Deduce the rate law for the converison of `H_(2)` and `I_(2)` to `HI` at `440^(@)C` corresponding to the following proposed mechanism:
step I: `I_(2) hArr 2I ("fast") (k_(1))`
Step II: `I+H_(2) hArr IH_(2) ("fast") (k_(2))`
Step III: `IH_(2) + I rarr 2HI` (slow) `(k)`

Explanation

To deduce the rate law for the conversion of \( H_2 \) and \( I_2 \) to \( HI \) based on the proposed mechanism, we will follow these steps:

### Step 1: Identify the Rate-Determining Step
The rate-determining step is the slowest step in the mechanism. In this case, Step III is the slow step:
\[ IH_2 + I \rightarrow 2HI \quad \text{(slow, rate constant } k\text{)} \]
The rate of this step can be expressed as:
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