For the reaction :
`C_(2)H_(5)I+OH^(-) rarr C_(2)H_(5)OH + I^(-)`
the rate constant was found to have a value of `5.03xx10^(-2)" mol"^(-1)" dm"^(3) s^(-1)" at "289 K and 6.71" mol"^(-1)" dm"^(3) s^(-1)` at 333 K What is the rate constant at 305 K.

Explanation

To find the rate constant at 305 K for the given reaction, we will use the Arrhenius equation and the provided rate constants at two different temperatures. Here’s a step-by-step solution:

### Step 1: Write down the given data
We have:
- \( K_1 = 5.03 \times 10^{-2} \, \text{mol}^{-1} \, \text{dm}^3 \, \text{s}^{-1} \) at \( T_1 = 289 \, \text{K} \)
- \( K_2 = 6.71 \, \text{mol}^{-1} \, \text{dm}^3 \, \text{s}^{-1} \) at \( T_2 = 333 \, \text{K} \)

We need to find \( K_3 \) at \( T_3 = 305 \, \text{K} \).
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