Question

For reactions $\text{A} \rightarrow \text{B}$ and $\text{P} \rightarrow \text{Q}$ Arrhenius constants are $10^{8}$ and $10^{10}$ respectively. If $\text{E}_{\text{A} \rightarrow \text{B}} \, \text{=} \, \text{600} \, \text{cal/mole}$ and $\text{E}_{\text{P} \rightarrow \text{Q}} \, \text{=} \, \text{1200} \, \text{cal/mole}$ , then find the temperature at which their rate constants are same.

(Given: $\text{R} \, \text{=} \, \text{2} \, \text{cal/mole/K}$ )

• A. $600 \, K$
• B. $300\times 4.606 \, K$
• C. $\frac{300}{4.606}K$
• D. $\frac{4.606}{600}K$

Answer 1

Answer: (C)

$A_{1}e^{- E a_{1} / R T}=A_{2}e^{- E a_{2} / R T}$

$\frac{A_{2}}{A_{1}}=e^{\left(E a_{2} - E a_{1}\right) / R T}$

$10^{2}=Exp\left\{\frac{600}{R T}\right\}$ $R=2 \, c a l / K-mol$

$2ln10=\frac{600}{2 T}$

$T=\left\{\frac{300}{2 \times 2.303}\right\}K$