Chapter 6

The approach to the following equilibrium was observed kinetically from both directions: $$ \mathrm{PtCl}_{4}^{2-}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}+\mathrm{Cl} $$ At \(25^{\circ} \mathrm{C}\), it was found that \(-\frac{\mathrm{d}\left[\mathrm{PtCl}_{4}^{2-}\right]}{\mathrm{d} t}=\left(3.9 \times 10^{-5} \mathrm{~s}^{-1}\right)\left[\mathrm{PtCl}_{4}{\underline{\phantom{xx}}}^{2}\right]\) \(-\left(2.1 \times 10^{-3} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\right)\left[\mathrm{Pt}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{3}\right][\mathrm{Cl}]\) The value of \(K_{\text {eq }}\) (equilibrium constant) for the complexation of the fourth \(\mathrm{Cl}^{-}\) by \(\mathrm{Pt}(\mathrm{II})\) is (a) \(53.8 \mathrm{~mol} \mathrm{~L}^{-1}\) (b) \(0.018 \mathrm{~mol} \mathrm{~L}^{-1}\) (c) \(53.8 \mathrm{~L} \mathrm{~mol}^{-1}\) (d) \(0.018 \mathrm{~L} \mathrm{~mol}^{-1}\)

The complexion of \(\mathrm{Fe}^{2+}\) with the chelating agent dipyridyl has been studied kinetically in both the forward and reverse directions. \(\mathrm{Fe}^{2+}+3\) dipy \(\rightleftharpoons\left[\mathrm{Fe}(\mathrm{dipy})_{3}\right]^{2+}\) For this reaction, the rates of forward and reverse reactions are \(\left(1.45 \times 10^{13}\right.\) \(\left.\mathrm{M}^{-3} \mathrm{~s}^{-1}\right)\left[\mathrm{Fe}^{2+}\right][\mathrm{dipy}]^{3}\) and \(\left(1.22 \times 10^{-4} \mathrm{~s}^{-1}\right)\) \(\left[\mathrm{Fe}(\mathrm{dipy})_{3}{\underline{\phantom{xx}}}^{2+}\right]\), at \(25^{\circ} \mathrm{C}\). What is the stability constant of the complex? (a) \(1.77 \times 10^{9}\) (b) \(8.4 \times 10^{-18}\) (c) \(1.18 \times 10^{17}\) (d) \(5.65 \times 10^{-10}\)

The concentration of a pure solid or liquid phase is not included in the expression of equilibrium constant because (a) solid and liquid concentrations are independent of their quantities. (b) solid and liquids react slowly. (c) solid and liquids at equilibrium do not interact with gaseous phase. (d) the molecules of solids and liquids cannot migrate to the gaseous phase.

The rate constant for the forward reaction: \(\mathrm{A}(\mathrm{g}) \rightleftharpoons 2 \mathrm{~B}(\mathrm{~g})\) is \(1.5 \times 10^{-3} \mathrm{~s}^{-1}\) at \(300 \mathrm{~K}\). If \(10^{-5}\) moles of 'A' and 100 moles of ' \(\mathrm{B}\) ' are present in a 10 litre vessel at equilibrium, then the rate constant of the backward reaction at this temperature is (a) \(1.5 \times 10^{-3} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) (b) \(1.5 \times 10^{-1} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) (c) \(1.5 \times 10^{-11} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) (d) \(1.5 \times 10^{-12} \mathrm{M}^{-1} \mathrm{~s}^{-1}\)

For the reversible reaction: \(\mathrm{N}_{2}(\mathrm{~g})\) \(+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) at \(500^{\circ} \mathrm{C}\), the value of \(K_{\mathrm{p}}\) is \(1.44 \times 10^{-5}\) when partial pressure is measured in atmospheres. The corresponding value of \(K_{c}\), with concentration in mole litre \(^{-1}\), is (a) \(\frac{1.44 \times 10^{-5}}{(0.082 \times 500)^{-2}}\) (b) \(\frac{1.44 \times 10^{-5}}{(8.314 \times 773)^{-2}}\) (c) \(\frac{1.44 \times 10^{-5}}{(0.082 \times 773)^{2}}\) (d) \(\frac{1.44 \times 10^{-5}}{(0.082 \times 773)^{-2}}\)

\(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{CuSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) \(+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), K_{\mathrm{e}}\) for this equilibrium is \(1.0 \times 10^{-4} \mathrm{~atm}^{2}\) at \(25^{\circ} \mathrm{C}\). What is the maximum pressure of water vapour (moisture) in the atmosphere, below which the pentahydrate is efflorescent? (a) \(7.60 \mathrm{~mm}\) (b) \(0.01 \mathrm{~mm}\) (c) \(0.076 \mathrm{~mm}\) (d) \(760 \mathrm{~mm}\)

At constant temperature, the equilibrium constant \(\left(K_{\mathrm{p}}\right)\) for the decomposition reaction: \(\mathrm{N}_{2} \mathrm{O}_{4} \rightleftharpoons 2 \mathrm{NO}_{2}\) is expressed by \(K_{\mathrm{p}}=\frac{4 x^{2} P}{1-x^{2}}\), where \(P=\) total pressure at equilibrium, \(x=\) extent of decomposition. Which one of the following statements is true? (a) \(K_{\mathrm{p}}\) increases with increase of \(P\). (b) \(K_{\mathrm{v}}\) increases with increase of \(x\). (c) \(K\), increases with decrease of \(x\). (d) \(K\), remains constant with change in \(P\) and \(x\).

\(\mathrm{XeF}_{6}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{XeOF}_{4}+2 \mathrm{HF}\) equilibrium constant \(=K_{1}\). \(\mathrm{XeO}_{4}+\mathrm{XeF}_{6} \rightleftharpoons \mathrm{XeOF}_{4}+\mathrm{XeO}_{3} \mathrm{~F}_{2}\) equilibrium constant \(=K_{2} .\) Then equilibrium constant for the following reaction will be: \(\mathrm{XeO}_{4}+2 \mathrm{HF} \rightleftharpoons \mathrm{XeO}_{3} \mathrm{~F}_{2}+\mathrm{H}_{2} \mathrm{O}\) (a) \(\frac{K_{1}}{K_{2}}\) (b) \(K_{1}+K_{2}\) (c) \(\frac{K_{2}}{K_{1}}\) (d) \(K_{2}-K_{1}\)

Eor a reversible reaction: \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}\), if the concentrations of the reactants are doubled at a definite temperature, then equilibrium constant will (a) be doubled (b) be halved (c) be one fourth (d) remain same

Under what pressure must an equimolar mixture of \(\mathrm{Cl}_{2}\) and \(\mathrm{PCl}_{3}\) be place at \(250^{\circ} \mathrm{C}\) in order to obtain \(75 \%\) conversion of \(\mathrm{PCl}_{3}\) into \(\mathrm{PCl}_{5}\) ? Given: \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons\) \(\mathrm{PCl}_{5}(\mathrm{~g}) ; K_{\mathrm{p}}=2 \mathrm{~atm}^{-1}\) (a) \(12 \mathrm{~atm}\) (b) \(6 \mathrm{~atm}\) (c) 15 atm (d) \(30 \mathrm{~atm}\)

The equilibrium constant for the reaction: \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) is \(K_{1}\) and the equilibrium constant for the reaction: \(\mathrm{NO}(\mathrm{g}) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})\) is \(K_{2}\), both at the same temperature. \(K_{1}\) and \(K_{2}\) are related as (a) \(K_{1}=\left(\frac{1}{K_{2}}\right)^{2}\) (b) \(K_{1}=K_{2}^{2}\) (c) \(K_{2}=\left(\frac{1}{K_{1}}\right)^{2}\) (d) \(K_{2}=K_{1}^{2}\)

Equilibrium constants for some reactions are given. In which of the following case does the reaction go farthest to completion? (a) \(K=10^{2}\) (b) \(K=10^{-2}\) (c) \(K=10\) (d) \(K=1\)

For a reversible reaction, the rate constants for the forward and backward reactions are \(0.16\) and \(4 \times 10^{4}\), respectively. What is the value of equilibrium constant of the reaction? (a) \(0.25 \times 10^{6}\) (b) \(2.5 \times 10^{5}\) (c) \(4 \times 10^{-6}\) (d) \(4 \times 10^{-4}\)

An amount of 3 moles of \(\mathrm{N}_{2}\) and some \(\mathrm{H}_{2}\) is introduced into an evacuated vessel. The reaction starts at \(t=0\) and equilibrium is attained at \(t=t_{1} .\) The amount of ammonia at \(t=2 t_{1}\) is found to be \(34 \mathrm{~g} .\) It is observed that \(\frac{w\left(\mathrm{~N}_{2}\right)}{w\left(\mathrm{H}_{2}\right)}=\frac{14}{3}\) at \(t=\frac{t_{1}}{3}\) and \(t=\frac{t_{1}}{2} .\) The only correct statement is (a) \(w\left(\mathrm{~N}_{2}\right)+w\left(\mathrm{H}_{2}\right)+w\left(\mathrm{NH}_{3}\right)=118 \mathrm{~g}\) at \(t=t_{1}\) (b) \(w\left(\mathrm{~N}_{2}\right)+w\left(\mathrm{H}_{2}\right)+w\left(\mathrm{NH}_{3}\right)=102 \mathrm{~g}\) at \(t=2 t_{1}\) (c) \(w\left(\mathrm{~N}_{2}\right)+w\left(\mathrm{H}_{2}\right)+w\left(\mathrm{NH}_{3}\right)=50 \mathrm{~g}\) at \(t=t_{1} / 3\) (d) \(w\left(\mathrm{~N}_{2}\right)+w\left(\mathrm{H}_{2}\right)+w\left(\mathrm{NH}_{3}\right)\) cannot be predicted

A gaseous mixture contains \(0.30\) moles \(\mathrm{CO}, 0.10 \mathrm{moles} \mathrm{H}_{2}\), and \(0.03\) moles \(\mathrm{H}_{2} \mathrm{O}\) vapour and an unknown amount of \(\mathrm{CH}_{4}\) per litre. This mixture is at equilibrium at \(1200 \mathrm{~K}\). \(\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) \(K_{\mathrm{C}}=3.9\) What is the concentration of \(\mathrm{CH}_{4}\) in this mixture? The equilibrium constant \(K_{\mathrm{c}}\) equals \(3.92\). (a) \(0.39 \mathrm{M}\) (b) \(0.039 \mathrm{M}\) (c) \(0.78 \mathrm{M}\) (d) \(0.078 \mathrm{M}\)

For the reaction: \(2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) \(+\mathrm{Cl}_{2}(\mathrm{~g}), \Delta \mathrm{H}^{\circ}=18 \mathrm{kcal}\) and \(\Delta S^{\circ}=30 \mathrm{cal} / \mathrm{K}\) at \(300 \mathrm{~K}\). The equilibrium constant, \(K_{\mathrm{p}}^{\circ}\) of the reaction at \(300 \mathrm{~K}\) is (a) \(\mathrm{e}^{15}\) (b) \(\mathrm{e}^{-15}\) (c) \(\mathrm{e}^{-18}\) (d) \(\mathrm{e}^{-12}\)

For the reaction: \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons\) \(2 \mathrm{NOCl}(\mathrm{g}), \mathrm{NO}\) and \(\mathrm{Cl}_{2}\) are initially taken in mole ratio of \(2: 1 .\) The total pressure at equilibrium is found to be \(1 \mathrm{~atm}\). If the moles of \(\mathrm{NOCl}\) are one-fourth of that of \(\mathrm{Cl}_{2}\) at equilibrium, \(K_{\mathrm{p}}\) for the reaction is (a) \(\frac{13}{36}\) (b) \(\frac{13}{256}\) (c) \(\frac{13}{512}\) (d) \(\frac{13}{128}\)

What is the approximate value of \(\log K_{\mathrm{p}}\) for the reaction: \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) at \(25^{\circ} \mathrm{C}\) The standard enthalpy of formation of \(\mathrm{NH}_{3}(\mathrm{~g})\) is \(-40.0 \mathrm{~kJ} / \mathrm{mol}\) and standard entropies of \(\mathrm{N}_{2}(\mathrm{~g}), \mathrm{H}_{2}(\mathrm{~g})\) and \(\mathrm{NH}_{3}(\mathrm{~g})\) are 191,130 and \(192 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\), respectively. (a) \(0.04\) (b) \(7.05\) (c) \(8.6\) (d) \(3.73\)

When \(\mathrm{CO}_{2}(\mathrm{~g})\) is dissolved in water, the following equilibrium is established: \(\mathrm{CO}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})\) \(+\mathrm{HCO}_{3}^{-}(\mathrm{aq})\) for which the equilibrium constant is \(3.8 \times 10^{-7}\). If the pH of solution is \(6.0\), what would be the ratio of concentration of \(\mathrm{HCO}_{3}^{-}(\mathrm{aq})\) to \(\mathrm{CO}_{2}(\mathrm{aq})\) ? (a) \(3.8 \times 10^{-13}\) (b) \(6.0\) (c) \(0.38\) (d) \(13.4\)

The equilibrium constants for the reaction: \(\mathrm{A}_{2} \rightleftharpoons 2 \mathrm{~A}\) at \(500 \mathrm{~K}\) and \(1000 \mathrm{~K}\) are \(1 \times 10^{-10^{2}}\) and \(1 \times 10^{-5}\), respectively. The reaction is (a) Exothermic (b) Very slow (c) Very fast (d) Endothermic

Reaction: \(\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightleftharpoons \mathrm{C}(\mathrm{g})\) \(+\mathrm{D}(\mathrm{g})\), occurs in a single step. The rate constant of forward reaction is \(2.0 \times 10^{-3} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1} .\) When the reaction is started with equimolar amounts of \(\mathrm{A}\) and \(\mathrm{B}\), it is found that the concentration of \(\mathrm{A}\) is twice that of \(\mathrm{C}\) at equilibrium. The rate constant of the backward reaction is (a) \(5.0 \times 10^{-4} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}\) (b) \(8.0 \times 10^{-3} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}\) (c) \(1.25 \times 10^{2} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}\) (d) \(2.0 \times 10^{3} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}\)

\(\Delta G^{\circ}\) for the reaction: \(\mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{C}\) is \(-4.606\) kcal at \(1000 \mathrm{~K}\). The equilibrium constant for the reverse mode of the reaction is (a) 100 (b) 10 (c) \(0.01\) (d) \(0.1\)

For a gaseous equilibrium: \(2 \mathrm{~A}(\mathrm{~g}) \rightleftharpoons\) \(2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g}), K_{\mathrm{p}}\) has a value \(1.8\) at \(700 \mathrm{~K}\). The value of \(K_{c}\) for the equilibrium: \(2 \mathrm{~B}(\mathrm{~g})\) \(+\mathrm{C}(\mathrm{g}) \rightleftharpoons 2 \mathrm{~A}(\mathrm{~g})\) at that temperature is about (a) \(0.031\) (b) 32 (c) \(57.4\) (d) \(103.3\)

Amounts of \(0.8 \mathrm{~mol}\) of \(\mathrm{PCl}_{5}\) and \(0.2\) mole of \(\mathrm{PCl}_{3}\) are mixed in a \(1 \mathrm{i}\) flask. At equilibrium, \(0.4\) mole of \(\mathrm{PCl}_{3}\) is present. The equilibrium constant for the reaction, \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) will be (a) \(0.05 \mathrm{~mol}^{-1}\) (b) \(0.13 \mathrm{~mol} 1^{-1}\) (c) \(0.013 \mathrm{~mol} 1^{-1}\) (d) \(0.60 \mathrm{~mol} 1^{-1}\)

In a closed tube, \(\mathrm{HI}(\mathrm{g})\) is heated at \(440^{\circ} \mathrm{C}\) up to establishment of equilibrium. If it dissociates into \(\mathrm{H}_{2}(\mathrm{~g})\) and \(\mathrm{I}_{2}(\mathrm{~g})\) up to \(22 \%\), the dissociation constant is (a) \(0.282\) (b) \(0.0796\) (c) \(0.0199\) (d) \(1.99\)

At \(444^{\circ} \mathrm{C}, \mathrm{HI}\) is \(30 \%\) dissociated. If initially 3 moles of HI are taken, the number of moles of \(\mathrm{HI}\) at equilibrium is (a) \(0.9\) (b) \(2.1\) (c) \(0.45\) (d) \(1.8\)

For the reaction: \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})\), the relation between the degree of dissociation, \(\alpha\), of \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) at pressure, \(P\), with its equilibrium constant \(K_{\mathrm{P}}\) is (a) \(\alpha=\frac{K_{P} / P}{4+K_{P} / P}\) (b) \(\alpha=\frac{K_{P}}{4+K_{P}}\) (c) \(\alpha=\left[\frac{K_{P} / P}{4+K_{P} / P}\right]^{1 / 2}\) (d) \(\alpha=\left[\frac{K_{P}}{4+K_{P}}\right]^{1 / 2}\)

An amount of 1 mole each of \(\mathrm{A}\) and \(\mathrm{D}\) is introduced in \(1 \mathrm{~L}\) container. Simultaneously the following two equilibria are established: \(\mathrm{A} \rightleftharpoons \mathrm{B}+\mathrm{C} ; K_{\mathrm{C}}=10^{6} \mathrm{M}^{2}\) and \(\mathrm{B}+\mathrm{D} \rightleftharpoons \mathrm{A} ; K_{\mathrm{C}}=10^{-6} \mathrm{M}^{-1}\) The equilibrium concentration of \(\mathrm{A}\) will be (a) \(10^{-6} \mathrm{M}\) (b) \(10^{-3} \mathrm{M}\) (c) \(10^{-12} \mathrm{M}\) (d) \(10^{-4} \mathrm{M}\)

At total pressure \(P_{1}\) atm and \(P_{2}\) atm, \(\mathrm{N}_{2} \mathrm{O}_{4}\) is dissociated to an extent of \(33.33 \%\) and \(50.00 \%\), respectively. The ratio of pressures \(P_{1}\) and \(P_{2}\) is (a) \(3: 8\) (b) \(2: 1\) (c) \(8: 3\) (d) \(1: 2\)

For a reversible reaction: \(\mathrm{A} \underset{K_{2}}{\stackrel{K_{1}}{K}} \mathrm{~B}\), the initial molar concentration of \(\mathrm{A}\) and \(\mathrm{B}\) are \(a \mathrm{M}\) and \(b \mathrm{M}\), respectively. If \(x \mathrm{M}\) of \(\mathrm{A}\) is reacted till the achievement of equilibrium, then \(x\) is (a) \(\frac{K_{1} a-K_{2} b}{K_{1}+K_{2}}\) (b) \(\frac{K_{1} a-K_{2} b}{K_{1}-K_{2}}\) (c) \(\frac{K_{1} a-K_{2} b}{K_{1} K_{2}}\) (d) \(\frac{K_{1} a+K_{2} b}{K_{1}+K_{2}}\)

At \(0^{\circ} \mathrm{C}\) and 1 atm pressure, \(1 \mathrm{~L}\) of \(\mathrm{N}_{2} \mathrm{O}_{4}\) decomposes to \(\mathrm{NO}_{2}\) according to the equation \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})\). To what extent has the decomposition proceeded when the original volume is \(25 \%\) less than that of existing volume? (a) \(0.67\) (b) \(0.33\) (c) \(0.25\) (d) \(0.75\)

Forty per cent of a mixture of \(0.2 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) and \(0.6 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) react to give \(\mathrm{NH}_{3}\) according to the equation: \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) at constant temperature and pressure. Then, the ratio of the final volume to the initial volumes of gases is (a) \(4: 5\) (b) \(5: 4\) (c) \(7: 10\) (d) \(8: 5\)

Steam decomposes at high temperature according to the equation: \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) ; \quad \Delta H^{\circ}\) \(=240 \mathrm{~kJ} / \mathrm{mole}\) and \(\Delta S^{\circ}=50 \mathrm{JK}^{-1} / \mathrm{mole}\) The temperature at which the equilibrium constant \(\left(K_{\mathrm{p}}^{\circ}\right)\) becomes \(1.0\), is (a) \(4.8 \mathrm{~K}\) (b) \(4800 \mathrm{~K}\) (c) \(480 \mathrm{~K}\) (d) Impossible

\(\Delta_{t} G^{\circ}\) for the formation of \(\mathrm{HI}(\mathrm{g})\) from its gaseous elements is \(-2.303 \mathrm{kcal} / \mathrm{mol}\) at \(500 \mathrm{~K}\). When the partial pressure of HI is \(10 \mathrm{~atm}\) and of \(\mathrm{I}_{2}(\mathrm{~g})\) is \(0.001 \mathrm{~atm}\), what must be the partial pressure of hydrogen be at this temperature to reduce the magnitude of \(\Delta G\) for the reaction to zero? (a) \(1000 \mathrm{~atm}\) (b) \(10000 \mathrm{~atm}\) (c) \(100 \mathrm{~atm}\) (d) \(31.63 \mathrm{~atm}\)

In a closed container maintained at 1 atm pressure and \(25^{\circ} \mathrm{C}, 2\) moles of \(\mathrm{SO}_{2}(\mathrm{~g})\) and 1 mole of \(\mathrm{O}_{2}(\mathrm{~g})\) were allowed to react to form \(\mathrm{SO}_{3}(\mathrm{~g})\) under the influence of a catalyst. \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) At equilibrium, it was found that \(50 \%\) of \(\mathrm{SO}_{2}(\mathrm{~g})\) was converted to \(\mathrm{SO}_{3}(\mathrm{~g})\). The partial pressure of \(\mathrm{O}_{2}(\mathrm{~g})\) at equilibrium will be (a) \(0.17\) atm (b) \(0.5 \mathrm{~atm}\) (c) \(0.33\) atm (d) \(0.20 \mathrm{~atm}\)

When \(\alpha\) -D-glucose is dissolved in water, it undergoes a partial conversion to \beta-D-glucose. This conversion, called mutarotation, stops when \(64.0 \%\) of the glucose is in the \(\beta\) -form. Assuming that equilibrium has been attained, what is \(\Delta G^{\circ}\) for the reaction: \(\alpha\) -D-glucose \(\rightleftharpoons \beta-\mathrm{D}\) glucose, at this experimental temperature? (a) \(-R T \log _{10}(1.6)\) (b) \(-R T \log _{10}(1.78)\) (c) \(-R T \log _{e}(1.78)\) (d) \(-R T \log _{e}(1.6)\)

One mole of ethanol is treated with one mole of ethanoic acid at \(25^{\circ} \mathrm{C}\). Onefourth of the acid changes into ester at equilibrium. The equilibrium constant for the reaction will be (a) \(1 / 9\) (b) \(4 / 9\) (c) 9 (d) \(9 / 4\)

One mole each of \(\mathrm{A}\) and \(\mathrm{B}\) and \(3 \mathrm{moles}\) each of \(\mathrm{C}\) and \(\mathrm{D}\) are placed in \(1 \mathrm{~L}\) flask. If equilibrium constant is \(2.25\) for the reaction: \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}\), equilibrium concentrations of \(\mathrm{A}\) and \(\mathrm{C}\) will be in the ratio (a) \(2: 3\) (b) \(3: 2\) (c) \(1: 2\) (d) \(2: 1\)

For the reaction: \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}\), the initial concentration of \(\mathrm{A}\) and \(\mathrm{B}\) is equal, but the equilibrium concentration of \(\mathrm{C}\) is twice that of equilibrium concentration of A. The equilibrium constant is (a) 4 (b) 9 (c) \(1 / 4\) (d) \(1 / 9\)

\(\mathrm{I}_{2}+\mathrm{I}^{-} \rightleftharpoons \mathrm{I}_{3}^{-} .\) This reaction is set up in aqueous medium. We start with \(1 \mathrm{~mol}\) of \(\mathrm{I}\), and \(0.5 \mathrm{~mol}\) of \(\mathrm{I}^{-}\) in \(1 \mathrm{~L}\) flask. After equilibrium is reached, excess of \(\mathrm{AgNO}_{3}\) gave \(0.25 \mathrm{~mol}\) of yellow precipitate. Equilibrium constant is (a) \(1.33\) (b) \(2.66\) (c) \(0.375\) (d) \(0.75\)

The equilibrium constant for the mutarotation, \(\alpha\) -D-glucose \(\rightleftharpoons \beta-D\) glucose is \(1.8 .\) What per cent of the \(\alpha\) -form remains under equilibrium? (a) \(35.7\) (b) \(64.3\) (c) \(55.6\) (d) \(44.4\)

At \(T \mathrm{~K}\), a compound \(\mathrm{AB}_{2}(\mathrm{~g})\) dissociates according to the reaction: \(2 \mathrm{AB}_{2}(\mathrm{~g})\) \(\rightleftharpoons 2 \mathrm{AB}(\mathrm{g})+\mathrm{B}_{2}(\mathrm{~g})\), with a degree of dissociation ' \(\mathrm{x}\) ' which is small compared with unity. The expression for 'x' in terms of the equilibrium constant, \(K_{\mathrm{p}}\) and the total pressure, \(P\), is (a) \(\frac{K_{P}}{P}\) (b) \(\left(K_{P}\right)^{1 / 3}\) (c) \(\left(\frac{2 K_{P}}{P}\right)^{1 / 3}\) (d) \(\left(\frac{K_{P}}{P}\right)^{1 / 3}\)

A quantity of \(25 \mathrm{~g}\) sample of \(\mathrm{BaO}_{2}\) is heated to \(954 \mathrm{~K}\) in a closed and rigid evacuated vessel of \(8.21\) L capacity. What percentage of peroxide is converted into oxide? \(2 \mathrm{BaO}_{2}(\mathrm{~s}) \rightleftharpoons 2 \mathrm{BaO}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g})\) \(K_{\mathrm{F}}=0.5 \mathrm{~atm}\) (a) \(20 \%\) (b) \(50 \%\) (c) \(75 \%\) (d) \(80 \%\)

For the reaction: \(\mathrm{NH}_{2} \mathrm{COONH}_{4}(\mathrm{~s}) \rightleftharpoons\) \(2 \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g}), K_{\mathrm{p}}=3.2 \times 10^{-5} \mathrm{~atm}^{3}\) The total pressure of the gaseous products when sufficient amount of reactant is allowed to achieve equilibrium, is (a) \(0.02 \mathrm{~atm}\) (b) \(0.04\) atm (c) \(0.06 \mathrm{~atm}\) (d) \(0.095 \mathrm{~atm}\)

At \(1000^{\circ} \mathrm{C}\) and a pressure of \(16 \mathrm{~atm}\), the equilibrium constant of the reaction: \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{C}(\mathrm{s}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g})\) is such that for every nine moles of \(\mathrm{CO}\), there is one mole of \(\mathrm{CO}_{2}\). For what pressure of the mixture, is the ratio \(\mathrm{CO}: \mathrm{CO}_{2}=4: 1 ?\) The temperature remains \(1000^{\circ} \mathrm{C}\). (a) \(40.5 \mathrm{~atm}\) (b) 81 atm (c) \(33.75 \mathrm{~atm}\) (b) \(6.7 \mathrm{~atm}\)

If \(0.3\) moles of hydrogen gas and \(2.0\) moles of sulphur solid are heated to \(87^{\circ} \mathrm{C}\) in a \(2.0 \mathrm{~L}\) vessel, what will be the partial pressure of \(\mathrm{H}_{2} \mathrm{~S}\) gas at equilibrium? (Given: \(R=0.081-\mathrm{atm} / \mathrm{K}-\mathrm{mol}\) ) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{S}(\mathrm{s}) \rightleftharpoons \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}) ; K_{\mathrm{c}}=0.08\) (a) \(0.32 \mathrm{~atm}\) (b) \(0.43 \mathrm{~atm}\) (c) \(0.62 \mathrm{~atm}\) (d) \(0.48 \mathrm{~atm}\)

Consider the following equilibrium in a closed container: \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})\) At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statement holds true regarding the equilibrium constant \(\left(K_{\mathrm{P}}\right)\) and degree of dissociation \((\alpha)\) ? (a) neither \(K_{\mathrm{p}}\) nor \(\alpha\) changes (b) both \(K_{\mathrm{p}}\) and \(\alpha\) changes (c) \(K_{\mathrm{p}}\) changes, but \(\alpha\) does not change (d) \(K_{\mathrm{p}}\) does not change, but \(\alpha\) changes

When pressure is applied to the equilibrium system: Ice \(\rightleftharpoons\) water, which of the following phenomenon will happen? (a) more ice will be formed (b) ice will sublime (c) more water will be formed (d) equilibrium will not disturb

The equilibrium: \(\mathrm{SOCl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g})\) \(+\mathrm{Cl}_{2}(\mathrm{~g})\) is attained at \(25^{\circ} \mathrm{C}\) in a closed container and helium gas is introduced. Which of the following statements is correct? (a) concentration of \(\mathrm{SO}_{2}\) is increased (b) more \(\mathrm{Cl}_{2}\) is formed (c) concentrations of all change (d) concentrations will not change

Densities of diamond and graphite are \(3.5\) and \(2.4 \mathrm{~g} / \mathrm{ml}\), respectively. The increase in pressure (at the constant temperature) at the equilibrium in \(\mathrm{C}\) (diamond) \(\rightleftharpoons\) \(\mathrm{C}\) (graphite) will (a) favour the forward reaction (b) favour the backward reaction (c) have no effect (d) increases the equilibrium constant