🤓 Based on our data, we think this question is relevant for Professor Parnis' class at Trent University.

We’re being asked to **calculate the rate constant (k)** of a second-order reaction with a half-life of **15.4 s** at an initial concentration of **0.67 M**.

Recall that ** half-life (t_{1/2})** is the time needed for the amount of a reactant to decrease by 50% or one-half.

The half-life of a second-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\mathbf{1}\mathbf{/}\mathbf{2}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{k}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}}}$

where:

**k** = rate constant

**[A] _{0}** = initial concentration

The half-life for the second-order decomposition of HI is 15.4 s when the initial concentration of HI is 0.67 M. What is the rate constant for this reaction?

A. 9.7 x 10^{-2}M^{-1}s^{-1}

B. 4.5 x 10^{-2}M^{-1}s^{-1}

C. 3.8 x 10^{-2}M^{-1}s^{-1}

D. 2.2 x 10^{-2}M^{-1}s^{-1}

E. 1.0 x 10^{-2}M^{-1}s^{-1}