The Arrehenius equation for the rate constant of decompoistion of methyl nitrite and ethyl nitrite are
`k_(1) (s^(-1)) =10^(13) exp ((-152300 J mol^(-1))/(RT))`
and `k_(2)(s^(-1)) = 10^(14)exp((-157700 J mol^(-1))/(RT))` respectively. Find the temperature at which the rate constant are equal.

Explanation

To find the temperature at which the rate constants \( k_1 \) and \( k_2 \) are equal for the decomposition of methyl nitrite and ethyl nitrite, we will set the two Arrhenius equations equal to each other and solve for temperature \( T \).

### Step-by-Step Solution:

1. **Write down the Arrhenius equations:**
\[ k_1 = 10^{13} e^{-\frac{152300}{RT}} \]
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