The reaction
`2NO_(2)rarr2NO+O_(2)`
has an activation energy of `110 KJ mol^(-)`. At `400^(@)C`, the rate constant is `7.8mol^(-1)Ls^(-1)`. What is the value of rate constant at `430^(@)C` ?

Explanation

To find the rate constant \( k_2 \) at \( 430^\circ C \) for the reaction \( 2NO_2 \rightarrow 2NO + O_2 \), we will use the Arrhenius equation in the logarithmic form:

\[ \log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \cdot \frac{T_2 - T_1}{T_1 T_2} \]

### Step 1: Convert temperatures to Kelvin
- \( T_1 = 400^\circ C = 400 + 273 = 673 \, K \)
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