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

For a certain reaction the variation of the rate constant with temperature is given by the equation

                            $In k_1=In k_0+\left(\frac{In 3}{10}\right)t \left(t\ge 0°C\right)$

The value of the temperature coefficient of the reaction rate is therefore –

(A) 4                                                  

(B) 3

(C) 2                                                   

(D) 10

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) $+23°C$

The rate of reaction triples when the temperature changes from \(20{ }^{\circ} \mathrm{C} \text { to } 50^{\circ} \mathrm{C}\). The energy of activation for the reaction will be:

The half-life time for the decomposition of a substance dissolved in ${\mathrm{CCl}}_4$ is 2.5 hours at $\mathrm{30 }°$C. The amount of substance that will be left after 10 hours if the initial weight of the substance is 160 gm is:

Given the following reaction:
N₂O₅   as   N₂O₅   ⇌ 2NO₂ + (1/2)O₂
The values of rate constants for the above reaction are 3.45 × 10^-5 and 6.9 × 10^-3 at 27 ^oC and 67 ^oC respectively. The activation energy for the above reaction is : 

1. $102$ $\times {10}^2$ $J$ $$ $$                                    

2. $488.5$ $kJ$

3. $112$ $J$ $$                                             

4. $112.5$ $kJ$

What is the percentage of the reactant molecules crossing over the energy barrier at 325 K?

Given that $∆{\mathrm{H}}_{325}=0.12$ $\mathrm{kcal},$ ${\mathrm{E}}_{\mathrm{a}\left(\mathrm{b}\right)}=+0.02$ $\mathrm{kcal}$

1 mole of a gas changes linearly from its initial state (2 atm, 10 lt) to its final state (8 atm, 4 lt). The maximum rate constant is equal to 20 $se{c}^{-1}$ and the value of activation energy is 40 kJ, assuming that the activation energy does not change in this temperature range. The value of the rate constant, at the maximum temperature that the gas can attain, is: 

1. $0.56$ $\times$ ${10}^{-3}$ $se{c}^{-1}$                                          

2. $3.16$ $\times$ ${10}^{-3}$ $se{c}^{-1}$

3. $1.56$ $\times$ ${10}^{-3}se{c}^{-1}$                                          

4. $5.12$ $\times$ ${10}^{-3}$ $se{c}^{-1}$

A first-order reaction was started with a decimolar solution of the reactant. After 8 minutes and 20 seconds, its concentration was found to be M/100. The rate constant of the reaction will be:

1. $4.6$ $\times$ ${10}^{-3}se{c}^{-1}$                                      

2. $16.6$ $\times$ ${10}^{-3}$ $se{c}^{-1}$

3. $24.6$ $\times$ ${10}^{-3}$ $se{c}^{-1}$                                   

4. $40.6$ $\times$ ${10}^{-3}$ $se{c}^{-1}$

87.5% of a radioactive substance disintegrates in 40 minutes. What is the half life of the substance ?

(1) 13.58 min                                                   

(2) 135.8 min

(3) 1358 min                                                    

(4) None of these