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The rate constant for a chemical reaction that takes place at 500 K is expressed as K = A e^-1000. The activation energy of the reaction will be:
1. 100 cal/mol
2. 1000 kcal/mol
3. 10⁴ kcal/mol
4. 10⁶ kcal/mol

Mechanism of a hypothetical reaction
${\mathrm{X}}_2 + {\mathrm{Y}}_2 \stackrel{ }{\to } 2\mathrm{XY}$ is given below
(i) ${\mathrm{X}}_2 \stackrel{ }{\rightleftharpoons } \mathrm{X} + \mathrm{X} \left(\mathrm{fast}\right)$
(ii) $\mathrm{X} + {\mathrm{Y}}_2 \stackrel{ }{\to } \mathrm{XY} + \mathrm{Y} \left(\mathrm{slowest}\right)$
(iii) $\mathrm{X} + \mathrm{Y} \stackrel{ }{\to }\mathrm{XY} \left(\mathrm{fast}\right)$
The overall order of the reaction will be
1. 1
2.  2
3. 0
4. 1.5

For a reaction of the type 2A+B $\to$2C, the rate of the reaction is given by $k{\left[A\right]}^2\left[B\right]$. When the volume of the reaction vessel is reduced to 1/4 th of the original volume, the rate of reaction changes by a factor of
(A) 0.25                                                          
(B) 16
(C) 64                                                             
(D) 4

A first-order reaction takes 40 min for 30 % decomposition. The t_1/2 for this reaction will be:

A catalyst lowers the activation energy of a reaction from $20 kJ mol{e}^{-1} to 10 kJ mol{e}^{-1}$. The temperature at which the uncatalysed reaction will have the same rate as that of the catalysed at $27°C$ is :
(1) $-123°C$                                                     
(2) $327°C$
(3) - 327°C                                                         
(4) $+23°C$

At 400 K, the energy of activation of a reaction is decreased by 0.8 kcal in the presence of a catalyst. As a result, the rate will be:

A reaction takes place in various steps. The rate constant for first, second, third and fifth steps are ${\mathrm{k}}_1, {\mathrm{k}}_2, {\mathrm{k}}_3 \mathrm{and} {\mathrm{k}}_5$ respectively. The overall rate constant is given by , $\mathrm{k}=\frac{{\mathrm{k}}_2}{{\mathrm{k}}_3}{\left(\frac{{\mathrm{k}}_1}{{\mathrm{k}}_5}\right)}^{1/2}$
If activation energy are 40, 60, 50 and 10 kJ/mol respectively, the overall energy of activation (kJ/mol) is:
(1) 10
(2) 20
(3) 25
(4) None of the above.

For reaction A$\to$B, the rate constant ${\mathrm{k}}_1={\mathrm{A}}_1{\mathrm{e}}^{-{\mathrm{Ea}}_1/\left(\mathrm{RT}\right)}$ and for the reaction X$\to$Y, the rate constant ${\mathrm{k}}_2={\mathrm{A}}_2{\mathrm{e}}^{-{\mathrm{Ea}}_2/\left(\mathrm{RT}\right)}$. If ${\mathrm{A}}_1={10}^8, {\mathrm{A}}_2={10}^{10} \mathrm{and} {\mathrm{E}}_{{\mathrm{a}}_1}=600 \mathrm{cal}/\mathrm{mol},$ ${\mathrm{E}}_{{\mathrm{a}}_1}=1800 \mathrm{cal}/\mathrm{mol}$, then the temperature at which ${\mathrm{k}}_1={\mathrm{k}}_2$ is (Given: R=2 cal/K-mol)
(1) 1200 K
(2) 1200$\times$4.606 K
(3) $\frac{1200}{4.606} K$
(4) $\frac{600}{4.606} K$

For a zero order reaction, the plot of conc. (a-x) vs time is linear with
(1) +ve slope and zero intercept
(2) -ve slope and zero intercept
(3) +ve slope and non-zero intercept
(4) -ve slope and non-zero intercept

The forward rate constant for the elementary reversible gaseous reaction
${\mathrm{C}}_2{\mathrm{H}}_6\rightleftharpoons 2{\mathrm{CH}}_3 \mathrm{is} 1.57\times {10}^{-3} {\mathrm{s}}^{-1} \mathrm{at} 100 \mathrm{K}$
What is the rate constant for the backward reaction at this temperature if ${10}^{-4}$ moles of ${\mathrm{CH}}_3$ and 10 moles of ${\mathrm{C}}_2{\mathrm{H}}_6$ are present in a 10 litre vessel at equilibrium.
(1) $1.57\times {10}^9 \mathrm{L} {\mathrm{mol}}^{-1} {\mathrm{s}}^{-1}$
(2) $1.57\times {10}^{10} \mathrm{L} {\mathrm{mol}}^{-1} {\mathrm{s}}^{-1}$
(3) $1.57\times {10}^{11} \mathrm{L} {\mathrm{mol}}^{-1} {\mathrm{s}}^{-1}$
(4) $1.57\times {10}^7 \mathrm{L} {\mathrm{mol}}^{-1} {\mathrm{s}}^{-1}$

The half-life of ⁹²U₂₃₈ against \(\alpha\)-decay is 4.5 × 10⁹ year.  The time taken in a year for the decay of the 15/16 part of this isotope will be:
1. $9.0\times {10}^9$
2. $1.8\times {10}^{10}$
3. $4.5\times {10}^9$
4. $2.7\times {10}^{10}$