Step 1: Understanding the Concept:
Order is the sum of exponents in the rate law. Molecularity is the number of reactant molecules in an elementary step.
Step 2: Key Formula or Approach:
Rate law: $\text{r} = \text{k}[\text{A}]^\text{x} \rightarrow \text{order} = \text{x}$.
Step 3: Detailed Explanation:
- From the given rate law $\text{r} = \text{k}[\text{C}_2\text{H}_5\text{I}]^1$, the power of concentration is 1. Thus, order $= 1$.
- Molecularity is defined for elementary reactions. This decomposition is a simple unimolecular process involving only one molecule of ethyl iodide. Hence, molecularity $= 1$.
Step 4: Final Answer:
Both order and molecularity are 1.