The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.34 M. What is the rate constant for this reaction?

Question

BlackTom AI · Accepted Answer

For a second-order reaction the half-life depends on the initial concentration according to t1/2 = 1/(k [A]0).

1. Relevant knowledge points and concepts
- Integrated rate law for a second-order reaction (rate = k[A]^2) is 1/[A] = kt + 1/[A]0.
- The half-life t1/2 is the time required for [A] to fall to [A]0/2. For second-order kinetics this gives t1/2 = 1/(k [A]0).
- Units of k for a second-order reaction are M^-1 s^-1.

2. Step-by-step reasoning
- Start from the second-order half-life relation: t1/2 = 1/(k [A]0).
- Solve for k: k = 1/(t1/2 × [A]0).

3. Calculations (all intermediate steps)
- Given t1/2 = 15.4 s and [A]0 = 0.34 M.
- Multiply t1/2 × [A]0 = 15.4 s × 0.34 M = 5.236 s·M.
- Invert: k = 1 / 5.236 s·M = 0.191101... M^-1 s^-1.
- Express with two significant figures (matching answer choices): k ≈ 1.9 × 10^-1 M^-1 s^-1.

4. Why this is correct
- The derivation used the correct integrated form for a second-order decomposition and applied the half-life definition correctly. Units M^-1 s^-1 confirm second-order behavior. Numerical inversion yields 0.191 M^-1 s^-1, matching the provided choice.

5. Why the other options are incorrect
- 2.2 × 10^-2 M^-1 s^-1 and 3.8 × 10^-2 M^-1 s^-1 are too small—these could arise from using an incorrect formula (e.g., first-order t1/2 = ln2/k) or arithmetic errors; they also give incorrect units if derived from first-order. 
- 5.2 M^-1 s^-1 and 45.2 M^-1 s^-1 are far too large and inconsistent with t1/2 and [A]0; they would correspond to much faster reactions than the given half-life.

6. Conclusion
The correct rate constant is 1.9 × 10^-1 M^-1 s^-1, which matches the provided answer.

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.34 M. What is the rate constant for this reaction?单项选择题

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