Chapter 11

The rate of a reaction may be expressed as: \(+\frac{1}{2} \frac{\mathrm{d}[\mathrm{C}]}{\mathrm{d} t}=-\frac{1}{3} \frac{\mathrm{d}[\mathrm{D}]}{\mathrm{d} t}=+\frac{1}{4} \frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}\) \(=-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t} .\) The reaction is (a) \(4 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}+3 \mathrm{D}\) (b) \(\mathrm{B}+3 \mathrm{D} \rightarrow 4 \mathrm{~A}+2 \mathrm{C}\) (c) \(4 \mathrm{~A}+2 \mathrm{C} \rightarrow \mathrm{B}+3 \mathrm{D}\) (d) \(2 \mathrm{~A}+3 \mathrm{~B} \rightarrow 4 \mathrm{C}+\mathrm{D}\)

Azomethane, \(\mathrm{CH}_{3} \mathrm{NNCH}_{3}\), decomposes according to the following equation: \(\mathrm{CH}_{3}-\mathrm{N} \equiv \mathrm{N}-\mathrm{CH}_{3}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g})\) The initial concentration of azomethane was \(1.50 \times 10^{-2}\) M. After 10 min, the concentration decreased to \(1.29 \times 10^{-2} \mathrm{M}\). The average rate of reaction during this time interval is (a) \(3.5 \times 10^{-6} \mathrm{Ms}^{-1}\) (b) \(2.1 \times 10^{-4} \mathrm{Ms}^{-1}\) (c) \(3.5 \times 10^{-6} \mathrm{M} \mathrm{h}^{-1}\) (d) \(2.1 \times 10^{-3} \mathrm{Mmin}^{-1}\)

For the reaction: \(2 \mathrm{HI} \rightarrow \mathrm{H}_{2}+\mathrm{I}_{2}\), the expression, \(-\frac{1}{2} \frac{\mathrm{d}[\mathrm{HI}]}{\mathrm{d} t}\) represents (a) the rate of formation of \(\mathrm{HI}\) (b) the rate of disappearance of \(\mathrm{HI}\) (c) the instantaneous rate of the reaction (d) the average rate of the reaction

For a gaseous reaction: \(\mathrm{A}(\mathrm{g}) \rightarrow\) Products (order \(=n\) ), the rate may be expressed as: (i) \(-\frac{\mathrm{d} P_{\mathrm{A}}}{\mathrm{d} t}=K_{1} \cdot P_{\mathrm{A}}^{n}\) (ii) \(-\frac{1}{V} \frac{\mathrm{d} n_{\mathrm{A}}}{\mathrm{d} t}=K_{2} \cdot C_{\mathrm{A}}^{n}\) The rate constants, \(K_{1}\) and \(K_{2}\) are related as \(\left(P_{A}\right.\) and \(C_{A}\) are the partial pressure and molar concentration of \(\mathrm{A}\) at time ' \(t^{\prime}\), respectively) (a) \(K_{1}=K_{2}\) (b) \(K_{2}=K_{1} \cdot(R T)^{n}\) (c) \(K_{2}=K_{1} \cdot(R T)^{1-n}\) (d) \(K_{2}=K_{1} \cdot(R T)^{n-1}\)

For reaction: \(4 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}+2 \mathrm{D}\), the only incorrect statement is (a) The rate of disappearance of \(\mathrm{B}\) is one-fourth the rate of disappearance of \(\mathrm{A}\) (b) The rate of appearance of \(\mathrm{C}\) is half the rate of disappearance of \(\mathrm{B}\) (c) The rate of formation of \(\mathrm{D}\) is half the rate of consumption of \(\mathrm{A}\) (d) The rates of formation of \(\mathrm{C}\) and \(\mathrm{D}\) are equal

For the reaction: \(2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}_{2}(\mathrm{~g})\) \(+\mathrm{O}_{2}(\mathrm{~g})\), the concentration of \(\mathrm{NO}_{2}\) increases by \(2.4 \times 10^{-2} \mathrm{M}\) in \(6 \mathrm{~s}\). What will be the average rate of appearance of \(\mathrm{NO}_{2}\) and the average rate of disappearance of \(\mathrm{N}_{2} \mathrm{O}_{5} ?\) (a) \(2 \times 10^{-3} \mathrm{Ms}^{-1}, 4 \times 10^{-3} \mathrm{Ms}^{-1}\) (b) \(2 \times 10^{-3} \mathrm{Ms}^{-1}, 1 \times 10^{-3} \mathrm{Ms}^{-1}\) (c) \(2 \times 10 \mathrm{Ms}^{-1}, 2 \times 10^{-3} \mathrm{Ms}^{-1}\) (d) \(4 \times 10^{-3} \mathrm{Ms}^{-1}, 2 \times 10^{-3} \mathrm{Ms}^{-1}\)

For the reaction: \(\mathrm{aA}+\mathrm{bB} \rightarrow \mathrm{P}\), \(r=K[\mathrm{~A}]^{a} \cdot[\mathrm{B}]^{b} .\) If concentration of \(\mathrm{A}\) is doubled, the rate is doubled. If concentration of \(\mathrm{B}\) is doubled, the rate becomes four times. The correct relation is (a) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=-\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t}\) (b) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=+2 \cdot \frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t}\) (c) \(-2 \cdot \frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=+\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t}\) (d) \(-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{d} t}=+\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{d} t}\)

Which is wrong about the rate of a reaction among the following? (a) Rate of a reaction cannot be negative. (b) Rate of a reaction is change in concentration of the reactant per unit time per unit stoichiometric coefficient of that component. (c) Average rate and instantaneous rate are always different. (d) Rate may depend upon surface area of the reactants.

The reaction: \(\mathrm{A}(\mathrm{g})+2 \mathrm{~B}(\mathrm{~g}) \rightarrow \mathrm{C}(\mathrm{g})+\mathrm{D}(\mathrm{g})\) is an elementary process. In an experiment, the initial partial pressure of \(\mathrm{A}\) and \(\mathrm{B}\) are \(P_{\mathrm{A}}=0.60 \mathrm{~atm}\) and \(P_{\mathrm{B}}=0.80 \mathrm{~atm}\). When \(P_{\mathrm{B}}=0.20 \mathrm{~atm}\), the rate of reaction, relative to the initial rate is (a) \(\frac{1}{16}\) (b) \(\frac{1}{24}\) (c) \(\frac{1}{32}\) (d) \(\frac{1}{48}\)

For a reaction \(2 \mathrm{NH}_{3} \rightarrow \mathrm{N}_{2}+3 \mathrm{H}_{2}\), it is observed that \(-\frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t}=K_{1}\left[\mathrm{NH}_{3}\right] ;+\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=K_{2}\left[\mathrm{NH}_{3}\right]\) and \(+\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t}=K_{3}\left[\mathrm{NH}_{3}\right]\) The correct relation between \(K_{1}, K_{2}\) and \(K_{3}\) is (a) \(K_{1}=K_{2}=K_{3}\) (b) \(2 K_{1}=3 K_{2}=6 K_{3}\) (c) \(3 K_{1}=6 K_{2}=2 K_{3}\) (d) \(6 K_{1}=3 K_{2}=2 K_{3}\)

Rate constant of a reaction depends upon (a) Concentration (b) Pressure (c) Temperature (d) All

The rate expression for the reaction: \(\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})\) is rate \(=K \cdot C_{\mathrm{A}}^{2} \cdot C_{\mathrm{B}}^{1 / 2} .\) What changes in the initial concentration of \(A\) and \(B\) will cause the rate of reaction increase by a factor of eight? (a) \(C_{\mathrm{A}} \times 2 ; C_{\mathrm{B}} \times 2\) (b) \(C_{\mathrm{A}} \times 2 ; C_{\mathrm{B}} \times 4\) (c) \(C_{\mathrm{A}} \times 1, C_{\mathrm{B}} \times 4\) (d) \(C_{\mathrm{A}} \times 4, C_{\mathrm{B}} \times 1\)

Iodide ion is oxidized to hypoiodite ion, \(\mathrm{IO}^{-}\), by hypochlorite ion, \(\mathrm{ClO}^{-}\), in basic solution as: $$ \begin{array}{ccccc} & \mathbf{I}^{-} & \mathbf{C l O}^{-} & \mathbf{O H}^{-} & \left(\mathrm{mol} \mathbf{L}^{-1} \mathbf{s}^{-1}\right) \\ \hline 1 & 0.010 & 0.020 & 0.010 & 12.2 \times 10^{-2} \\ 2 & 0.020 & 0.010 & 0.010 & 12.2 \times 10^{-2} \\ 3 & 0.010 & 0.010 & 0.010 & 6.1 \times 10^{-2} \\ 4 & 0.010 & 0.010 & 0.020 & 3.0 \times 10^{-2} \\ \hline \end{array} $$ The correct rate law for the reaction is (a) \(r=K\left[\mathrm{I}^{-}\right]\left[\mathrm{ClO}^{-}\right]\left[\mathrm{OH}^{-}\right]^{0}\) (b) \(r=K\left[\mathrm{I}^{-}\right]^{2}\left[\mathrm{ClO}^{-}\right]^{2}\left[\mathrm{OH}^{-}\right]^{0}\) (c) \(r=K\left[\mathrm{I}^{-}\right]\left[\mathrm{ClO}^{-}\right]\left[\mathrm{OH}^{-}\right]\) (d) \(r=K\left[\mathrm{I}^{-}\right]\left[\mathrm{ClO}^{-}\right]\left[\mathrm{OH}^{-}\right]^{-1}\)

For the chemical reaction: \(\mathrm{A} \rightarrow\) products, the rate of disappearance of \(\mathrm{A}\) is a given by $$ r_{A}=-\frac{\mathrm{d} C_{\mathrm{A}}}{\mathrm{d} t}=\frac{K_{1} \cdot C_{\mathrm{A}}}{1+K_{2} \cdot C_{\mathrm{A}}} $$ At low concentration of A, \(C_{A}\), the reaction is of the first order with the rate constant (a) \(\frac{K_{1}}{K_{2}}\) (b) \(K_{1}\) (c) \(\frac{K_{2}}{K_{1}}\) (d) \(\frac{K_{1}}{K_{1}+K_{2}}\)

Rate of a reaction: \(\mathrm{A}+2 \mathrm{~B} \rightarrow \mathrm{P}\) is \(2 \times 10^{-2} \mathrm{M} / \mathrm{min}\), when concentrations of each \(A\) and \(B\) are \(1.0 \mathrm{M}\). If the rate of reaction, \(r=K[\mathrm{~A}]^{2}[\mathrm{~B}]\), the rate of reaction when half of the \(\mathrm{B}\) has reacted should be (a) \(5.625 \times 10^{-3} \mathrm{M} / \mathrm{min}\) (b) \(3.75 \times 10^{-3} \mathrm{M} / \mathrm{min}\) (c) \(9.375 \mathrm{M} / \mathrm{min}\) (d) \(2.5 \times 10^{-3} \mathrm{M} / \mathrm{min}\)

For the reaction: \(\mathrm{A}_{2}(\mathrm{~g}) \rightarrow \mathrm{B}(\mathrm{g})+\frac{1}{2} \mathrm{C}(\mathrm{g})\) pressure of the system increases from 100 to \(120 \mathrm{~mm}\) in 5 min. The average rate of disappearance of \(\mathrm{A}_{2}\) (in \(\mathrm{mm} / \mathrm{min}\) ) in this time interval is (a) 4 (b) 8 (c) 2 (d) 16

The condition at which average rate can be equal to instantaneous rate of the reaction is (a) \(\Delta n=0\) (b) \(\Delta t \rightarrow 0\) (c) reaction is elementary (d) reaction is complex

Consider the chemical reaction: \(\mathrm{N}_{2}(\mathrm{~g})\) \(+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\). The rate of this reaction can be expressed in terms of time derivative of concentration of \(\mathrm{N}_{2}(\mathrm{~g})\), \(\mathrm{H}_{2}(\mathrm{~g})\) or \(\mathrm{NH}_{3}(\mathrm{~g})\). Identify the correct relationship amongst the rate expressions (a) rate \(\begin{aligned} \text { (b) rate } &=-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\ &=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t} \\ &=+2 \frac{\mathrm{d}\left[\mathrm{NH}_{2}\right]}{\mathrm{d} t}=-3 \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\ \mathrm{~d} t \end{aligned}\) (c) rate \(\begin{aligned} &=-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\ &=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t} \\ \text { (d) rate } &=-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=-\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\\ &=+\frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t} \end{aligned}\)

For a zero-order reaction: \(2 \mathrm{NH}_{3}(\mathrm{~g})\) \(\rightarrow \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})\), the rate of reac- tion is \(0.1 \mathrm{~atm} / \mathrm{s}\). Initially only \(\mathrm{NH}_{3}(\mathrm{~g})\) was present at 3 atm and the reaction is performed at constant volume and temperature. The total pressure of gases after \(10 \mathrm{~s}\) from the start of reaction will be (a) \(4 \mathrm{~atm}\) (b) \(5 \mathrm{~atm}\) (c) \(3.5 \mathrm{~atm}\) (d) \(4.5\) atm

For the reaction: \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})\) \(\rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\) under certain conditions of temperature and partial pressure of the reactants, the rate of formation of \(\mathrm{NH}_{3}\) is \(10^{-3} \mathrm{~kg} \mathrm{~h}^{-1}\). The rate of consumption of \(\mathrm{H}_{2}\) under same condition is (a) \(1.5 \times 10^{-3} \mathrm{~kg} \mathrm{~h}^{-1}\) (b) \(1.76 \times 10^{-4} \mathrm{~kg} \mathrm{~h}^{-1}\) (c) \(6.67 \times 10^{-4} \mathrm{~kg} \mathrm{~h}^{-1}\) (d) \(3 \times 10^{-3} \mathrm{~kg} \mathrm{~h}^{-1}\)

A substance 'A' decomposes in solution following first-order kinetics. Flask 1 contains 11 of \(1 \mathrm{M}\) solution of \(\mathrm{A}^{\prime}\) and flask 2 contains \(100 \mathrm{ml}\) of \(0.6 \mathrm{M}\) solution of 'A'. After \(8.0 \mathrm{~h}\), the concentration of 'A' in flask 1 becomes \(0.25 \mathrm{M}\). In what time, the concentration of 'A' in flask 2 becomes \(0.3 \mathrm{M}\) ? (a) \(8.0 \mathrm{~h}\) (b) \(3.2 \mathrm{~h}\) (c) \(4.0 \mathrm{~h}\) (d) \(9.6 \mathrm{~h}\)

A kinetic study of the reaction: \(\mathrm{A} \rightarrow\) products provides the data: \(t=0 \mathrm{~s},[\mathrm{~A}]=2.00 \mathrm{M} ;\) \(\begin{array}{llll}500 \mathrm{~s}, & 1.00 \mathrm{M} ; 1500 \mathrm{~s}, 0.50 \mathrm{M} ; 3500 \mathrm{~s}\end{array}\) \(0.25 \mathrm{M}\). In the simplest possible way determine, whether this reaction is of (a) zero order (b) first order (c) second order (d) third order

The incorrect statement is (a) Rate law is an experimental fact whereas law of mass action is a theoretical proposal. (b) Rate law is always different from the expression of law of mass action. (c) Rate law is more informative than law of mass action for the development of mechanism. (d) Order of a reaction is equal to the sum of powers of concentration terms in the rate law.

After \(20 \%\) completion, the rate of reaction: \(\mathrm{A} \rightarrow\) products, is 10 unit and after \(80 \%\) completion, the rate is \(0.625\) unit. The order of the reaction is (a) zero (b) first (c) second (d) third

A zero-order reaction is one (a) in which reactants do not react. (b) in which one of the reactants is in large excess. (c) whose rate does not change with time. (d) whose rate increases with time.

Hydrolysis of ethyl acetate is catalysed by \(\mathrm{HCl}\). The rate is proportional to the concentration of both the ester and HCl. The rate constant is \(0.1 \mathrm{M}^{-1} \mathrm{~h}^{-1}\). What is the half-life, if the initial concentrations are \(0.02 \mathrm{M}\) for the ester and \(0.01 \mathrm{M}\) for the catalysing acid? (a) \(347 \mathrm{~h}\) (b) \(519 \mathrm{~h}\) (c) \(836 \mathrm{~h}\) (d) \(693 \mathrm{~h}\)

If the rate of a gaseous reaction is independent of partial pressure of reactant, the order of reaction is (a) 0 (b) 1 (c) 2 (d) 3

Two substances, 'A' and 'B' are initially present as \(\left[A_{0}\right]=8\left[B_{0}\right]\) and \(t_{1 / 2}\) for the firstorder decomposition of 'A' and 'B' are 10 and \(20 \mathrm{~min}\), respectively. If they start decomposing at the same time, after how much time, the concentration of both of them would be same? (a) \(20 \mathrm{~min}\) (b) \(40 \mathrm{~min}\) (c) \(60 \mathrm{~min}\) (d) \(200 \mathrm{~min}\)

For a first-order reaction: \(\mathrm{A} \rightarrow\) Product, the initial concentration of \(\mathrm{A}\) is \(0.1 \mathrm{M}\) and after time \(40 \mathrm{~min}\), it becomes \(0.025 \mathrm{M}\). What is the rate of reaction at reactant concentration \(0.01 \mathrm{M} ?\) (a) \(3.465 \times 10^{-4} \mathrm{~mol} \mathrm{lit}^{-1} \mathrm{~min}^{-1}\) (b) \(3.465 \times 10^{-5} \mathrm{~mol} \mathrm{lit}^{-1} \mathrm{~min}^{-1}\) (c) \(6.93 \times 10^{-4} \mathrm{~mol} \mathrm{lit}^{-1} \mathrm{~min}^{-1}\) (d) \(1.7325 \times 10^{-4} \mathrm{~mol} \mathrm{lit}^{-1} \mathrm{~min}^{-1}\)

For a chemical reaction: \(\mathrm{X} \rightarrow \mathrm{Y}\), the rate of reaction increases by a factor of \(1.837\) when the concentration of \(\mathrm{X}\) is increased by \(1.5\) times. The order of the reaction with respect to \(\mathrm{X}\) is (a) 1 (b) \(1.5\) (c) 2 (d) \(-1\)

A solution of \(\mathrm{N}_{2} \mathrm{O}_{5}\) in \(\mathrm{CCl}_{4}\) yields by decomposition at \(45^{\circ} \mathrm{C}, 4.8 \mathrm{ml}\) of \(\mathrm{O}_{2}\), 20 min after the start of the experiment and \(9.6 \mathrm{ml}\) of \(\mathrm{O}_{2}\) after a very long time. The decomposition obeys first-order kinetics. What volume of \(\mathrm{O}_{2}\) would have evolved, 40 min after the start? (a) \(7.2 \mathrm{ml}\) (b) \(2.4 \mathrm{ml}\) (c) \(9.6 \mathrm{ml}\) (d) \(6.0 \mathrm{ml}\)

A first-order reaction: \(\mathrm{A}(\mathrm{g}) \rightarrow n \mathrm{~B}(\mathrm{~g})\) is started with 'A'. The reaction takes place at constant temperature and pressure. If the initial pressure was \(P_{0}\) and the rate constant of reaction is ' \(K\), then at any time, \(t\), the total pressure of the reaction system will be (a) \(P_{0}\left[n+(1-n) e^{-k t}\right]\) (b) \(P_{0}(1-n) e^{-k t}\) (c) \(P_{0} \cdot n \cdot e^{-k t}\) (d) \(P_{0}\left[n-(1-n) e^{-k t}\right.\)

For a reaction of order \(n\), the integrated form of the rate equation is: \((n-1) \cdot K \cdot t\) \(=\left(C_{0}\right)^{1-n}-(C)^{1-n}\), where \(C_{0}\) and \(C\) are the values of the reactant concentration at the start and after time ' \(t\) '. What is the relationship between \(t_{3 / 4}\) and \(t_{1 / 2}\), where \(t_{3 / 4}\) is the time required for \(C\) to become \(C_{0} / 4\). (a) \(t_{3 / 4}=t_{1 / 2} \cdot\left[2^{n-1}+1\right]\) (b) \(t_{3 / 4}=t_{1 / 2}\left[2^{n-1}-1\right]\) (c) \(t_{3 / 4}=t_{1 / 2}\left[2^{n+1}-1\right]\) (d) \(t_{3 / 4}=t_{1 / 2} \cdot\left[2^{n+1}+1\right]\)

The rate law for a reaction between the substances \(\mathrm{A}\) and \(\mathrm{B}\) is given by rate \(=\) \(K[\mathrm{~A}]^{n}[\mathrm{~B}]^{m} .\) 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 (a) \(1 / 2^{m+n}\) (b) \((m+n)\) (c) \((n-m)\) (d) \(2^{(n-m)}\)

For a reaction \(2 \mathrm{~A}+\mathrm{B}+3 \mathrm{C} \rightarrow \mathrm{D}+3 \mathrm{E}\), the following date is obtained: $$ \begin{array}{ccccc} \hline \text { Reaction } & \multicolumn{2}{c} {\text { Concentration in }} & \text { Initial rate of } \\ & \multicolumn{2}{c} {\text { mole per litre }} & \text { formation of } \\ & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D}\left(\text { torr } \mathbf{s}^{-1}\right) \\ \hline 1 & 0.01 & 0.01 & 0.01 & 2.5 \times 10^{-4} \\ 2 & 0.02 & 0.01 & 0.01 & 1.0 \times 10^{-3} \\ 3 & 0.01 & 0.02 & 0.01 & 2.5 \times 10^{-4} \\ 4 & 0.01 & 0.02 & 0.02 & 5.0 \times 10^{-4} \\ \hline \end{array} $$ The order with respect to \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are, respectively, (a) \(0,1,2\) (b) \(2,0,1\) (c) \(1,0,2\) (d) \(2,1,1\)

When the concentration of 'A' is 0.1 M, it decomposes to give ' \(\mathrm{X}\) ' by a firstorder process with a rate constant of \(6.93 \times 10^{-2} \mathrm{~min}^{-1}\). The reactant 'A', in the presence of catalyst, gives ' \(\mathrm{Y}\) ' by a secondorder mechanism with the rate constant of \(0.2 \mathrm{~min}^{-1} \mathrm{M}^{-1} .\) In order to make half-life of both the processes, same, one should start the second-order reaction with an initial concentration of 'A' equal to (a) \(0.01 \mathrm{M}\) (b) \(2.0 \mathrm{M}\) (c) \(1.0 \mathrm{M}\) (d) \(0.5 \mathrm{M}\)

In the gas phase, two butadiene molecules can dimerizes to give larger molecules according to the reaction: \(2 \mathrm{C}_{4} \mathrm{H}_{6}(\mathrm{~g})\) \(\rightarrow \mathrm{C}_{8} \mathrm{H}_{12}(\mathrm{~g})\). The rate law for this reac- tion is, \(r=K\left[\mathrm{C}_{4} \mathrm{H}_{6}\right]^{2}\) with \(K=6.1 \times 10^{-2}\) \(1 \mathrm{~mol}^{-1} \mathrm{~s}^{-1}\) at the temperature of reaction. The rate of formation of \(\mathrm{C}_{8} \mathrm{H}_{12}\), when the concentration of \(\mathrm{C}_{4} \mathrm{H}_{6}\) is \(0.02 \mathrm{M}\), is (a) \(2.44 \times 10^{-5} \mathrm{Ms}^{-1}\) (b) \(1.22 \times 10^{-5} \mathrm{Ms}^{-1}\) (c) \(1.22 \times 10^{-3} \mathrm{Ms}^{-1}\) (d) \(2.44 \times 10^{-6} \mathrm{Ms}^{-1}\)

The half-life periods of two first-order reactions are in the ratio \(3: 2\). If \(t_{1}\) is the time required for \(25 \%\) completion of the first reaction and \(t_{2}\) is the time required for \(75 \%\) completion of the second reaction, then the ratio, \(t_{1}: t_{2}\), is \((\log 3=0.48\), \(\log 2=0.3\) ) (a) \(3: 10\) (b) \(12: 25\) (c) \(3: 5\) (d) \(3: 2\)

A complex reaction: \(2 \mathrm{X}+\mathrm{Y} \rightarrow \mathrm{Z}\), takes place in two steps $$ \begin{array}{l} \mathrm{X}+\mathrm{Y} \stackrel{K_{1}}{\longrightarrow} 2 \mathrm{~W} \\ \mathrm{X}+2 \mathrm{~W} \stackrel{K_{2}}{\longrightarrow} \mathrm{Z} \end{array} $$ If \(K_{1}

The suggested mechanism for the reaction: \(\mathrm{CHCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{CCl}_{4}(\mathrm{~g})\) \(+\mathrm{HCl}(\mathrm{g})\), is $$ \mathrm{Cl}_{2} \underset{K_{2}}{\stackrel{K_{1}}{\leftrightarrows}} 2 \mathrm{C} \mathrm{C} \text { (fast) } $$ \(\mathrm{CHCl}_{3}+\mathrm{Ci} \stackrel{K_{3}}{\longrightarrow} \mathrm{HCl}+\dot{\mathrm{C}} \mathrm{Cl}_{3}(\mathrm{slow})\) $$ \dot{\mathrm{C}} \mathrm{Cl}_{3}+\mathrm{C} \mathrm{\textrm{l }} \stackrel{K_{4}}{\longrightarrow} \mathrm{CCl}_{4} \text { (fast) } $$ The experimental rate law consistent with the mechanism is (a) rate \(=K_{3}\left[\mathrm{CHCl}_{3}\right]\left[\mathrm{Cl}_{2}\right]\) (b) rate \(=K_{4}\left[\mathrm{CCl}_{3}\right][\mathrm{Cl}]\) (c) rate \(=K_{\text {eq }}\left[\mathrm{CHCl}_{3}\right]\left[\mathrm{Cl}_{2}\right]\) (d) rate \(=K_{3} K_{\text {eq }}^{1 / 2}\left[\mathrm{CHCl}_{3}\right]\left[\mathrm{Cl}_{2}\right]^{1 / 2}\)

The acid catalysed reaction of acetic acid with ethanol: \(\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} \rightarrow \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}\) \(+\mathrm{H}_{2} \mathrm{O}\) follows the rate law: \(-\frac{\mathrm{d}\left[\mathrm{CH}_{3} \mathrm{COOH}\right]}{\mathrm{d} t}\) \(=K\left[\mathrm{H}^{+}\right] \quad\left[\mathrm{CH}_{3} \mathrm{COOH}\right] \quad\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]\) \(=K^{\prime}\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right] .\) When \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]_{0}=\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]_{0}=0.2 \mathrm{M}\) and \(\mathrm{pH}=3\), the half-life for the reaction is \(50 \mathrm{~min}\). The value of true rate constant, \(K\), of the reaction is (a) \(1.386 \times 10^{-2} \mathrm{~min}^{-1}\) (b) \(0.1 \mathrm{M}^{-1} \mathrm{~min}^{-1}\) (c) \(100 \mathrm{M}^{-2} \mathrm{~min}^{-1}\) (d) \(13.86 \mathrm{~min}^{-1}\)

The time taken in \(75 \%\) completion of a zero-order reaction is \(10 \mathrm{~h}\). In what time, he reaction will be \(90 \%\) completed? a) \(12.0 \mathrm{~h}\) (b) \(16.6 \mathrm{~h}\) c) \(10.0 \mathrm{~h}\) (d) \(20.0 \mathrm{~h}\)

A zero-order reaction \(\mathrm{A} \rightarrow \mathrm{B}\). At the end of \(1 \mathrm{~h}, \mathrm{~A}\) is \(75 \%\) reacted. How much of it will be left unreacted at the end of \(2 \mathrm{~h}\). (a) \(12.5 \%\) (b) \(6.25 \%\) (c) \(3.12 \%\) (d) \(0 \%\)

In Lindemann theory of unimolecular reactions, it is shown that the apparent rate constant for such a reaction is \(k_{\text {app }}\) \(=\frac{k_{1} C}{1+\alpha C}\), where \(C\) is the concentration of the reactant, \(k_{1}\) and a are constants. The value of \(C\) for which \(k_{\text {app }}\) has \(90 \%\) of its limiting value at \(C\) tending to infinitely large is \(\left(\alpha=9 \times 10^{5}\right)\) (a) \(10^{-6}\) mole/litre (b) \(10^{-4}\) mole/litre (c) \(10^{-5}\) mole/litre (d) \(5 \times 10^{-5}\) mole/litre

Which of the following represents the expression for \(3 / 4^{\text {th }}\) the life of a first-order reaction? (a) \(\frac{k}{2.303} \log \frac{4}{3}\) (b) \(\frac{2.303}{k} \log \frac{4}{3}\) (c) \(\frac{2.303}{k} \log 4\) (d) \(\frac{2.303}{k} \log 3\)

For the first-order reaction \(t_{99 \%}=x \times t_{90 \%}\). The value of ' \(x\) ' will be (a) 10 (b) 6 (c) 3 (d) 2

The rate equation for an autocatalytic reaction \(\mathrm{A}+\mathrm{R} \stackrel{k}{\longrightarrow} \mathrm{R}+\mathrm{R}\) is \(r_{\mathrm{A}}=-\frac{\mathrm{d} C_{\mathrm{A}}}{\mathrm{d} t}=k C_{\mathrm{A}} C_{\mathrm{R}}\) The rate of disappearance of reactant \(\mathrm{A}\) is maximum when (a) \(C_{\mathrm{A}}=2 C_{\mathrm{R}}\) (b) \(C_{\mathrm{A}}=C_{\mathrm{R}}\) (c) \(C_{\mathrm{A}}=C_{\mathrm{R}} / 2\) (d) \(C_{\mathrm{A}}=\left(C_{\mathrm{R}}\right)^{1 / 2}\)

For the second-order reaction: \(2 \mathrm{~A} \rightarrow \mathrm{B}\), time taken for the \([\mathrm{A}]\) to fall to one-fourth value is how many times the time it takes for \([\mathrm{A}]\) to fall to half of its initial value? (a) two (b) three (c) four (d) seven

For the following first-order competing reaction: $$ \begin{array}{l} \text { A + Reagent } \rightarrow \text { Product } \\ \text { B + Reagent } \rightarrow \text { Product } \end{array} $$ the ratio of \(K_{1} / K_{2}\), if only \(50 \%\) of ' \(\mathrm{B}\) ' will have been reacted when \(94 \%\) of ' \(\mathrm{A}\) ' has been reacted is \((\log 2=0.3, \log 3=0.48)\) (a) \(4.06\) (b) \(0.246\) (c) \(8.33\) (d) \(0.12\)

In \(80 \%\) ethanol at \(55^{\circ} \mathrm{C}\), isopropyl bromide reacts with hydroxide ion according to the following kinetics: $$ \begin{array}{l} -\frac{\mathrm{d}[\mathrm{RX}]}{\mathrm{d} t}=\left(4.8 \times 10^{-5} \mathrm{M}^{-1} \mathrm{~s}^{-1}\right) \\ {[\mathrm{RX}]\left[\mathrm{OH}^{-}\right]+2.4 \times 10^{-6} \mathrm{~s}^{-1}[\mathrm{RX}]} \end{array} $$ What percentage of isopropyl bromide reacts by the \(S_{\mathrm{N}_{2}}\) mechanism when \(\left[\mathrm{OH}^{-}\right]=0.01 \mathrm{M} ?\) (a) \(16.67 \%\) (b) \(83.33 \%\) (c) \(66.67 \%\) (d) \(33.33 \%\)