The half-life of a substance in a first-order reaction is 100 minutes at 323.2 K and 15 minutes at 353.2 K. Calculate the temperature coefficient of the rate constant of this reaction.

Explanation

To solve the problem, we need to calculate the temperature coefficient of the rate constant for a first-order reaction using the given half-lives at two different temperatures.

### Step 1: Calculate the rate constants (K1 and K2)
For a first-order reaction, the rate constant \( K \) can be calculated using the formula:
\[ K = \frac{0.693}{t_{1/2}} \]
where \( t_{1/2} \) is the half-life of the reaction.
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