Concept:The unit for the rate constant (\( k \)) adjusts based on the reaction order so that multiplying it by the concentration terms always yields the fixed units of reaction rate (Concentration/time).
Formula:$$ \text{Rate} = k[\text{Concentration}]^{1} $$
Solution:- Note on Source Key: The book's official answer key incorrectly lists D as the answer, but the book's own Explanatory Notes correctly calculate it as option C. We apply the scientifically accurate answer here.
- For a first-order reaction: \( \text{Rate} (\text{M s}^{-1}) = k \times [\text{A}] (\text{M}) \).
- Isolating \( k \): \( k = \frac{\text{M s}^{-1}}{\text{M}} \).
- The Molarity (M) units cancel out entirely, leaving only \( \text{s}^{-1} \).
Why other options are incorrect:Option D (\( \text{M}^{-1}\text{s}^{-1} \)) is the unit for a second-order reaction. Option A represents zero-order. Option B implies a negative first-order reaction.
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