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The rate of the reaction A → B depends only on the concentration of A and follows the rate law: rate = k[A]^(3/2), where the rate constant k = 1 M^(-1/2) s^(-1). Which of the following statements is/are correct? (A) The molecularity of the reaction must be one. (B) The reaction is definitely an elementary reaction. (C) The value of the rate constant is 1 M^(-1/2) s^(-1). (D) The reaction is definitely a complex (multi-step) reaction.
- A only
- B only
- C only
- D only
Correct answer: C only
Solution
The rate law rate = k[A]^(3/2) shows the reaction is of order 3/2, which is fractional. Molecularity must be a whole number, so it cannot be 1 for a rate law with a non-integer order; moreover molecularity applies only to elementary reactions. A fractional order rules out an elementary step, proving the reaction is complex (multi-step). The rate constant k has units derived from [rate]/[A]^(3/2) = (M s^(-1)) / M^(3/2) = M^(-1/2) s^(-1), so the numerical value 1 M^(-1/2) s^(-1) is exactly what the graph gives. Statement C is correct.
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