Question

The ratio constants for $k_1$ and $k_2$ for two different reactions are ${10}^{16}{e}^{-2000T}$ and ${10}^{15}{e}^{-1000/T}$ respectively. Temperature at which $k_1=k_2$ is:

• A. $\frac{2000}{2.303}K$
• B. $2000K$
• C. $\frac{1000}{2.303}K$
• D. $1000K$

Answer 1

The correct option is C $\frac{1000}{2.303}K$

$k_1=k_2$

${10}^{16}{e}^{-2000T}={10}^{15}{e}^{-1000/T}$

$\Rightarrow 10e^{-200T}=e^{-1000/T}$

$ln10-2000/T=-1000/T$

$2.303=\frac{1000}{T}$

$\Rightarrow T=\frac{1000}{2.303}K$