Chapter 7

An element \(X\) being with oxygen and CO present in air as \(\mathrm{X}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{XO}_{2}(\mathrm{~g}) ; \mathrm{K}_{P_{1}}=27\) \(\mathrm{X}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{XCO}(\mathrm{g}) ; \mathrm{K}_{\mathrm{p}_{2}}=10^{4}\) When \(\mathrm{X}\) at \(1 \mathrm{~atm}\) is treated with air, \(25 \%\) of it is bound to \(\mathrm{CO}(\mathrm{g}) .\) The partial pressure of \(\mathrm{CO}(\mathrm{g})\) in air at equilibrium, if partial pressure of \(\mathrm{O}_{2}(\mathrm{~g})\) in air at equilibrium is \(0.2 \mathrm{~atm}\), would be (a) \(1.9 \times 10^{4} \mathrm{~atm}\) (b) \(1.9 \times 10^{-4} \mathrm{~atm}\) (c) \(2.08 \times 10^{4} \mathrm{~atm}\) (d) \(2.08 \times 10^{-4} \mathrm{~atm}\)

For the 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 \(\mathrm{K}_{\mathrm{n}}\) is \(1.44 \times 10^{-5}\) when the partial pressures are measured in atmosphere. The value of \(\mathrm{K}_{\text {s }}^{\text {p }}\) with concentration in \(\mathrm{mol} \mathrm{L}^{-1}\) is (a) \(\frac{1.44 \times 10^{-5}}{(8.314 \times 773)^{-2}}\) (b) \(\frac{1.44 \times 10^{-5}}{(0.082 \times 500)^{-2}}\) (c) \(\frac{1.44 \times 10^{-5}}{(0.082 \times 773)^{-2}}\) (d) \(\frac{1.44 \times 10^{-5}}{(0.082 \times 773)^{-2}}\)

At \(550 \mathrm{~K}\), the \(\mathrm{Kc}\) for the following reaction is \(10^{4}\) \(\mathrm{mol}^{-1} \mathrm{~L}\) \(\mathrm{X}(\mathrm{g})+\mathrm{Y}(\mathrm{g}) \rightleftharpoons \mathrm{Z}(\mathrm{g})\) At equilibrium, it was observed that \([\mathrm{X}]=\frac{1}{2}[\mathrm{Y}]=\frac{1}{2}[\mathrm{Z}]\) What is the value of \([\mathrm{Z}]\) at equilibrium? (a) \(10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}\) (b) \(2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}\) (c) \(2 \times 10^{4} \mathrm{~mol} \mathrm{~L}^{-1}\) (d) \(10^{4} \mathrm{~mol} \mathrm{~L}^{-1}\)

One mole of \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) at \(300 \mathrm{~K}\) is kept in a closed container under one atmospheric pressure. It is heated to \(600 \mathrm{~K}\) when \(20 \%\) by mass of \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) decomposes to \(\mathrm{NO}_{2}(\mathrm{~g})\). The resultant pressure is (a) \(1.0 \mathrm{~atm}\) (b) \(2.4 \mathrm{~atm}\) (c) \(2.0 \mathrm{~atm}\) (d) \(1.2 \mathrm{~atm}\)

The equilibrium constant (K) of the reaction, \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}\) at \(298 \mathrm{~K}\) is 100 . If the rate con- stant of the forward reaction is \(4 \times 10^{5}\), the rate constant of the reverse reaction is (a) 4 (b) \(4 \times 10^{2}\) (c) \(4 \times 10^{3}\) (d) \(4 \times 10^{5}\)

\(K_{\text {p }}\) has the value of \(10^{-6} \mathrm{~atm}^{3}\) and \(10^{-4} \mathrm{~atm}^{3}\) at \(298 \mathrm{~K}\) and \(323 \mathrm{~K}\) respectively for the reaction \(\mathrm{CuSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{CuSO}_{4}(\mathrm{~s})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) \(\Delta_{r} H^{\circ}\) for the reaction is: (a) \(7.7 \mathrm{~kJ} / \mathrm{mol}\) (b) \(-147.41 \mathrm{~kJ} / \mathrm{mol}\) (c) \(147.41 \mathrm{~kJ} / \mathrm{mol}\) (d) None of these

A flask containing \(0.5\) atm pressure of \(\mathrm{A}_{2}(\mathrm{~g})\), some solid AB added into flask which undergoes dissociation according to \(2 \mathrm{AB}(\mathrm{s}) \rightleftharpoons \mathrm{A}_{2}(\mathrm{~g})+\mathrm{B}_{2}(\mathrm{~g}) \mathrm{K}_{\mathrm{P}}=\) \(0.06 \mathrm{~atm}^{2} .\) The total pressure (in \(\mathrm{atm}\) ) at equilibrium is: (a) \(0.70\) (b) \(0.6\) (c) \(0.10\) (d) None of these

\(\frac{\mathrm{K}_{\mathrm{p}}}{\mathrm{K}_{c}}\) for the reaction \(\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})\) will be (a) \(\sqrt{\mathrm{RT}}\) (b) RT (c) \(\frac{1}{\sqrt{\mathrm{RT}}}\) (d) 1

At \(25^{\circ} \mathrm{C}\), the standard emf of a cell having reaction involving two electron exchange is found to be \(0.295 \mathrm{~V} .\) The equilibrium constant of the reaction is approximately (a) \(9.50 \times 10^{9}\) (b) \(1 \times 10^{10}\) (c) 10 (d) \(9.51 \times 10^{\top}\)

Assume that the decomposition of \(\mathrm{HNO}_{3}\) can be represented by the following equation \(4 \mathrm{HNO}_{3}(\mathrm{~g}) \rightleftharpoons 4 \mathrm{NO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g})\) and the reaction approaches equilibrium at \(400 \mathrm{~K}\) temperature and 30 atm pressure. At equilibrium, partial pressure of \(\mathrm{HNO}_{3}\) is \(2 \mathrm{~atm} .\) Calculate \(\mathrm{K}_{\mathrm{c}}\) in \((\mathrm{mol} / \mathrm{L})^{3}\) at \(400 \mathrm{~K}\) : (Use : \(\mathrm{R}=0.08 \mathrm{~atm}-\mathrm{L} / \mathrm{mol}-\mathrm{K})\) (a) 4 (b) 8 (c) 16 (d) 32

The equilibrium constants for the reactions \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3}\) and \(\frac{1}{2} \mathrm{~N}_{2}+\frac{3}{2} \mathrm{H}_{2} \rightleftharpoons \mathrm{NH}_{3}\) are \(K_{1}\) and \(K_{2}\) respectively. The correct relationship between \(\mathrm{K}_{1}\) and \(\mathrm{K}\), is (a) \(\mathrm{K}_{1}=\frac{\mathrm{K}_{2}}{2}\) (b) \(\mathrm{K}_{2}=\sqrt{\mathrm{K}_{\mathrm{t}}}\) (c) \(\mathrm{K}_{2}=\mathrm{K}_{1}^{2}\) (d) \(\mathrm{K}_{1}=\mathrm{K}_{2}\)

The coagulation of \(100 \mathrm{ml}\) of colloidal solution of gold is completely prevented by addition of \(0.25 \mathrm{~g}\) of a substance " \(\mathrm{X}\) " to it before addition of \(10 \mathrm{ml}\) of \(10 \% \mathrm{NaCl}\) solution. The gold number of "X" is (a) 25 (b) 250 (c) \(2.5\) (d) \(0.25\)

One mole of \(\mathrm{N}_{2}(\mathrm{~g})\) is mixed with 2 moles of \(\mathrm{H}_{2}(\mathrm{~g})\) in a 4 litre vessel. If \(50 \%\) of \(\mathrm{N}_{2}(\mathrm{~g})\) is converted to \(\mathrm{NH}_{3}(\mathrm{~g})\) by the following reaction: \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) What will be the value of \(\mathrm{K}\) for the following equilibrium? $$ \mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{3}{2} \mathrm{H}_{2}(\mathrm{~g}) $$ (a) 256 (b) 16 (c) \(\frac{1}{16}\) (d) None of these

If \(\mathrm{pKa}=-\log \mathrm{K}=4\) and \(\mathrm{K}=\mathrm{Cx}^{2}\) then van't Hoff factor weak monobasic acid when \(\mathrm{C}=0.01 \mathrm{M}\) is (a) \(1.02\) (b) \(1.01\) (c) \(1.20\) (d) \(1.10\)

Which of the following will favour the formation of \(\mathrm{NH}_{3}\) by Haber's Process? (a) Increase of temperature (b) Increase of pressure (c) Addition of catalyst (d) Addition of promoter

When solid \(\mathrm{NaNO}_{3}\) is heated in a closed vessel, \(\mathrm{O}_{2}\) is liberated and solid \(\mathrm{NaNO}_{2}\) is left behind. At equilibrium (a) Addition of \(\mathrm{NaNO}_{2}\) favours reverse reaction. (b) Addition of \(\mathrm{NaNO}_{3}\) favours forward reaction. (c) Increasing the pressure favours reverse reaction. (d) Increasing the temperature favours forward reaction.

\(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) At constant temperature, forward reaction is favoured by (a) introducing inert gas at constant volume (b) introducing inert gas at constant pressure (c) introducing chlorine gas at constant volume (d) increasing the volume of the container

If the concentrations of two monobasic acids are same, their relative strengths can be compared by (a) \(\left(\frac{\mathrm{K}_{\mathrm{l}}}{\mathrm{K}_{2}}\right)\) (b) \(\left(\frac{\alpha_{1}}{\alpha_{2}}\right)\) (c) \(\left(\sqrt{\frac{K_{1}}{K_{2}}}\right)\) (d) \(\frac{\left[\mathrm{H}^{+}\right]_{1}}{\left[\mathrm{H}^{+}\right]_{2}}\)

Match the following Column-I (a) \(\mathrm{N}_{2} \mathrm{O}_{4(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NO}_{2(8)}\) (b) \(\mathrm{PCl}_{\text {s(g) }} \rightleftharpoons \mathrm{PCl}_{3(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}\) (c) \(\mathrm{NH}_{2} \mathrm{COONH}_{4(\mathrm{~s})} \rightleftharpoons 2 \mathrm{NH}_{3(\mathrm{~g})}+\mathrm{CO}_{2(\mathrm{~g})}\) (d) \(\mathrm{H}_{2(\mathrm{~g})}+\mathrm{I}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{HI}_{(8)}\) Column-II (p) \(\mathrm{K}_{\mathrm{p}}=\frac{4 \mathrm{x}^{2} \mathrm{P}}{\mathrm{a}^{2}-\mathrm{x}^{2}}\) (q) \(\mathrm{K}_{\mathrm{p}}=\frac{4 \mathrm{P}^{3}}{27}\) (r) \(K_{p}=K_{c}\) (s) \(\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{c^{\circ}} \mathrm{RT}\) (t) \(\Delta n_{g}>0\)

Match the following Column-I (a) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})\) (b) \(\mathrm{CaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) (d) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) Column-II (p) Unaffected by inert gas addition at constant volume (q) Forward shift by rise in pressure (r) Unaffected by increase in pressure (s) Backward shift by rise in pressure (t) reaction has \(\Delta n_{g}>0\)

Match the following Column-I (a) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) (b) \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) (d) \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons(\mathrm{g}) \mathrm{SO}_{3}(\mathrm{~g})\) Column-II (p) \(\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{c}}\) (q) \(\Delta \mathrm{G}^{\circ}=-\mathrm{RT} \ln \mathrm{k}\) (r) Addition of He at constant pressure shifts the equilibrium to right hand side (s) \(\mathrm{K}_{\mathrm{p}}>\mathrm{K}_{\mathrm{c}}\) (t) Increase of pressure favours forward reaction.

Assertion: Adding an inert gas todissociation equilibrium of gaseous \(\mathrm{N}_{2} \mathrm{O}_{4}\) at constant pressure and temperature increases the dissociation. Reason: Molar concentration of the reactants and products decreases on the addition of inert gas.

The equilibrium constant \(\mathrm{K}_{\mathrm{P}}\) and \(\mathrm{K}_{\mathrm{P}_{0}}\) for the reactions \(\mathrm{X}=2 \mathrm{Y}\) and \(\mathrm{Z} \rightleftharpoons{\mathrm{P}}+\mathrm{Q} ;\) respectively are in the ratio of \(1: 9\). If the degree of dissociation of \(\mathrm{X}\) and \(\mathrm{Z}\) be equal then calculate the value of \(\sqrt{\frac{\mathrm{p}_{2}}{\mathrm{p}_{1}}}\).

For the following reaction in gaseous phase \(\mathrm{CO}+1 / 2 \mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}\) \(\mathrm{K}_{\mathrm{c}} / \mathrm{K}_{\mathrm{p}}\) is (a) \((\mathrm{RT})^{1 / 2}\) (b) \((\mathrm{RT})^{-1 / 2}\) (c) (RT) (d) \((\mathrm{RT})^{-1}\)

One of the following equilibria is not affected by change in volume of the flask: (a) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g}) \mathrm{Cl}_{2}(\mathrm{~g})\) (b) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) (d) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\)

At \(700 \mathrm{~K}\), the equilibrium constant \(\mathrm{K}\) for the reaction \(2 \mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})\) is \(1.80 \times 10^{-3} .\) What is the numerical value in mole per litre of equilibrium constant \(\mathrm{K}_{\mathrm{c}}\) for this reaction at the same temperature? (a) \(8.1 \times 10^{-8}\) (b) \(9.1 \times 10^{-9} \mathrm{~mol} \mathrm{~L}^{-1}\) (c) \(3.1 \times 10^{-7}\) (d) \(6.1 \times 10^{-7} \mathrm{~mol} \mathrm{~L}^{-1}\)

Consider the reaction equilibrium, \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g}) ; \Delta \mathrm{H}^{\circ}=-198 \mathrm{~kJ}\) on the basis of Le Chatelier's principle, the condition favourable for the forward reaction is (a) lowering of temperature as well as pressure (b) increasing temperature as well as pressure (c) lowering the temperature and increasing the pressure (d) any value of temperature and pressure

What is the equilibrium expression for the reaction [2004] \(\mathrm{P}_{4}(\mathrm{~s})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(\mathrm{~s}) ?\) (a) \(\mathrm{K}_{\mathrm{c}}=\frac{\left[\mathrm{P}_{4} \mathrm{O}_{10}\right]}{5\left[\mathrm{P}_{4}\right]\left[\mathrm{O}_{2}\right]^{5}}\) (b) \(\mathrm{K}_{c}=\frac{1}{\left[\mathrm{O}_{2}\right]^{5}}\) (c) \(\mathrm{K}_{\mathrm{c}}=\frac{\left[\mathrm{P}_{4} \mathrm{O}_{10}\right]}{\left[\mathrm{P}_{4}\right]\left[\mathrm{O}_{2}\right]^{5}}\) (d) \(\mathrm{K}_{\mathrm{c}}=\left[\mathrm{O}_{2}\right]^{5}\)

The equilibrium constant for the reaction, \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) At temperature \(\mathrm{T}\) is \(4 \times 10^{-4} .\) The value of \(\mathrm{K}_{6}\) for the reaction \(\mathrm{NO}(\mathrm{g}) \rightleftharpoons 1 / 2 \mathrm{~N}_{2}(\mathrm{~g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g})\) at the same temperature is (a) \(4 \times 10^{-6}\) (b) \(2.5 \times 10^{2}\) (c) \(0.02\) (d) 50

Consider an endothermic reaction \(\mathrm{X} \longrightarrow \mathrm{Y}\) with the activation energies \(\mathrm{E}_{\mathrm{b}}\) and \(\mathrm{E}_{\mathrm{f}}\) for the backward and forward reactions, respectively. In general \([\mathbf{2 0 0 5}]\) (a) \(\mathrm{E}_{b}<\mathrm{E}_{\mathrm{f}}\) (b) \(E_{b}>E_{f}\) (c) \(E_{b}=E_{f}\) (d) there is no definite relation between \(\mathrm{E}_{\mathrm{b}}\) and \(\mathrm{E}_{\mathrm{f}}\)

An amount of solid \(\mathrm{NH}_{4} \mathrm{HS}\) in placed in a flask already containing ammonia gas at a certain temperature and \(0.50\) atm pressure. Ammonium hydrogen sulphide decomposes to yield \(\mathrm{NH}_{2}\) and \(\mathrm{H}_{2} \mathrm{~S}\) gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure is the flask rises to \(0.84 \mathrm{~atm}\), the equilibrium constant for \(\mathrm{NH}_{4}\) HS decomposition at this temperature is [2005] (a) \(0.30\) (b) \(0.18\) (c) \(0.17\) (d) \(0.11\)

The exothermic formation of \(\mathrm{ClF}_{3}\) is represented by the equation \(\mathrm{Cl}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{ClF}_{3}(\mathrm{~g}) ; \Delta \mathrm{H}=-329 \mathrm{~kJ}\) Which of the following will increase the quantity of \(\mathrm{CIF}_{3}\) in an equilibrium mixture of \(\mathrm{Cl}_{2}, \mathrm{~F}_{2}\) and \(\mathrm{ClF}_{3} ?\) (a) increasing the temperature (b) removing \(\mathrm{Cl}_{2}\) (c) increasing the volume of the container (d) adding \(\mathrm{F}_{2}\)

Phosphorous pentachloride dissociates as follows, in a closed reaction vessel \(\mathrm{PCI}_{5}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) If total pressure at equilibrium of the reaction mixture is \(\mathrm{P}\) and degree of dissociation of \(\mathrm{PCl}_{5}\) is \(\mathrm{x}\), the partial pressure of \(\mathrm{PCl}_{3}\) will be (a) \(\left(\frac{x}{(x+1)}\right) \mathrm{P}\) (b) \(\left(\frac{2 x}{(x-1)}\right) \mathrm{P}\) (c) \(\left(\frac{x}{(x-1)}\right) P\) (d) \(\left(\frac{x}{(1-x)}\right) \mathrm{P}\)

The equilibrium constant for the reaction \(\mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g})\) is \(K_{c}=4.9 \times 10^{-2}\). the value of \(K_{c}\) for the reaction \(2 \mathrm{SO}_{2}\) \((\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) will be (a) 416 (b) \(2.40 \times 10^{-3}\) (c) \(9.8 \times 10^{-2}\) (d) \(4.9 \times 10^{-2}\)

The equilibrium constants \(\mathrm{K}_{\mathrm{P}}\), and \(\mathrm{K}_{\mathrm{p}}\) for the reactions \(\mathrm{X} \rightleftharpoons 2 \mathrm{Y}\) and \(\mathrm{Z} \rightleftharpoons \mathrm{P}+\mathrm{Q}\), respectively are in the ratio of \(1: 9\). If the degree of dissociation of \(X\) and \(\mathrm{Z}\) be equal then the ratio of total pressure at these equilibria is (a) \(1: 36\) (b) \(1: 1\) (c) \(1: 3\) (d) \(1: 9\)

For the following three reactions \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\), equilibrium constants are given: \(\quad\) (a) \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) ; \mathrm{K}_{1}\) (b) \(\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) ; \mathrm{K}_{2}\) (c) \(\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2}(\mathrm{~g}) ; \mathrm{K}_{3}\) Which of the following relation is correct? (a) \(\mathrm{K}_{1} \sqrt{\mathrm{K}}_{2}=\mathrm{K}_{2}\) (b) \(\mathrm{K}_{2} \mathrm{~K}_{3}=\mathrm{K}_{1}\) (c) \(\mathrm{K}_{3}=\mathrm{K}_{1} \mathrm{~K}_{2}\) (d) \(\mathrm{K}_{3} \cdot \mathrm{K}_{2}^{3}=\mathrm{K}_{1}^{2}\)

If \(10^{4} \mathrm{dm}^{3}\) of water is introduced into \(1.0 \mathrm{dm}^{3}\) flask at \(300 \mathrm{~K}\), how many moles of water are in the vapour phase when equilibrium is established? (Given: Vapour pressure of \(\mathrm{H}_{2} \mathrm{O}\) at \(300 \mathrm{~K}\) is \(3170 \mathrm{~Pa} ; \mathrm{R}=8.314 \mathrm{JK}^{-1}\) \(\left.\mathrm{mol}^{-1}\right)\) (a) \(5.56 \times 10^{-3} \mathrm{~mol}\) (b) \(1.53 \times 10^{-2} \mathrm{~mol}\) (c) \(4.46 \times 10^{-2} \mathrm{~mol}\) (d) \(1.27 \times 10^{-3} \mathrm{~mol}\)

A vessel at \(1000 \mathrm{~K}\) contains \(\mathrm{CO}_{2}\) with a pressure of \(0.5 \mathrm{~atm}\). Some of the \(\mathrm{CO}_{2}\) is converted into \(\mathrm{CO}\) on the addition of graphite. If the total pressure at equilibrium is \(0.8 \mathrm{~atm}\), the value of \(\mathrm{K}\) is: (a) \(3.6 \mathrm{~atm}\) (b) \(1 \mathrm{~atm}\) (c) 2 atm (d) \(1.8 \mathrm{~atm}\)

The equilibrium constant \((\mathrm{K})\) for the reaction \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NO}(\mathrm{g}) \quad\) at temperature \(\mathrm{T}\) is \(4 \times 10^{-4} .\) The value of \(K_{c}\) for the reaction, \(\mathrm{NO}(\mathrm{g}) \rightarrow \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})\) at the same temperature is (a) \(4 \times 10^{-4}\) (b) \(0.02\) (c) \(2.5 \times 10^{2}\) (d) \(50.0\)

For the reaction \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})=\mathrm{SO}_{3}(\mathrm{~g})\) if \(\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{C}}(\mathrm{RT})^{\mathrm{x}}\) where the symbols have usual meaning then the value of \(\mathrm{x}\) is: (assuming ideality) (a) \(\frac{1}{2}\) (b) 1 (c) \(-1\) (d) \(-\frac{1}{2}\)

The equilibrium constant at \(298 \mathrm{~K}\) for a reaction \(\mathrm{A}+\) \(\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}\) is 100 . If the initial concentration of all the four species were \(1 \mathrm{M}\) each, then equilibrium concentration of \(\mathrm{D}\) (in \(\mathrm{mol} \mathrm{L}^{-1}\) ) will be: (a) \(0.818\) (b) \(1.818\) (c) \(1.182\) (d) \(0.182\)