Chapter 10

Hydrogenation of vegetable ghee at \(27^{\circ} \mathrm{C}\) reduces the pressure of \(\mathrm{H}_{2}\) from \(3 \mathrm{~atm}\) to \(2.18 \mathrm{~atm}\) in 40 minutes. The rate of reaction in terms of molarity per second is \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-t}\right)\) (a) \(1.357 \times 10^{-6}\) (b) \(1.537 \times 10^{-5}\) (c) \(1.375 \times 10^{-5}\) (d) \(6.250 \times 10^{-4}\)

In a certain reaction \(8 \%\) of the reactant decomposes in 30 minutes, \(24 \%\) in 90 minutes and \(48 \%\) in 180 minutes. What are the dimensions of the rate constant? (a) Mol lit \(^{-1} \sec ^{-1}\) (b) \(\mathrm{Mol} \mathrm{sec}^{-1}\) (c) Lit \(\mathrm{mol}^{-1} \mathrm{sec}^{-1}\) (d) Hour \(^{-1}\)

For the reaction, \(2 \mathrm{NO}+\mathrm{Cl}_{2} \longrightarrow 2 \mathrm{NOCl}\) The following mechanism has been proposed \(\mathrm{NO}+\rightleftharpoons \mathrm{Cl} \quad \mathrm{NOCl}_{2}\) (fast) \(\mathrm{NOCl}_{2}+\mathrm{NO} \longrightarrow 2 \mathrm{NOCl}\) (slow) (a) Rate \(=\mathrm{k}[\mathrm{NO}]\left[\mathrm{Cl}_{2}\right]^{2}\) (b) Rate \(=\mathrm{k}[\mathrm{NO}]^{2}\left[\mathrm{Cl}_{2}\right]\) (c) Rate \(=\mathrm{k}[\mathrm{NOCl}]^{2}\) (d) Rate \(=\mathrm{k}\left[\mathrm{NOCl}_{2}\right][\mathrm{NO}]\)

In general the rate of a chemical reaction is doubled with every \(10^{\circ}\) rise in temperature. If the reaction is carried out in the vicinity at \(27^{\circ} \mathrm{C}\), the activation energy of the reaction is (a) \(51.85 \mathrm{~kJ}\) (b) \(58.15 \mathrm{~kJ}\) (c) \(5.81 \mathrm{~kJ}\) (d) \(8.51 \mathrm{~kJ}\)

Consider the following statements (a) The rate of a process is always proportional to its free energy change. (b) The molecularity of an elementary chemical reaction step can be determined by examining its stoichiometry. (c) The first order reactions follow an exponential time course. (d) Energy of activation is inversely proportional to temperature. The correct statement (s) is/are (a) \(1,2,3\) (b) \(1,2,3,4\) (c) 2 and 3 (d) 1 and 3

The hypothetical reaction, \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB}\) follows the following mechanism: \(\mathrm{A}_{2}=\mathrm{A}+\mathrm{A}\) (fast) \(\mathrm{A}+\mathrm{B}_{2} \longrightarrow \mathrm{AB}+\mathrm{B} \quad\) (slow) \(\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{AB} \quad\) (fast) The order of the overall reaction is: (a) \(\underline{1}\) (b) 2 (c) \(3 / 2\) (d) 0

The chemical kinetics of the reaction \(\mathrm{aA}+\mathrm{bB} \rightarrow\) \(\mathrm{C}\) at \(298 \mathrm{~K}\) were followed. The initial rates were recorded rates were recorded under different initial conditions and are summarized as follows. \begin{tabular}{lll} \hline Initial conc. \([\mathrm{A}]_{0}(\mathrm{~mol} / \mathrm{L})\) & Initial conc. \([\mathrm{B}]_{0}(\mathrm{~mol} / \mathbf{L})\) & Initial rate \((\mathrm{mol} / \mathrm{L} \mathrm{s})\) \\ \hline \(0.1\) & \(0.1\) & \(2.4 \times 10^{-3}\) \\ \(0.2\) & \(0.1\) & \(4.8 \times 10^{-3}\) \\ \(0.4\) & \(0.1\) & \(9.7 \times 10^{-3}\) \\ \(0.1\) & \(0.2\) & \(9.6 \times 10^{-3}\) \\ \(0.1\) & \(0.4\) & \(3.8 \times 10^{-2}\) \\ \hline \end{tabular} Which of the following statements is incorrect? (a) The rate constant \(\mathrm{k}\) is governed by the activation energy of the reaction (b) Reaction rate \(=\mathrm{k}[\mathrm{A}][\mathrm{B}]^{2}\) (c) In the chemical equation of \(a \mathrm{~A}+\mathrm{bB} \rightarrow \mathrm{C}, \mathrm{a}\) is 0 and \(b\) is 3 . (d) The overall order of reaction is third order.

If a is the initial concentration of reactant and \((a-x)\) is the remaining concentration after time "t' in a first order reaction of rate constant \(\mathrm{k}_{1}\), then which of the following relations is /are correct? (a) \(k_{1}=\frac{2.303}{t} \log \left(\frac{a}{a-x}\right)\) (b) \(x=a\left(1-c^{k_{1} t}\right)\) (c) \(t_{1 / 2}=\frac{1.414}{k_{1}}\) (d) \(t_{a v}=\frac{1}{k_{1}}\)

Identify the correct statements: (a) The order of an elementary reaction is equal to its molecularity (b) The order of a reaction can be zero (c) For second order reaction, order of reaction \(=2 \times\) molecularity. (d) The order of inversion of cane sugar is 2 .

Which of the following statement(s) is/are correct? (a) An increase in temperature inereases the rate constant as well as the equilibrium constant of an exothermic reaction. (b) Densities of diamond and graphite are \(\mathrm{x}\) and \(\mathrm{y}(\mathrm{x}>\mathrm{y})\). Increase in pressure on the equilibrium favours backward reaction. \(\mathrm{C}(\) diamond) \(=\mathrm{C}\) (graphite) (c) Solubility of a solute (s) is dependent upon temperature as \(\mathrm{S}=\) A.e \(^{-\text {- } H R T}\) (Here \(\Delta H\) is the enthalpy of solution) (d) For the reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})=2 \mathrm{NO}_{2}(\mathrm{~g})\), if degrees of dissociation of \(\mathrm{N}_{2} \mathrm{O}_{4}\) are \(25 \%, 50 \%\) and \(75 \%\), then gradation of observed molar masses is \(\mathrm{M}_{1}>\) \(\mathrm{M}_{2}>\mathrm{M}_{3}\left(\mathrm{M}_{1}, \mathrm{M}_{2}\right.\) and \(\mathrm{M}_{3}\) are molar masses corre- sponding to vapour densities are \(25 \%, 50 \%\) and \(75 \%\) dissociation respectively)

A radioactive element, \(\mathrm{X}\), decays by the sequence and with half lives, given below: $$ \begin{array}{ll} \mathrm{X}\left(\mathrm{t}_{12}=30 \mathrm{~min}\right) & \stackrel{\lambda_{1}}{\longrightarrow} \mathrm{Y}+\alpha \\ \mathrm{Y}\left(\mathrm{t}_{12}=2 \text { days }\right) & \stackrel{\lambda_{2}}{\longrightarrow} \mathrm{Z}+2 \beta \end{array} $$ Which of the following statement(s) is/are incorrect? (a) Atomic numbers of \(\mathrm{X}\) and \(Z\) are same (b) Disintegration constant \(\lambda_{2}>\lambda_{1}\) (c) The mass number of \(\mathrm{Y}\) is greater than that of \(\mathrm{X}\). (d) \(\mathrm{Y}\) and \(Z\) are isotopes.

In a hypothetical reaction \(\mathrm{X} \rightarrow \mathrm{Y}\), the activation energy for the forward and backward reaction is 15 and \(9 \mathrm{~kJ}\) mol \(^{-1}\) respectively. The potential energy of \(X\) is \(10 \mathrm{~kJ}\) \(\mathrm{mol}^{-1}\), Identify the correct statement(s). (a) The threshold energy of the reaction is \(25 \mathrm{~kJ}\). (b) The potential energy \(\mathrm{fY}\) is \(16 \mathrm{~kJ}\) (c) Heat of reaction is \(6 \mathrm{~kJ}\). (d) The reaction is endothermic.