{array} \)
.
Q.56. If 0.561 g of KOH is dissolved in water and given 200 mL of solution at 298 K, calculate the concentrations of potassium, hydrogen and hydroxyl ions. What is its pH?
Ans.
[KOH(aq)] = 0.561 / (1/5)g/L
= 2.805 g/L
= 2.805 x (1/56.11)
= 0.05M
KOH(aq) → K+ (aq) + OH–(aq)
[OH–] = 0.05M = [K+]
[H+][OH–] = Kw
[H+] = Kw/[OH–]
[H+] = 10-14/0.05
[H+] = 2 × 10-13M
pH = -log[H+]
pH = -log[2 × 10-13]
pH = 12.70.
Q.57. The solubility of Sr(OH)2 at 298 K is 19.23 g/L of solution. Calculate the concentrations of strontium and hydroxyl ions and the pH of the solution.
Ans.
Solubility of Sr(OH)2 = 19.23 g/L
Then, concentration of Sr(OH)2=
⇒
\(\begin{array}{l}[H^{+}]=3.2\times 10^{-14}\end{array} \)
∴ pH = 13.50.
Q.58. The ionisation constant of propanoic acid is
\(\begin{array}{l}1.32 \times × 10^{-5}\end{array} \)
. Calculate the degree of ionisation of the acid in its 0.05M solution and also its pH. What will be its degree of ionisation if the solution is 0.01 M in HCl also?
Ans.
Let the degree of ionisation of propanoic acid be α.
Then, representing propionic acid as HA, we have:
HA + H2O ↔ H3O+ + A–
(0.05-0.0α) ≈ 0.05 0.05α 0.05α
\(\begin{array}{l}K_{\alpha }=\frac{[H_{3}O^{+}][A^{-}]}{[HA]}\end{array} \)
=
\(\begin{array}{l}\frac{(0.05\alpha )(0.05\alpha )}{0.05}\end{array} \)
= 0.05α2
\(\begin{array}{l}\alpha =\sqrt{\frac{K_{\alpha }}{0.05}}\end{array} \)
α = 1.63 × 10-2
Then, [ H3O+ ]= 0.05α = 0.05 × 1.63× 10-2= Kb. 15×10-4M
∴ pH = 3.09.
In the presence of 0.1M of HCl, let α´ be the degree of ionisation.
Then, [H3O+] = 0.01
[A–] = 0.05α’
[HA] = 0.05
Ka = 0.01 x 0.05α’ / 0.05
⇒ 1.32 x 10-5 = 0. 01 α’
α’ = 1.32 x 10-3.
Q.59. The pH of 0.1 M solution of cyanic acid (HCNO) is 2.34. Calculate the ionisation constant of the acid and its degree of ionisation in the solution.
Ans.
c = 0.1 M
pH = 2.34
-log [H+] = pH
-log [H+] = 2.34
[H+] = 4.5× 10-3
Also,
[H+]=cα
4.5 × 10-3 = 0.1× α
α = 0.1/(4.5 × 10-3)
α = 0.045
Ka = cα2
Ka = 0.1 × (0.045)2
Ka = 0.0002025
Ka = 2.025 x 10-4.
Q.60. The ionisation constant of nitrous acid is 4.5 × 10–4. Calculate the pH of 0.04 M sodium nitrite solution and also its degree of hydrolysis.
Ans.
Sodium nitrite is a salt of NaOH (strong base) and HNO2 (weak acid).
\(\begin{array}{l}NO_{2}^{-} + H_{2}O \leftrightarrow HNO_{2} + OH^{-}\end{array} \)
\(\begin{array}{l}K_{h} = \frac{[HNO_{2}][OH^{-}]}{[NO_{2}^{-}]}\end{array} \)
\(\begin{array}{l}\Rightarrow \;\frac{K_{w}}{K_{a}} = \frac{10^{-14}}{4.5\times 10^{-4}} = 0.22\times 10^{-10}\end{array} \)
Let y mole of salt has undergone hydrolysis, then the concentration of various species present in the solution will be:
\(\begin{array}{l}[NO_{2}^{-}] = 0.04 – y; 0.04\end{array} \)
\(\begin{array}{l}[HNO_{2}] = y\end{array} \)
\(\begin{array}{l}[OH^{-}] = y\end{array} \)
\(\begin{array}{l}K_{h} = \frac{y^{2}}{0.04} = 0.22\times 10^{-10}\end{array} \)
\(\begin{array}{l}y^{2} = 0.0088\times 10^{-10}\end{array} \)
\(\begin{array}{l}y = 0.093\times 10^{-5}\end{array} \)
\(\begin{array}{l} ∴ [OH^{-}]= 0.093\times 10^{-5}M\end{array} \)
\(\begin{array}{l}[H_{3}O^{+}] = \frac{10^{-14}}{0.093\times 10^{-5}} = 10.75\times 10^{-9}M\end{array} \)
Thus,
\(\begin{array}{l}pH = -\log (10.75\times 10^{-9})\end{array} \)
= 7.96.
Thus, the degree of hydrolysis is
\(\begin{array}{l} = \frac{y}{0.04} = \frac{0.093\times 10^{-5}}{0.04}\end{array} \)
\(\begin{array}{l} = 2.325\times 10^{-5}\end{array} \)
.
Q.61. A 0.02M solution of pyridinium hydrochloride (C5H6ClN) has a pH of 3.44. Calculate the ionisation constant of C5H5N (pyridine).
Ans.
pH = 3.44As
we know,
\(\begin{array}{l}pH = \log [H^{+}]\end{array} \)
\(\begin{array}{l} ∴ [H^{+}] = 3.63\times 10^{-4}\end{array} \)
Now,
\(\begin{array}{l}K_{h} = \frac{3.63\times 10^{-4}}{0.02}\end{array} \)
;
(Given that concentration = 0.02M)
\(\begin{array}{l}\Rightarrow K_{h} = 6.6\times 10^{-6}\end{array} \)
As we know,
\(\begin{array}{l}K_{h} = \frac{K_{w}}{K_{a}}\end{array} \)
\(\begin{array}{l}K_{a} = \frac{K_{w}}{K_{h}} = \frac{10^{-14}}{6.6\times 10^{-6}}\end{array} \)
=
\(\begin{array}{l}1.51\times 10^{-9}\end{array} \)
.
Q.62. Predict if the solutions of the following salts are neutral, acidic or basic: NaCl, KBr, NaCN, NH4NO3, NaNO2 and KF.
Ans.
KBr + H2O
\(\begin{array}{l}\leftrightarrow\end{array} \)
KOH (Strong base)+ HBr (Strong acid). Thus, it is a neutral solution.
NH4NO3 + H2O
\(\begin{array}{l}\leftrightarrow\end{array} \)
NH4OH(Weak base) + HNO2 (Strong acid). Thus, it is an acidic solution.
KF + H2O
\(\begin{array}{l}\leftrightarrow\end{array} \)
KOH (Strong base) + HF (weak acid). Thus, it is a basic solution.
NaNO2 + H2O
\(\begin{array}{l}\leftrightarrow\end{array} \)
NH4OH(Strong base) + HNO2(Weak acid). Thus, it is a basic solution.
NaCN + H2O
\(\begin{array}{l}\leftrightarrow\end{array} \)
HCN (Weak acid) + NaOH (Strong base). Thus, it is a basic solution.
NaCl + H2O
\(\begin{array}{l}\leftrightarrow\end{array} \)
NaOH (Strong base) + HCL (Strong acid). Thus, it is a neutral solution.
Q.63. The ionisation constant of chloroacetic acid is 1.35 × 10–3. What will be the pH of 0.1 M acid and its 0.1 M sodium salt solution?
Ans.
The Ka for chloroacetic acid (ClCH2COOH) is
\(\begin{array}{l}1.35\times 10^{-3}\end{array} \)
.
\(\begin{array}{l}\Rightarrow K_{a} = c\alpha ^{2}\end{array} \)
\(\begin{array}{l}∴ \alpha = \sqrt{\frac{K_{a}}{c}}\end{array} \)
=
\(\begin{array}{l}\sqrt{\frac{1.35\times 10^{-3}}{0.1}}\end{array} \)
; (given concentration = 0.1M)
\(\begin{array}{l}\alpha = \sqrt{1.35\times 10^{-2}}\end{array} \)
= 0.116
\(\begin{array}{l} ∴ [H^{+}] = c\alpha = 0.1×0.116 = 0.0116\end{array} \)
ClCH2COONa is a salt of strong base, i.e. NaOH, and weak acid, i.e. ClCH2COOH
\(\begin{array}{l}ClCH_{2}COO^{-} + H_{2}O \leftrightarrow ClCH_{2}COOH + OH^{-}\end{array} \)
\(\begin{array}{l}K_{h} = \frac{[ClCH_{2}COO][OH^{-}]}{[ClCH_{2}COO^{-}]}\end{array} \)
Now,
\(\begin{array}{l}K_{h} = \frac{K_{w}}{K_{a}}\end{array} \)
\(\begin{array}{l}K_{h} = \frac{10^{-14}}{1.35\times 10^{-3}}\end{array} \)
\(\begin{array}{l}= 0.740\times 10^{-11}\end{array} \)
Also,
\(\begin{array}{l}K_{h} = \frac{y^2}{0.1}\end{array} \)
\(\begin{array}{l}\Rightarrow \; 0.740\times 10^{-11} = \frac{y^2}{0.1}\end{array} \)
\(\begin{array}{l}\Rightarrow \; 0.0740\times 10^{-11} = y^2\end{array} \)
\(\begin{array}{l}y = 0.86\times 10^{-6}\end{array} \)
\(\begin{array}{l}[OH^{-}] = 0.86\times 10^{-6}\end{array} \)
\(\begin{array}{l}∴ [H^{+}] =\frac{K_{w}}{0.86\times 10^{-6}}\end{array} \)
\(\begin{array}{l}=\frac{10^{-14}}{0.86\times 10^{-6}}\end{array} \)
\(\begin{array}{l}[H^{+}] = 1.162\times 10^{-3}\end{array} \)
pH =
\(\begin{array}{l}- \log [H^{+}]\end{array} \)
= 7.94.
Q.64. Ionic product of water at 310 K is 2.7 × 10–14. What is the pH of neutral water at this temperature?
Ans.
Ionic Product,
\(\begin{array}{l}K_{w} = [H^{+}][OH^{-}]\end{array} \)
Assuming,
\(\begin{array}{l}[H^{+}]\end{array} \)
= y
As,
\(\begin{array}{l}[H^{+}] = [OH^{-}]\end{array} \)
,
Kw = y2.Kw at 310 K is
\(\begin{array}{l}2.7\times 10^{-14}\end{array} \)
\(\begin{array}{l}∴ 2.7\times 10^{-14} = y^{2}\end{array} \)
- y = \(\begin{array}{l}1.64\times 10^{-7}\end{array} \)
- \(\begin{array}{l}[H^{+}] = 1.64\times 10^{-7}\end{array} \)
- pH = \(\begin{array}{l}-\log [H^{+}]\end{array} \)
=
\(\begin{array}{l}-\log [1.64\times 10^{-7}]\end{array} \)
= 6.78
Thus, the pH of neutral water at 310 K temperature is 6.78.
Q.65. The solubility product constant of Ag2CrO4 and AgBr are 1.1 × 10–12 and 5.0 × 10–13, respectively. Calculate the ratio of the molarities of their saturated solutions.
Ans.
Ag2CrO4→ 2Ag2+ +
\(\begin{array}{l}CrO_{4}^{-}\end{array} \)
Now, Ksp = [Ag2+]2
\(\begin{array}{l}[CrO_{4}^{-}]\end{array} \)
Assuming the solubility of Ag2CrO4 is ‘x’.
Thus, [Ag2+] = 2x and
\(\begin{array}{l}CrO_{4}^{-}\end{array} \)
= x
Assuming the solubility of AgBr is y.
AgBr(s) → Ag2+ + Br–
y =
\(\begin{array}{l}7.07\times 10^{-7}M\end{array} \)
The ratio of molarities to their saturated solution is:
\(\begin{array}{l}\frac{x}{y} = \frac{0.65\times10^{-4}M}{7.07\times10^{-7}M} = 91.9\end{array} \)
.
Q.66. Equal volumes of 0.002 M solutions of sodium iodate and cupric chlorate are mixed together. Will it lead to the precipitation of copper iodate? (For cupric iodate Ksp = 7.4 × 10–8 ).
Ans.
If cupric chlorate and sodium iodate having equal volumes are mixed together, then the molar concentration of cupric chlorate and sodium iodate will reduce to half. So, the molar concentration of cupric chlorate and sodium iodate in a mixture is 0.001 M.
Na(IO3)2 → Na+ +
\(\begin{array}{l}IO_{3}^{-}\end{array} \)
0.0001M 0.001 M
Cu(ClO3)2→ Cu2+ +
\(\begin{array}{l}2CIO_{3}^{-}\end{array} \)
0.001M 0.001 M
The Solubility for Cu(IO3)2 ⇒ Cu2+ (aq) + 2IO3– (aq)
Now, the ionic product of the copper iodate = [Cu2+]
\(\begin{array}{l}[IO_{3}^{-}]^{2}\end{array} \)
= (0.001)(0.001)2=
\(\begin{array}{l}1.0\times 10^{-9}M\end{array} \)
As the value of Ksp is more than the ionic product, precipitation will not occur.
Q.67. The ionisation constant of benzoic acid is 6.46 × 10–5, and Ksp for silver benzoate is 2.5 × 10–13. How many times is silver benzoate more soluble in a buffer of pH 3.19 compared to its solubility in pure water?
Ans.
Here, pH = 3.19
[H3O+] =
\(\begin{array}{l}6.46\times 10^{-4}M\end{array} \)
C6H5COOH + H2O →
\(\begin{array}{l}C_{6}H_{5}COO^{-}\end{array} \)
+ H3O
\(\begin{array}{l}K_{a}=\frac{[C_{6}H_{5}COO^{-}][H_{3}O^{+}]}{C_{6}H_{5}COOH}\end{array} \)
\(\begin{array}{l}K_{a}=\frac{[C_{6}H_{5}COOH]}{C_{6}H_{5}COO^{-}} = \frac{[H_{3}O^{+}]}{K_{a}} = \frac{6.46\times 10^{-4}}{6.46\times 10^{-5}} = 10\end{array} \)
Assuming the solubility of silver benzoate (C6H5COOAg) is y mol/L,
Now, [Ag+] = y
[C6H5COOH] =
\(\begin{array}{l}[C_{6}H_{5}COO^{-}]\end{array} \)
= y
10
\(\begin{array}{l}[C_{6}H_{5}COO^{-}]\end{array} \)
+
\(\begin{array}{l}[C_{6}H_{5}COO^{-}]\end{array} \)
= y
\(\begin{array}{l}[C_{6}H_{5}COO^{-}]\end{array} \)
= y/11
Ksp= [Ag+]
\(\begin{array}{l}[C_{6}H_{5}COO^{-}]\end{array} \)
\(\begin{array}{l}2.5\times 10^{-13} = y\frac{y}{11}\end{array} \)
y =
\(\begin{array}{l}1.66\times 10^{-6}\end{array} \)
mol/L
Hence, solubility of C6H5COOAg in buffer of pH = 3.19 is
\(\begin{array}{l}1.66\times 10^{-6}\end{array} \)
mol/L.
For water: Assuming the solubility of silver benzoate (C6H5COOAg) is x mol/L,
Now, [Ag+] = y’ M and [CH3COO–] = y’M
Ksp = [Ag+]
\(\begin{array}{l}[C_{6}H_{5}COO^{-}]\end{array} \)
Ksp = (y’)2 =
\(\begin{array}{l}\sqrt{K_{sp}} = \sqrt{2.5\times 10^{-13}} = 5\times 10^{-7} mol/L\end{array} \)
\(\begin{array}{l}∴ \frac{y}{x} = \frac{1.66\times 10^{-6}}{5\times 10^{-7}} = 3.32\end{array} \)
Thus, the solubility of silver benzoate in water is 3.32 times the solubility of silver benzoate in pH = 3.19.
Q.68. What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, Ksp = 6.3 × 10–18).
Ans.
Assuming the maximum concentration of each solution is y mol/L,
On mixing the solutions, the volume of the concentration of each solution is reduced to half. After mixing, the maximum concentration of each solution is y/2 mol/L.
Thus, [FeSO4] = [Na2S] = y/2 MSo, [Fe2+] = [FeSO4] = y/2 M
FeS(s)
\(\begin{array}{l}\leftrightarrow\end{array} \)
\(\begin{array}{l}Fe^{2+}_{(aq)} + S^{2-}_{(aq)}\end{array} \)
Ksp = [Fe2+][S2-]
\(\begin{array}{l}6.3\times 10^{-18} = (\frac{y}{2})(\frac{y}{2})\end{array} \)
\(\begin{array}{l}\frac{y^{2}}{4} = 6.3\times 10^{-18}\end{array} \)
Thus, y =
\(\begin{array}{l}5.02\times 10^{-9}\end{array} \)
Thus, if the concentration of FeSO4 and Na2SO4 is equal to or less than that of
\(\begin{array}{l}5.02\times 10^{-9}M\end{array} \)
, then there won’t be precipitation of FeS.
Q.69. What is the minimum volume of water required to dissolve 1 g of calcium sulphate at 298 K? (For calcium sulphate, Ksp is 9.1 × 10–6).
Ans.
\(\begin{array}{l}CaSO_{4(s)}\leftrightarrow Ca^{2+}_{(aq)} + SO_{4}^{2-}(aq)\end{array} \)
Ksp =
\(\begin{array}{l}[Ca^{2+}][SO_{4}^{2-}]\end{array} \)
Assuming the solubility of calcium sulphate is x,
Ksp = x2
\(\begin{array}{l}∴ \;9.1\times 10^{-6} = x^{2}\end{array} \)
\(\begin{array}{l}∴ \;x = 3.02\times 10^{-3} mol/L\end{array} \)
Now, the molecular mass os calcium sulphate is 136g/mol. Solubility in calcium sulphate in g/mol is
\(\begin{array}{l}= 3.02\times 10^{-3} \times 136\end{array} \)
= 0.41 g/L.
i.e., 1 litre of H2O will be required to dissolve 0.41 g of calcium sulphate.
Thus, the minimum volume of H2O required to dissolve 1 gram of CaSO4 at 298 K is =
\(\begin{array}{l}\frac{1}{0.41} L = 2.44 L\end{array} \)
.
Q.70. The concentration of sulphide ion in 0.1 M HCl solution saturated with hydrogen sulphide is 1.0 × 10–19 M. If 10 mL of this is added to 5 mL of 0.04 M solution of FeSO4, MnCl2, ZnCl2 and CdCl2, in which of these solutions precipitation will take place?
Ans.
If the ionic product exceeds the Ksp value, then only precipitation can take place.
Before mixing: [S2-] = Ksp =
\(\begin{array}{l}1.0\times 10^{-19}M\end{array} \)
[M2+] = 0.04 M
Volume = 10 mL
Volume = 5 mL
After mixing:[S2-] = ? and [M2+] = ?
Total volume = (10 + 5) = 15 mL
Volume = 15 mL
[S2-] =
\(\begin{array}{l}\frac{1.0\times 10^{-19}\times 10}{15} = 6.67\times 10^{-20}M\end{array} \)
[M2+] =
\(\begin{array}{l}\frac{0.04\times 5}{15} = 1.33\times 10^{-2}M\end{array} \)
Now, the ionic product = [M2+][S2-]=
\(\begin{array}{l}(1.33\times 10^{-2})(6.67\times 10^{-20})\end{array} \)
=
\(\begin{array}{l}8.87\times 10^{-22}\end{array} \)
Here, the ionic product of CdS and ZnS exceeds its corresponding Ksp value. Thus, precipitation will occur in ZnCl2 and CdCl2 solutions.
Important Topics Covered in NCERT Solutions for Class 11 Chemistry Chapter 7 are listed below:
- Law of chemical equilibrium
- Equilibrium constant
- Homogeneous and heterogeneous equilibria
- Applications of equilibrium constants
- Relationship between different equilibrium constants
- Factors affecting equilibria
- Ionic equilibrium in solution
- Ionisation of acids and bases
- Buffer Solutions
Why are ANAND CLASSES (A School Of Competitions) NCERT Solutions a cut above the rest?
ANAND CLASSES (A School Of Competitions) primary mission is to create top-notch educational content accessible to each and every student in the country. The NCERT Solutions that we offer have been structured carefully to offer maximum benefits to the students to study well and obtain good marks in the annual exam. These NCERT Solutions for Class 11 Chemistry Chapter 7 are concept-focused and can, therefore, be used for revisions.
Designed by subject-matter experts to be highly student-friendly, these NCERT Solutions for Class 11 Chemistry feature simple, explanative solutions to even relatively complex questions. Also, the ANAND CLASSES (A School Of Competitions) support team is always available to clear doubts and solve any issues faced by students.
Frequently Asked Questions on NCERT Solutions for Class 11 Chemistry Chapter 7
Q1
List out the important topics covered in NCERT Solutions for Class 11 Chemistry Chapter 7.
The important concepts covered in NCERT Solutions for Class 11 Chemistry Chapter 7 are as follows:
Solid-liquid Equilibrium
Equilibrium in Chemical Processes – Dynamic Equilibrium
Law of Chemical Equilibrium and Equilibrium Constant
Homogeneous Equilibria
Heterogeneous Equilibria
Applications of Equilibrium Constants
Relationship between Equilibrium Constant K, Reaction Quotient Q and Gibbs Energy G
Factors Affecting Equilibria
Ionic Equilibrium in Solution
Acids, Bases And Salts
Ionisation of Acids and Bases
Buffer Solutions
Solubility Equilibria of Sparingly Soluble Salts
Q2
What is the meaning of buffer solution in NCERT Solutions for Class 11 Chemistry Chapter 7?
According to NCERT Solutions for Class 11 Chemistry Chapter 7, a buffer solution is a water solvent-based solution that consists of a mixture containing a weak acid and the conjugate base of the weak acid or a weak base and the conjugate acid of the weak base. They resist a change in pH upon dilution or upon the addition of small amounts of acid/alkali to them.
Q3
How are the NCERT Solutions for Class 11 Chemistry Chapter 7 helpful for annual exam preparation?
Practising NCERT Solutions for Class 11 Chemistry Chapter 7 helps the students to score well in the annual exams. These solutions are devised based on the updated CBSE Syllabus, covering all the crucial concepts of the respective topic. Solving these questions will boost their confidence to face the annual exams fearlessly. Topics covered in these solutions form the basis for high scores. It also helps the students to get familiar with answering questions of all difficulty levels. Hence, it is highly recommended that the students of Class 11 should practise these solutions to prepare well for their annual exams.
Q4.
List Subtopics included in NCERT Class 11 Chemistry Chapter 7 – Equilibrium
- Solid-liquid Equilibrium
- Liquid-vapour Equilibrium
- Solid-vapour Equilibrium
- Equilibrium Involving Dissolution of Solid or Gases in Liquids
- General Characteristics of Equilibria Involving Physical Processes
- Equilibrium in Chemical Processes – Dynamic Equilibrium
- Law of Chemical Equilibrium and Equilibrium Constant
- Homogeneous Equilibria
- Equilibrium Constant in Gaseous Systems
- Heterogeneous Equilibria
- Applications of Equilibrium Constants
- Predicting the Extent of a Reaction
- Predicting the Direction of the Reaction
- Calculating Equilibrium Concentrations
- Relationship between Equilibrium Constant K, Reaction Quotient Q and Gibbs Energy G
- Factors Affecting Equilibria
- Effect of Concentration Change
- Effect of Pressure Change
- Effect of Inert Gas Addition
- Effect of Temperature Change
- Effect of a Catalyst
- Ionic Equilibrium in Solution
- Acids, Bases and Salts
- Arrhenius Concept of Acids and Bases
- The Bronsted-lowry Acids and Bases
- Lewis Acids and Bases
- Ionisation of Acids and Bases
- The Ionisation Constant of Water and Its Ionic Product
- The pH Scale
- Ionisation Constants of Weak Acids
- Ionisation of Weak Bases
- The Relation Between Ka and Kb
- Di- and Polybasic Acids and Di- and Polyacidic Bases
- Factors Affecting Acid Strength
- Common Ion Effect in the Ionisation of Acids and Bases
- Hydrolysis of Salts and the Ph of Their Solutions
- Buffer Solutions
- Solubility Equilibria of Sparingly Soluble Salts
- Solubility Product Constant
- Common Ion Effect on Solubility of Ionic Salts