Chapter 10

The energy of activation and specific rate constant for a first order reaction at \(25^{\circ} \mathrm{C}\) are \(100 \mathrm{~kJ} / \mathrm{mol}\) and \(3.46\) \(\times 10^{-5} \mathrm{sec}^{-1}\) respectively. Determine the temperature at which half life of reaction is 2 hour. \(2 \mathrm{~N}_{2} \mathrm{O}_{5} \rightarrow 2 \mathrm{~N}_{2} \mathrm{O}_{4}+\mathrm{O}_{2}\) (in \(\left.\mathrm{CCl}_{4}\right) \quad\) (in \(\left.\mathrm{CCl}_{4}\right)\) (a) \(300 \mathrm{~K}\) (b) \(302 \mathrm{~K}\) (c) \(304 \mathrm{~K}\) (d) \(306 \mathrm{~K}\)

A redox reaction is carried out at \(127^{\circ} \mathrm{C}\). If the same reaction is carried out in presence of a catalyst at the same temperature, the rate of reaction is doubled. To what extent is the energy barrier lowered by the catalyst? [Use \(\mathrm{R}=2 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\) and \(\left.\log 2=0.301\right]\) (a) \(455 \mathrm{cal}\) (b) \(231 \mathrm{cal}\) (c) \(693 \mathrm{cal}\) (d) \(554 \mathrm{cal}\)

The rate constant, the activation energy and Arrhenius parameter of a chemical reaction at \(300 \mathrm{~K}\) are \(\mathrm{K}, \mathrm{Ea}\) and \(\mathrm{A}\) respectively. The value of rate constant at \(\mathrm{T} \rightarrow\) \(\infty\) is (a) \(\mathrm{A}\) (b) \(\mathrm{Ea}\) (c) \(\mathrm{Ea} \mathrm{x} \mathrm{A}\) (d) \(\mathrm{A}-\mathrm{Ea}\)

An aqueous solution of sugar undergoes acid catalysed hydrolysis. 50 g sugar in \(125 \mathrm{~mL}\) water rotates the plane of plane polarized light by \(+13.1^{\circ}\) at \(\mathrm{t}=0\). After complete hydrolysis, it shows a rotation of \(-3.75^{\circ} .\) The percentage hydrolysis of sugar at time ' \(\mathrm{t}\) ' in the same solution having a rotation of \(5^{\circ}\) is (a) \(42 \%\) (b) \(58 \%\) (c) \(48 \%\) (d) \(55 \%\)

Nitrous oxide decomposes into \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) where reactants and products are in gas phase. If the reaction is first order then the rate constants for this reaction in terms of pressure, i.e., \(\mathrm{P}_{i}=\) initial pressure \(\mathrm{P}_{\mathrm{f}}=\) final pressure of reaction mixture may be denoted as: (a) \(\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}_{\mathrm{i}}}{\mathrm{P}_{\mathrm{i}}-\mathrm{P}_{\mathrm{f}}}\) (b) \(\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}_{\mathrm{i}}}{\mathrm{P}_{f}}\) (c) \(\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}_{\mathrm{i}}}{3 \mathrm{P}_{\mathrm{i}}-2 \mathrm{P}_{\mathrm{f}}}\) (d) \(\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}_{\mathrm{i}}}{2 \mathrm{P}_{\mathrm{f}}-3 \mathrm{P}_{\mathrm{i}}}\)

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 \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)\) (a) \(1.357 \times 10^{-6}\) (b) \(1.537 \times 10^{-5}\) (c) \(1.375 \times 10^{-5}\) (d) \(6.250 \times 10^{-4}\)

The half life \(\left(\mathrm{t}_{1}\right)\) of the first order reaction and half life \(\left(\mathrm{t}_{2}\right)\) of the second order reaction are in the ratio 2:1. Hence the ratio of the rates of the above first and second order reactions at the start is (a) \(1: 0.4365\) (b) \(0.3465: 1\) (c) \(2: 1\) (d) \(1: 2\)

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 \(=\mathrm{k}\left[\mathrm{NOCl}_{2}\right][\mathrm{NO}]\)

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: \(\mathrm{A}_{2}=\mathrm{A}+\mathrm{A} \quad\) (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) 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. 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 \(\mathrm{aA}+\mathrm{bB} \rightarrow \mathrm{C}, \mathrm{a}\) is 0 and \(\mathrm{b}\) is 3 . (d) The overall order of reaction is third order.

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

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 .

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

Match the following (a) \(\mathrm{t}_{1 / 2}=\frac{0.693}{\mathrm{k}}\) (p) Zero order (b) \(\mathrm{t}_{1 / 2}=\frac{\mathrm{a}}{2 \mathrm{k}}\) (q) First order (c) \(\mathrm{t}=\frac{1}{\mathrm{k}}\) (r) Average life (d) \(\mathrm{t}_{\frac{1}{2}}=\frac{1}{\mathrm{ak}}\) (s) Second order (t) Nuclear disintegration

Assertion: For a first order reaction, A (g) \(\rightarrow\) Product the time required to reduce successively the concentration of reactant by a constant fraction is always same. Reason: At any instant, the rate of a first order reaction is given by \(\mathrm{k}[\mathrm{A}]\).

The \(\mathrm{t}_{1 / 2}\) for the decomposition of \(\mathrm{CH}_{3} \mathrm{CHO}\) at constant temperature and at initial pressure of \(340 \mathrm{~mm}\) and 170 \(\mathrm{mm}\) of \(\mathrm{Hg}\) were 410 and \(820 \mathrm{~s}\) respectively. The order of the reaction is

The rate of a first order reaction at \(20 \mathrm{~min}\) is \(0.55 \mathrm{~mol}\) \(\mathrm{L}^{-1} \min ^{-1}\) and \(0.055 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}\) at \(40 \mathrm{~min}\) after initi- ation. Find half life of the reaction in minutes.

In gaseous reactions important for understanding the upper atmosphere, \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{O}\) react bimolecularly to form two \(\mathrm{OH}\) radicals. \(\Delta \mathrm{H}\) for this reaction is \(72 \mathrm{~kJ}\) at \(500 \mathrm{~K}\) and \(\mathrm{Ea}=77 \mathrm{~kJ} \mathrm{~mol}^{-1}\), then \(\mathrm{E}\) for the bimolecular recombination of \(2 \mathrm{OH}\) radicals to form \(\mathrm{H}_{2} \mathrm{O} \& \mathrm{O}\) at \(500 \mathrm{~K}\) is

Two first order reactions \(\mathrm{A}\) and \(\mathrm{B}\) have the same frequency factor and activation energy of \(\mathrm{A}\) exceeds that of \(\mathrm{B}\) by \(10.46 \mathrm{~kJ} \mathrm{~mol}^{-1} .\) If \(\mathrm{A}\) is \(30 \%\) complete in \(60 \mathrm{~min}\). at \(100^{\circ} \mathrm{C}\), how long will the B take for \(70 \%\) decomposition. [Given: \(\log 3=0.4771, \log 7=0.845\), antilog \(0.4633=2.9\) ]

A reaction, \(\mathrm{A}(\mathrm{g})+2 \mathrm{~B}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})\) was studied using an initial concentration of B which was \(1.5\) times that of \(\mathrm{A}\). But the equilibrium concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) were found to be equal. What is the value of \(K_{p}\) for above equilibrium?

Units of rate constant for the first and zero-order reactions in terms of molarity \(\mathrm{M}\), units are respectively [2002] (a) \(\mathrm{s}^{-1}, \mathrm{Ms}^{-1}\) (b) \(\mathrm{s}^{-1}, \mathrm{M}\) (c) \(\mathrm{M} \mathrm{s}^{-1}, \mathrm{~s}^{-1}\) (d) \(\mathrm{M}, \mathrm{s}^{-1}\)

For a reaction \(\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{C}\), rate is given by \(+\mathrm{d}[\mathrm{C}] / \mathrm{dt}=k[\mathrm{~A}][\mathrm{B}]\), hence the order of the reaction is [2002] (a) 3 (b) 2 (c) 1 (d) 0

Rate constant of the first-order reaction when initial concentration \(\mathrm{C}_{\mathrm{o}}\) and concentration \(\mathrm{C}_{\mathrm{t}}\) at time \(\mathrm{t}\) is given by equation \(k_{\mathrm{t}}=\log \mathrm{C}_{0}-\log \mathrm{C}_{\mathrm{t}}\) Graph is a straight line if we plot (a) \(\mathrm{t} \operatorname{vs} \log \mathrm{C}_{0}\) (b) \(\mathrm{t}\) vs \(\log \mathrm{C}_{\mathrm{t}}\) (c) \(\mathrm{t}^{-1}\) vs \(\log \mathrm{C}_{\mathrm{t}}\) (d) \(\log \mathrm{C}_{\mathrm{o}}\) vs \(\log \mathrm{C}_{\mathrm{t}}\)

The rate law for a reaction between the substances A and is given by Rate \(=[A]^{n}[B]^{m}\) on doubling the concentration of \(\mathrm{A}\) and halving the-concentration of \(\mathrm{B}\), the ratio of the new rate to the earlier rate of the reaction will be as \(\quad\) [2003] (a) \(1 / 2^{(\mathrm{m}+\mathrm{n})}\) (b) \((\mathrm{m}+\mathrm{n})\) (c) \((\mathrm{n}-\mathrm{m})\) (d) \(2^{(\mathrm{n}-\mathrm{m})}\)

In the respect of the equation \(k=\mathrm{Ae}^{-\mathrm{Ea} \mathrm{KT}}\) in chemical kinetics, which one of the following statements is correct? (a) \(k\) is equilibrium constant (b) A is adsorption factor (c) \(\mathrm{E}_{\mathrm{o}}\) is energy of activation (d) \(\mathrm{R}\) is Rydberg constant

In a first-order reaction, the concentration of the reactant, decreases from \(0.8 \mathrm{M}\) to \(0.4 \mathrm{M}\) in 15 minutes. The time taken for the concentration to change from \(0.1 \mathrm{M}\) to \(0.025 \mathrm{M}\) is (a) 30 minutes (b) 60 minutes (c) \(7.5\) minutes (d) 15 minutes

Consider an endothermic reaction \(\mathrm{X} \longrightarrow \mathrm{Y}\) with the activation energies \(E_{b}\) and \(E_{f}\) for the backward and forward reactions respectively. In general, \(\quad\) [2005] (a) \(\mathrm{E}_{\mathrm{b}}<\mathrm{E}_{\mathrm{f}}\) (b) \(E_{b}>E_{f}\) (c) \(\mathrm{E}_{\mathrm{b}}-\mathrm{E}_{f}\) (d) there is no definite relation between \(E_{b}\) and \(E_{f}\)

A reaction involving two different reactants can never be? (a) Unimoleculur reaction (b) Ist order reaction (c) IInd order reaction (d) Bimoleculur reaction

The following mechanism has been proposed for the reaction of \(\mathrm{NO}\) with \(\mathrm{Br}_{2}\) to form NO Br \(\mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{NOBr}_{2}(\mathrm{~g})\) \(\mathrm{NOBr}_{2}(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})\) If the second step is the rate determining step, the order of the reaction with respect to \(\mathrm{NO}(\mathrm{g})\) is (a) 1 (b) 0 (c) 3 (d) 2

A reaction was found to be second-order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will \([2006]\) (a) remain unchanged (b) triple (c) increase by a factor of 4 (d) double

Rate of a reaction can be expressed by Arrhenius 2 equation as, \(k=\mathrm{Ae}^{-\mathrm{E} \mathrm{kT}}\) In this equation, E represents [2006] (a) the energy above which all the colliding molecules will react (b) the energy below which colliding molecules will not react (c) the total energy of the reacting molecules at a tem perature, T (d) the fraction of molecules with energy greater than the activation energy of the reaction

The energies of activation for forward and reverse reactions for \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}\) are \(180 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(200 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by \(100 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The enthalpy change of the reaction \(\left(\mathrm{A}_{2}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB}\right)\) in the presence of catalyst will be (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) [2007] (a) 120 (b) 280 (c) 20 (d) 300

Consider the reaction, \(2 \mathrm{~A}+\mathrm{B} \longrightarrow\) Products When concentration of alone was doubled, the half life did not change. When the concentration of \(\mathrm{A}\) alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is \(\quad\) [2008] (a) no unit (b) \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\) (c) \(\mathrm{s}^{-1}\) (d) \(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~s}^{-1}\)

For a reaction \(1 / 2 \mathrm{~A} \longrightarrow 2 \mathrm{~B}\), rate of disappearance of ' \(\mathrm{A}\) ' is related to the rate of appearance of ' \(\mathrm{B}\) ' by the expression [2008] (a) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}\) (b) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\frac{1}{4} \frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}\) (c) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}\) (d) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}=4 \frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}\)

The half life period of a first order chemical reaction is \(6.93\) minutes. The time required for the completion of \(99 \%\) of the chemical reaction will be \((\log 2=0.301):\) (a) \(23.03\) minutes (b) \(46.06\) minutes (c) \(460.6\) minutes (d) \(230.3\) minutes

The time for half life period of a certain reaction \(\mathrm{A} \longrightarrow\) products is 1 hour. When the initial concentration of the reactant ' \(A\) ', is \(2.0 \mathrm{~mol} \mathrm{~L}^{-1}\), how much time does it take for its concentration to come from \(0.50\) to \(0.25 \mathrm{~mol} \mathrm{~L}^{-1}\) if it is a zero order reaction? [2010] (a) \(4 \mathrm{~h}\) (b) \(0.5 \mathrm{~h}\) (c) \(0.25 \mathrm{~h}\) (d) \(1 \mathrm{~h}\)

Consider the reaction: \(\mathrm{Cl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq}) \longrightarrow \mathrm{S}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})\) The rate equation for this reaction is Rate \(=\mathrm{k}\left[\mathrm{Cl}_{2}\right]\left[\mathrm{H}_{2} \mathrm{~S}\right]\) Which of these mechanisms is/are consistent with this rate equation? [2010] (1) \(\mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{~S} \longrightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{Cl}^{+}+\mathrm{HS}^{-}\)(slow) \(\mathrm{Cl}^{+}+\mathrm{HS}^{-} \longrightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{S}\) (fast \()\) (2) \(\mathrm{H}_{2} \mathrm{~S} \Leftrightarrow \mathrm{H}^{+}+\mathrm{HS}^{-}\)(fast equilibrium) \(\mathrm{Cl}_{2}+\mathrm{HS}^{-} \longrightarrow 2 \mathrm{Cl}^{-}+\mathrm{H}^{+}+\mathrm{S}\) (slow) (a) 2 only (b) Both 1 and 2 (c) Neither 1 nor 2 (d) 1 only

The rate of a chemical reaction doubles for every \(10^{\circ} \mathrm{C}\) rise of temperature. If the temperature is raised by \(50^{\circ} \mathrm{C}\), the rate of the reaction increases by about: [2011] (a) 16 times (b) 42 times (c) 32 times (d) 20 times

For a first order reaction, (A) \(\rightarrow\) products, the concentration of A changes from \(0.10 \mathrm{M}\) to \(0.025\) Min 40 minutes. The rate of reaction when the concentration of \(\mathrm{A}\) is \(0.01 \mathrm{M}\), is: (a) \(3.47 \times 10^{-5} \mathrm{M} / \mathrm{min}\) (b) \(3.47 \times 10^{-4} \mathrm{M} / \mathrm{min}\) (c) \(1.73 \times 10^{-5} \mathrm{M} / \mathrm{min}\) (d) \(1.73 \times 10^{-4} \mathrm{M} / \mathrm{min}\)

The rate of a reaction doubles when its temperature changes from \(300 \mathrm{~K}\) to \(310 \mathrm{~K}\). Activation energy of such a reaction will be: \(\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right.\) and \(\left.\log 2=0.301\right)\) (a) \(58.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(60.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(53.6 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(48.6 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Deomposition of \(\mathrm{H}_{2} \mathrm{O}_{2}\) follows a first order reaction. In fifty minutes the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) decreases from \(0.5\) to \(0.125 \mathrm{M}\) in one such decomposition. When the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) reaches \(0.05 \mathrm{M}\), the rate of formation of \(\mathrm{O}_{2}\) will be: (a) \(6.93 \times 10^{-4} \mathrm{~mol} \mathrm{~min}^{-1}\) (b) \(2.66 \mathrm{~L} \mathrm{~min}^{-1}\) at \(\mathrm{STP}\) (c) \(1.34 \times 10^{-2} \mathrm{~mol} \mathrm{~min}^{-1}\) (d) \(6.93 \times 10^{-2} \mathrm{~mol} \mathrm{~min}^{-1}\)