Chapter 11

For a given reaction, the concentration of the reactant plotted against time gave a straight line with negative slope. The order of the reaction is (a) 3 (b) 2 (c) 1 (d) 0

\(\begin{array}{lll}\text { For the } & \text { sequential } & \text { reactions: }\end{array}\) \(\mathrm{A} \stackrel{K_{1}=0.02 \mathrm{~min}^{-1}}{\longrightarrow} \mathrm{B} \stackrel{K_{2}=0.02 \mathrm{~min}^{-1}}{\longrightarrow} \mathrm{C}\), the initial concentration of 'A' was \(0.2 \mathrm{M}\) and initially 'B' and 'C' were absent. The time at which the concentration of ' \(\mathrm{B}\) ' becomes maximum and the maximum concentration of ' B' are, respectively, (a) \(50 \mathrm{~min},\left(\frac{0.2}{e}\right) \mathrm{M}\) (b) \(50 \mathrm{~min}, 0.2 \mathrm{M}\) (c) infinite, \(0.2 \mathrm{M}\) (d) \(25 \mathrm{~min},\left(\frac{0.2}{e}\right) \mathrm{M}\)

For a certain reaction involving a single reactant, it is found that \(C_{0} \sqrt{T}\) is constant, where \(C_{0}\) is the initial concentration of the reactant and \(T\) is the half-life. What is the order of the reaction? (a) 1 (b) \(1.5\) (c) 2 (d) 3

For a certain reaction of order ' \(n\) ', the time for half change, \(t_{1 / 2}\), is given by \(t_{1 / 2}=\frac{[2-\sqrt{2}]}{k} \times C_{0}^{1 / 2}\), where \(k\) is the rate constant and \(C_{0}\) is the initial concentration. The value of \(n\) is (a) 1 (b) 2 (c) \(1.5\) (d) \(0.5\)

An organic compound A decomposes following two parallel first-order reactions: \(\mathrm{A} \stackrel{K_{1}}{\longrightarrow} \mathrm{B}\) and \(\mathrm{A} \stackrel{K_{2}}{\longrightarrow} \mathrm{C}\). If \(K_{1}\) is \(1.25 \times 10^{-5} \mathrm{~s}^{-1}\) and \(\frac{K_{1}}{K_{2}}=\frac{1}{9}\), the value of \(\frac{[\mathrm{C}]}{[\mathrm{A}]}\) after one hour of start of reaction by taking only \(A\), is \((\ln 1.568=0.45)\) (a) \(\frac{1}{9}\) (b) \(0.5112\) (c) \(1.4112\) (d) \(\frac{9}{20}\)

The reaction: \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{NO}_{2}+\mathrm{OH}^{-}\) \(\rightarrow \mathrm{H}_{3} \mathrm{C}-\mathrm{CH}^{-}-\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O}\) obeys the rate law for pseudo first-order kinetics in the presence of a large excess of hydroxide ion. If \(1 \%\) of nitro ethane undergoes reaction in half a minute when the reactant concentration is \(0.002 \mathrm{M}\), what is the pseudo first-order rate constant? (a) \(2 \times 10^{-2} \mathrm{~min}^{-1}\) (b) \(6 \times 10^{-3} \mathrm{~min}^{-1}\) (c) \(4 \times 10^{-2} \mathrm{~min}^{-1}\) (d) \(1 \times 10^{-2} \mathrm{~min}^{-1}\)

For the consecutive first-order reactions: \(\mathrm{A} \stackrel{K_{1}}{\longrightarrow} \mathrm{B} \stackrel{K_{2}}{\longrightarrow} \mathrm{C}\), the concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) are \(0.2 \mathrm{M}\) and \(0.01 \mathrm{M}\), respectively, at steady state. If \(K_{1}\) is \(2.5 \times 10^{-4} \mathrm{~min}^{-1}\), what is the value of \(K_{2} ?\) (a) \(5.0 \times 10^{-3} \mathrm{~min}^{-1}\) (b) \(2.5 \times 10^{-4} \mathrm{~min}^{-1}\) (c) \(1.25 \times 10^{-5} \mathrm{~min}^{-1}\) (d) \(5.0 \times 10^{-4} \mathrm{~min}^{-1}\)

As the initial concentration increases from \(0.75\) to \(1.55 \mathrm{M}\) in a reaction, \(t_{1 / 2}\) decreases from 60 to \(29 \mathrm{~s}\). The order of the reaction is (a) zero (b) first (c) second (d) third

For a bimolecular gaseous reaction of type: \(2 \mathrm{~A} \rightarrow\) Products, the average speed of reactant molecules is \(2 \times 10^{4} \mathrm{~cm} / \mathrm{s}\), the molecular diameter is \(4 \AA\) and the number of reactant molecules per \(\mathrm{cm}^{3}\) is \(2 \times 10^{19}\). The maximum rate of reaction should be (a) \(\left.4.72 \times 10^{7} \mathrm{~mol}\right]^{-1} \mathrm{~s}^{-1}\) (b) \(1.18 \times 10^{7} \mathrm{~mol} 1^{-1} \mathrm{~s}^{-1}\) (c) \(9.44 \times 10^{7} \mathrm{~mol} 1^{-1} \mathrm{~s}^{-1}\) (d) \(2.36 \times 10^{7} \mathrm{~mol} 1^{-1} \mathrm{~s}^{-1}\)

Which is correct about first-order reaction? (a) \(t_{0.5}=50 \mathrm{~s}, t_{0.75}=100 \mathrm{~s}\) (b) \(t_{0.5}=50 \mathrm{~s}, t_{0,75}=75 \mathrm{~s}\) (c) \(t_{0.5}=50 \mathrm{~s}, t_{0,75}=50 \mathrm{~s}\) (d) \(t_{0.5}=50 \mathrm{~s}, t_{0,25}=25 \mathrm{~s}\)

\(t_{1 / 2}\) of a reaction: \(\mathrm{A} \rightarrow\) Products \(\left(\right.\) order \(\left.=\frac{3}{2}\right)\) is represented by \(t_{1 / 2} \alpha \frac{1}{\left[A_{0}\right]^{m}}\). The value of \(m\) is (a) \(0.5\) (b) \(-0.5\) (c) \(1.5\) (d) \(-1.5\)

For two parallel first-order reactions, what is the overall activation energy of reaction? The yields of \(\mathrm{B}\) and \(\mathrm{C}\) in products are \(40 \%\) and \(60 \%\), respectively. \(\mathrm{A} \stackrel{\mathrm{Ea}=20 \mathrm{kcal} / \mathrm{mol}}{\longrightarrow} \mathrm{B} \quad \mathrm{A} \stackrel{\mathrm{Ea}=40 \mathrm{kcal} / \mathrm{mol}}{\longrightarrow} \mathrm{C}\) (a) \(60 \mathrm{kcal} / \mathrm{mol}\) (b) \(32 \mathrm{kcal} / \mathrm{mol}\) (c) \(28 \mathrm{kcal} / \mathrm{mol}\) (d) \(20 \mathrm{kcal} / \mathrm{mol}\)

If \(t_{1 / 2}\) of a second-order reaction is \(1.0 \mathrm{~h}\). After what time, the amount will be \(25 \%\) of the initial amount? (a) \(1.5 \mathrm{~h}\) (b) \(2 \mathrm{~h}\) (c) \(2.5 \mathrm{~h}\) (d) \(3 \mathrm{~h}\)

In a first-order reaction, the activity of reactant drops from \(800 \mathrm{~mol} / \mathrm{dm}^{3}\) to \(50 \mathrm{~mol} / \mathrm{dm}^{3}\) in \(2 \times 10^{4} \mathrm{~s}\). The rate constant of the reaction, in \(\mathrm{s}^{-1}\), is (a) \(1.386 \times 10^{-4}\) (b) \(1.386 \times 10^{-3}\) (c) \(1.386 \times 10^{-5}\) (d) \(5.0 \times 10^{3}\)

For a first-order reaction, the ratio of time for \(99.9 \%\) of the reaction to complete and half of the reaction to complete is (a) 1 (b) 2 (c) 4 (d) 10

For a first-order reaction, \(t_{0.75}=1386 \mathrm{~s}\). Its specific reaction rate is (a) \(10^{-3} \mathrm{~s}^{-1}\) (b) \(10^{-2} \mathrm{~s}^{-1}\) (c) \(10^{-4} \mathrm{~s}^{-1}\) (d) \(10^{-5} \mathrm{~s}^{-1}\)

At \(325^{\circ} \mathrm{C}, \quad 1, \quad 3\) -butadiene dimerizes according to the equation: \(2 \mathrm{C}_{4} \mathrm{H}_{6}(\mathrm{~g})\) \(\rightarrow \mathrm{C}_{8} \mathrm{H}_{12}(\mathrm{~g}) .\) It is found that the partial pressure, \(P\), of the reactant obeys the law: \(\frac{1}{P}=k t+\frac{1}{P_{0}}\). Order of the reaction is (a) 1 (b) \(0.5\) (c) 2 (d) \(1.5\)

Which of the following statements is incorrect? (a) For endothermic reactions, energy of activation is always greater than heat of reaction. (b) For exothermic reactions, energy of activation is always smaller than heat of reaction. (c) Rate of elementary reaction always increases with increase in temperature. (d) Temperature coefficient of a reaction is \(1.0\), when \(T \rightarrow \infty\).

The half-life for the first-order reaction: \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})\) is \(30 \mathrm{~min}\) If the volume of \(\mathrm{O}_{2}(\mathrm{~g})\) collected is \(100 \mathrm{ml}\) after a long time, then the volume of \(\mathrm{O}_{2}(\mathrm{~g})\) collected (at the same pressure and temperature) after \(60 \mathrm{~min}\) from the start of reaction is (a) \(25 \mathrm{ml}\) (b) \(12.5 \mathrm{ml}\) (c) \(75 \mathrm{~m}\) ] (d) \(50 \mathrm{ml}\)

The decomposition of hydrogen peroxide in aqueous solution is a first-order reaction: Time in min \(0 \quad 10\) Volume \((V\), in \(\mathrm{ml}) \quad 25.0 \quad 20.0\) where \(V\) is the number of \(\mathrm{ml}\) of potassium permanganate required to decompose a definite volume of hydrogen peroxide solution, at the given time. From the following data, the rate constant (in \(\min ^{-1}\) ) of reaction is \((\ln 5=1.6, \ln 2=0.7)\) (a) \(0.09\) (b) \(0.02\) (c) \(0.2\) (d) \(0.16\)

For irreversible elementary reactions in parallel: \(\mathrm{A} \stackrel{K_{1}}{\longrightarrow} \mathrm{R}\) and \(\mathrm{A} \stackrel{K_{2}}{\longrightarrow} \mathrm{S}\), the rate of disappearance of reactant ' \(\mathrm{A}\) ' is (a) \(\left(k_{1}-k_{2}\right) C_{\mathrm{A}}\) (b) \(\left(k_{1}+k_{2}\right) C_{\mathrm{A}}\) (c) \(1 / 2\left(k_{1}+k_{2}\right) C_{\mathrm{A}}\) (d) \(k_{1} C_{\mathrm{A}}\)

For the consecutive unimolecular-type first-order reaction: \(\mathrm{A} \stackrel{k_{1}}{\longrightarrow} \mathrm{R} \stackrel{k_{2}}{\longrightarrow} \mathrm{S}\), the concentration of component ' \(\mathrm{R}\) ', \(C_{\mathrm{R}}\), at any time, ' \(t\) ' is given by \(C_{\mathrm{R}}=C_{\mathrm{AO}} \cdot K_{1}\left[\frac{e^{-k_{1} t}}{\left(k_{2}-k_{1}\right)}+\frac{e^{-k_{2} t}}{\left(k_{1}-k_{2}\right)}\right]\) If \(C_{\mathrm{A}}=C_{\mathrm{AO}}, C_{\mathrm{R}}=C_{\mathrm{s}}=0\) at \(t=0\), the time at which the maximum concentration of 'R' occurs is (a) \(t_{\max }=\frac{k_{2}-k_{1}}{\ln \left(k_{2} / k_{1}\right)}\) (b) \(t_{\max }=\frac{\ln \left(k_{2} / k_{1}\right)}{k_{2}-k_{1}}\) (c) \(t_{\max }=\frac{e^{k_{2} / k_{1}}}{k_{2}-k_{1}}\) (d) \(t_{\max }=\frac{e^{k_{2}-k_{1}}}{k_{2}-k_{1}}\)

Consider the following consecutive firstorder reaction: $$ \mathrm{A} \stackrel{K_{1}}{\longrightarrow} \mathrm{B} \stackrel{K_{2}}{\longrightarrow} \mathrm{C} $$ If \(K_{1}=0.01 \mathrm{~min}^{-1}\) and \(K_{1}: K_{2}=1: 2\), after what time from the start of reaction, the concentration of ' B' will be maximum? \((\ln 2=0.7)\) (a) \(70 \mathrm{~min}\) (b) \(140 \mathrm{~min}\) (c) \(35 \mathrm{~min}\) (d) \(700 \mathrm{~min}\)

When excess toluene- \(\alpha\) -d \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{D}\right)\) was photochemically monochlorinated at \(80^{\circ} \mathrm{C}\) with \(0.1\) mole of chlorine, there was obtained \(0.0212\) mole DCl and \(0.0848\) mole HCl. What is the value of the isotope effect, \(K^{\mathrm{H}} / \mathrm{K}^{\mathrm{D}}\) ? (a) \(\frac{1}{4}\) (b) \(\frac{4}{1}\) (c) \(\frac{5}{1}\) (d) \(\frac{1}{5}\)

The activation energy of a reaction can be lowered by (a) increasing temperature (b) lowering temperature (c) adding a catalyst (d) removing one or more products.

At a certain temperature, the reaction between \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) to form \(\mathrm{NO}_{2}\) is fast, while that between \(\mathrm{CO}\) and \(\mathrm{O}_{2}\) is slow. It may be concluded that (a) \(\mathrm{NO}\) is more reactive than \(\mathrm{CO}\). (b) CO is smaller in size than NO. (c) activation energy for the reaction: \(2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}\) is less. (d) activation energy for the reaction: \(2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}\) is high.

Rate of which type of elementary reaction increases with increase in temperature? (a) Thermal (b) Exothermic (c) Endothermic (d) All

The rate constant is given by the equation: \(K=P \cdot A \cdot e^{-E_{a} / R T}\). Which factor should register a decrease for the reaction to proceed more rapidly? (a) \(T\) (b) \(A\) (c) \(E_{\text {a }}\) (d) \(P\)

According to the collisions theory, the rate of reaction increases with temperature due to (a) increase in number of collisions between reactant molecules. (b) increase in speed of reacting molecules. (c) increase in number of molecules having sufficient energy for reaction. (d) decrease in activation energy of reaction.

The rate of a reaction is approximately doubled for every \(10^{\circ} \mathrm{C}\) rise in temperature. If the temperature is raised by \(50^{\circ} \mathrm{C}\), the reaction rate increases by about (a) 10 times (b) 16 times (c) 32 times (d) 64 times

In general, the rate of a reaction can be increased by all the factors except (a) increasing the temperature (b) increasing the concentration of reactants (c) increasing the activation energy (d) using a catalyst

Which of the following statements is not correct? (a) The efficiency of a solid catalyst depends upon its surface area. (b) Catalyst operates by providing alternate path for the reaction that involves lower activation energy. (c) Catalyst lowers the energy of activation of the forwards direction without affecting the energy of activation of the backward direction. (d) Catalyst does not affect the overall enthalpy change of the reaction.

The values of enthalpies of reactants and products are \(x\) and \(y \mathrm{~J} / \mathrm{mol}\), respectively. If the activation energy for the backward reaction is \(z \mathrm{~J} / \mathrm{mol}\), then the activation energy for forward reaction will be (in \(\mathrm{J} / \mathrm{mol}\) ) (a) \(x-y-z\) (b) \(x-y+z\) (c) \(y-x-z\) (d) \(y-x+z\)

If \(I\) is the intensity of absorbed light and \(C\) is the concentration of \(\mathrm{AB}\) for the photochemical process: \(\mathrm{AB}+h \mathrm{v} \rightarrow \mathrm{AB}^{*}\), the rate of formation of \(\mathrm{AB}^{*}\) is directly proportional to (a) \(C\) (b) \(I\) (c) \(I^{2}\) (d) \(C \cdot I\)