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Q. No.Find concentration of \(X^{2-}\) at equilibrium in 0.1 M \(H_2X\) ? (in order of \(10^{-15}\))
[Given: \(K_{a_1}=2.5 \times 10^{-8}, K_{a_2}=1 \times 10^{-13} .\)]
1. 100
2. 1000
3. 400
4. 250
[Given: \(K_{a_1}=2.5 \times 10^{-8}, K_{a_2}=1 \times 10^{-13} .\)]
1. 100
2. 1000
3. 400
4. 250
Subtopic: Ionisation Constant of Acid, Base & Salt |
Level 4: Below 35%
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Hints
Two moles each of the gases \(P_2, Q_2\) and PQ are present in a vessel at equilibrium. If 1 mole each of \(P_2\) and \(Q_2\) is added at equilibrium, then determine the composition (in mole) of each species at the new equilibrium ?
1. \(\mathrm{n}_{\mathrm{P}_2}=0.5, \mathrm{n}_{\mathrm{Q}_2}=0.5, \mathrm{n}_{\mathrm{PQ}}=1 \)
2. \(\mathrm{n}_{\mathrm{P}_2}=1.33, \mathrm{n}_{\mathrm{Q}_2}=1.33, \mathrm{n}_{\mathrm{PQ}}=1.67\)
3. \(\mathrm{n}_{\mathrm{P}_2}=2.67, \mathrm{n}_{\mathrm{O}_2}=2.67, \mathrm{n}_{\mathrm{PQ}}=2.33 \)
4. \(\mathrm{n}_{\mathrm{P}_2}=2.67, \mathrm{n}_{\mathrm{Q}_2}=2.67, \mathrm{n}_{\mathrm{PQ}}=2.67\)
1. \(\mathrm{n}_{\mathrm{P}_2}=0.5, \mathrm{n}_{\mathrm{Q}_2}=0.5, \mathrm{n}_{\mathrm{PQ}}=1 \)
2. \(\mathrm{n}_{\mathrm{P}_2}=1.33, \mathrm{n}_{\mathrm{Q}_2}=1.33, \mathrm{n}_{\mathrm{PQ}}=1.67\)
3. \(\mathrm{n}_{\mathrm{P}_2}=2.67, \mathrm{n}_{\mathrm{O}_2}=2.67, \mathrm{n}_{\mathrm{PQ}}=2.33 \)
4. \(\mathrm{n}_{\mathrm{P}_2}=2.67, \mathrm{n}_{\mathrm{Q}_2}=2.67, \mathrm{n}_{\mathrm{PQ}}=2.67\)
Subtopic: Ionisation Constant of Acid, Base & Salt |
Level 4: Below 35%
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Hints
Which of the following buffer solution will have a pH of 9.25?
(Given that \(pK_b\) of \(NH_3:4.75)\)
1. \(0.2 ~\mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(0.4 \ell)+0.1 ~\mathrm{M}~ \mathrm{HCl}(1 \ell) \)
2. \(0.4~ \mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(1 \ell)+0.1 ~\mathrm{M} ~\mathrm{HCl}(1 \ell) \)
3. \(0.5 ~\mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(0.5 \ell)+0.2 ~\mathrm{M} ~\mathrm{HCl}(0.5 \ell) \)
4. \(0.2 ~\mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(0.5 \ell)+0.1 ~\mathrm{M}~ \mathrm{HCl}(0.5 \ell)\)
(Given that \(pK_b\) of \(NH_3:4.75)\)
1. \(0.2 ~\mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(0.4 \ell)+0.1 ~\mathrm{M}~ \mathrm{HCl}(1 \ell) \)
2. \(0.4~ \mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(1 \ell)+0.1 ~\mathrm{M} ~\mathrm{HCl}(1 \ell) \)
3. \(0.5 ~\mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(0.5 \ell)+0.2 ~\mathrm{M} ~\mathrm{HCl}(0.5 \ell) \)
4. \(0.2 ~\mathrm{M} ~\mathrm{NH}_4 \mathrm{OH}(0.5 \ell)+0.1 ~\mathrm{M}~ \mathrm{HCl}(0.5 \ell)\)
Subtopic: pH calculation | Buffer |
Level 3: 35%-60%
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Hints
For the reaction:
\(\begin{array}{ll} \mathrm{A}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{~A}(\mathrm{~g}) \\ \Delta \mathrm{G}_{\mathrm{f}\left(\mathrm{~A}_2\right)}^{\circ}=-100 \mathrm{KJ} / \mathrm{mol} \\ & \\ \Delta\mathrm{G}_{\mathrm{f}(\mathrm{~A})}^{\circ}=-50.8625 \mathrm{KJ} / \mathrm{mol} \end{array}\)
At 300K and 1 atm, degree of dissociation of \(A_2\) gas at equilibrium is \(x\times 10^{-2}.\) Find x:\(\left[\mathrm{R}=8.3 ~\mathrm{Jmol}^{-1} \mathrm{~K}^{-1}\right]\)
1. 52.70
2. 55.18
3. 57.73
4. 59.30
\(\begin{array}{ll} \mathrm{A}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{~A}(\mathrm{~g}) \\ \Delta \mathrm{G}_{\mathrm{f}\left(\mathrm{~A}_2\right)}^{\circ}=-100 \mathrm{KJ} / \mathrm{mol} \\ & \\ \Delta\mathrm{G}_{\mathrm{f}(\mathrm{~A})}^{\circ}=-50.8625 \mathrm{KJ} / \mathrm{mol} \end{array}\)
At 300K and 1 atm, degree of dissociation of \(A_2\) gas at equilibrium is \(x\times 10^{-2}.\) Find x:\(\left[\mathrm{R}=8.3 ~\mathrm{Jmol}^{-1} \mathrm{~K}^{-1}\right]\)
1. 52.70
2. 55.18
3. 57.73
4. 59.30
Subtopic: Ionisation Constant of Acid, Base & Salt | Solubility Product |
Level 3: 35%-60%
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Hints
For given reaction
\(\mathrm{X}_2(\mathrm{~g})+\mathrm{Y}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{~g})\)
Moles of \(X_2, Y_2~\&~Z\) at equilibrium are 3 moles, 3 moles & 9 moles respectively. If 10 moles of Z are added at constant T then find moles of Z at reestablished equilibrium:
1. 8
2. 12
3. 15
4. 21
\(\mathrm{X}_2(\mathrm{~g})+\mathrm{Y}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{~g})\)
Moles of \(X_2, Y_2~\&~Z\) at equilibrium are 3 moles, 3 moles & 9 moles respectively. If 10 moles of Z are added at constant T then find moles of Z at reestablished equilibrium:
1. 8
2. 12
3. 15
4. 21
Subtopic: Le Chatelier's principle |
65%
Level 2: 60%+
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Hints
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For a given reaction, \( K_P=9~\text{atm}\)
\(\mathrm{NH}_{3(\mathrm{~g})} \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2(\mathrm{~g})}+\frac{3}{2} \mathrm{H}_{2(\mathrm{~g})}\)
Total pressure at equilibrium is \(\sqrt 3\) atm.
Find the value of \(7~\alpha ^2,\) where \(\alpha \) is degree of dissociation of \(NH_{3(g)}?\)
1. 2.8
2. 5.2
3. 5.6
4. 8.4
\(\mathrm{NH}_{3(\mathrm{~g})} \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2(\mathrm{~g})}+\frac{3}{2} \mathrm{H}_{2(\mathrm{~g})}\)
Total pressure at equilibrium is \(\sqrt 3\) atm.
Find the value of \(7~\alpha ^2,\) where \(\alpha \) is degree of dissociation of \(NH_{3(g)}?\)
1. 2.8
2. 5.2
3. 5.6
4. 8.4
Subtopic: Kp, Kc & Factors Affecting them | Ionisation Constant of Acid, Base & Salt |
58%
Level 3: 35%-60%
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Hints
For a given reaction at 400 K:
(R=0.082 atm-L/mol-K)
\(\mathrm{xA} \rightleftharpoons \mathrm{yB}\)
Given:
(i) \( \mathrm{K}_{\mathrm{p}}=0.82, \mathrm{~K}_{\mathrm{c}}=25.7\)
(ii) \(\mathrm{K}_{\mathrm{P}}=8.2, \mathrm{~K}_{\mathrm{c}}=0.25\)
Then what is the correct combination of x & y for above set (i) & set (ii) data:
(R=0.082 atm-L/mol-K)
\(\mathrm{xA} \rightleftharpoons \mathrm{yB}\)
Given:
(i) \( \mathrm{K}_{\mathrm{p}}=0.82, \mathrm{~K}_{\mathrm{c}}=25.7\)
(ii) \(\mathrm{K}_{\mathrm{P}}=8.2, \mathrm{~K}_{\mathrm{c}}=0.25\)
Then what is the correct combination of x & y for above set (i) & set (ii) data:
| set (i) (x,y) |
set (ii) (x,y) |
|
| 1. | (1,2) | (2,1) |
| 2. | (2,1) | (1,2) |
| 3. | (1,1) | (2,1) |
| 4. | (1,2) | (1,1) |
Subtopic: Kp, Kc & Factors Affecting them |
79%
Level 2: 60%+
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Hints
Consider the given equilibrium:
\(\mathrm{CO}(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g})\)
If the pressure applied to the system increases twofold at constant temperature, then
Choose the correct answer from the options given below:
\(\mathrm{CO}(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{~g})\)
If the pressure applied to the system increases twofold at constant temperature, then
| (A) | Concentration of the reactants and the products increases. |
| (B) | Equilibrium will shift in the forward direction. |
| (C) | The equilibrium constant increases since the concentration of the products increases. |
| (D) | The equilibrium constant remains unchanged as the concentration of the reactants and the products remains the same. |
Choose the correct answer from the options given below:
| 1. | (A) and (B) only | 2. | (A), (B), and (D) only |
| 3. | (B) and (C) only | 4. | (A), (B), and (C) only |
Subtopic: Le Chatelier's principle |
Level 3: 35%-60%
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Hints
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At temperature T, compound \(\mathrm{AB}_{2(\mathrm{~g})}\) dissociates as \(\mathrm{AB}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{AB}_{(\mathrm{g})}+\frac{1}{2} \mathrm{~B}_{2(\mathrm{~g})} \) , having degree of dissociation x (small compared to unity). The correct expression for x in terms of Kp and p is:
| 1. | \(\sqrt[3]{\frac{2 K_p}{p}} \) | 2. | \(\sqrt[4]{\frac{2 \mathrm{~K}_{\mathrm{p}}}{\mathrm{p}}}\) |
| 3. | \(\sqrt[3]{\frac{2 \mathrm{~K}_{\mathrm{p}}^2}{\mathrm{p}}} \) | 4. | \(\sqrt{\mathrm{K}_{\mathrm{p}}} \) |
Subtopic: Kp, Kc & Factors Affecting them |
60%
Level 2: 60%+
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Hints
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\(\text K_{sp}\) for Cr(OH)3 is 1.6 × 10–30. What is the molar solubility of this salt in water?
| 1. | \(\sqrt[4]{\dfrac{1.6 \times 10^{-30}}{27}}\) | 2. | \(\dfrac{1.8 \times 10^{-30}}{27}\) |
| 3. | \(\sqrt[5]{1.8 \times 10^{-30}} \) | 4. | \(\sqrt[2]{1.6 \times 10^{-30}}\) |
Subtopic: Solubility Product |
84%
Level 1: 80%+
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