# Problem: 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 10-2M-1s-1B. 4.5 x 10-2M-1s-1C. 3.8 x 10-2M-1s-1D. 2.2 x 10-2M-1s-1E. 1.0 x 10-2M-1s-1

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###### FREE Expert Solution

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 (t1/2) 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

###### Problem Details

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 10-2M-1s-1

B. 4.5 x 10-2M-1s-1

C. 3.8 x 10-2M-1s-1

D. 2.2 x 10-2M-1s-1

E. 1.0 x 10-2M-1s-1