We’re being asked to **calculate the half-life **of a second-order reaction with a rate constant of 0.50 min^{-1} M^{-1} initially at 0.75 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

Given that N_{2}O_{4} is 2nd order for the reaction: N_{2}O_{4} → 2 NO_{2, }if a reaction started with 0.75 M N_{2}O_{4}, what is the half-time when the rate constant is 0.50 min^{-1} M^{-1}

A. 1.33 min

B. 2.25 min

C. 0.50 min

D. 2.67 min

E. 10.3 min

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