Problem 47
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) \(13.86 \mathrm{~min}^{-1}\)
Problem 47
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) \(20.0 \mathrm{~h}\)
Problem 48
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) \(0 \%\)
Problem 49
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
Problem 49
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) \(\frac{2.303}{k} \log 3\)
Problem 51
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
Problem 52
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) \(C_{\mathrm{A}}=\left(C_{\mathrm{R}}\right)^{1 / 2}\)
Problem 53
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
Problem 54
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) \(0.12\)
Problem 55
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) \(33.33 \%\)
