Question

For $X\to Y;$ $k={10}^{10}{e}^{-500/T}$, and for $W\to Z;$ $k={10}^{12}{e}^{-1000/T}$ at what temperature '$T$' both reactions will have same value of $k$?

• A. $500$ $K$
• B. $1500$ $K$
• C. $\frac{500}{4.606}K$
• D. $\frac{5000}{2.303}K$

Answer 1

Answer: (C)

$\frac{500}{4.606}K$

$k_1={10}^{10}{e}^{\frac{-500}{T}};k_2={10}^{12}{e}^{\frac{-1000}{T}}For{k}_1=k_2{10}^{10}{e}^{\frac{-500}{T}}={10}^{20}{e}^{\frac{-1000}{T}}{e}^{\frac{-500}{T}+\frac{1000}{T}}={10}^2\frac{1}{T}.500=2\ln \left(10\right)T=\frac{500}{4.606}k$