Arrhenius Equation

Q. A reactant (A) forms two products :
$A\stackrel{k_1}{⟶}B,$ Activation energy $E{a}_1$
$A\stackrel{k_2}{⟶}B,$ Activation energy $E_{a_2}$
[Assuming same value of pre-expotential factor (A) for both reactions]

1. $k_1=k_2{e}^{\frac{E_{a_1}}{RT}}$
2. $k_2=k_1{e}^{\frac{E_{a_2}}{RT}}$
3. $k_2=k_1{e}^{\frac{E_{a_1}}{RT}}$
4. $k_1=2k_2{e}^{\frac{E_{a_2}}{RT}}$

Q. Milk turns sour at ${40}^{\circ }$C three times as faster as $0^{\circ }$C. Hence, $E_a$ in the process of turning of milk sour is

1. $\frac{2.303\times 2\times 40}{273\times 313}log3cal$
2. $\frac{2.303\times 2\times 313\times 273}{40}log3$
3. $\frac{2.303\times 2\times 313\times 273}{40}log\left(1/3\right)cal$
4. $Noneofthese$

Q. Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows the Arrhenius equation is

1. 
2. 
3. 
4. 

Q. A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be $K_1$ and $K_2$ respectively then

1. $K_2\approx 0.5K_1$
2. $K_2\approx 0.25K_1$
3. $K_2\approx 2K_1$
4. $K_2\approx 4K_1$

Q.

The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be:

$(R=8.314J{K}^{-1}mo{l}^{-1}andlog2=0.301)$

(IIT-JEE-2013)

1. $48.6kJmo{l}^{-1}$

2. $58.5kJmo{l}^{-1}$

3. $60.5kJmo{l}^{-1}$
4. $53.6kJmo{l}^{-1}$

Q. Velocity constant of a reaction at 290 K was found to $3.2\times {10}^{-3}se{c}^{-1}$. When the temperature is raised to 310 K, it will be about:

1. $6.4\times {10}^{-3}$
2. $3.2\times {10}^{-4}$
3. $9.6\times {10}^{-3}$
4. $1.28\times {10}^{-2}$

Q. Let’s assume you are a student of Arrhenius. He asked you to calculate $E_a$ for a reaction so that he can study a reaction on which he is working for a long time. He told you the rate constants of the reaction at 500 K and 700 K are $0.02s^{-1}and0.07s^{-1}$ respectively. Calculate the value of $E_a$.

1. 18431 J
2. 19231 J
3. 12831 J
4. 18231 J

Q. He is impressed with your work but he wants you to calculate the value of A as well. Calculate the value of A at the same conditions. (The rate constants of the reaction at 500 K and 700 K are $0.02s^{-1}$ and $0.07s^{-1}$ respectively.)

1. 18231 J
2. 12831 J
3. 18431 J
4. 19231 J

Q. The energy of activation of a first order reaction is $187.06kJmo{l}^{-1}$ at 750 K and the value of pre-exponential factor A is $1.97\times {10}^{12}{s}^{-1}$. Calculate the half life. $(e^{-30}=9.35\times {10}^{-14})$

1. 9.76s
2. 5.76s
3. 8.76s
4. 3.76s

Q.

For a first order reaction A ⟶ P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = -2000(1/T) + 6.0. The pre-exponential factor A and the activation energy $E_a,$ respectively, are

(IIT-JEE, 2009)

1. $1.0\times {10}^6{s}^{-1}and9.2kJmo{l}^{-1}$

2. $1.0\times {10}^6{s}^{-1}and38.3kJmo{l}^{-1}$

3. $6.0s^{-1}and16.6kJmo{l}^{-1}$

4. $1.0\times {10}^6{s}^{-1}and16.6kJmo{l}^{-1}$