The elementary reaction
$2 \mathrm { NO } _ { 2 }$ (g) ? 2NO(g) + $\mathrm { O } _ { 2 }$ (g)
is second order in $\mathrm { NO } _ { 2 }$ and the rate constant at 515 K is 1.64 × 10^-2

$\mathrm { L } \mathrm { mol } ^ { - 1 }$ $s ^ { - 1 }$ .The reaction half-life at this temperature when $\left[ \mathrm { NO } _ { 2 } \right] _ { 0 }$ = 0.45 mol L^-1 is ________ s.

Question

The elementary reaction

2 \mathrm { NO } _ { 2 }

(g) ? 2NO(g) +

\mathrm { O } _ { 2 }

(g)
is second order in

\mathrm { NO } _ { 2 }

and the rate constant at 515 K is 1.64 × 10^-2

\mathrm { L } \mathrm { mol } ^ { - 1 }

s ^ { - 1 }

.The reaction half-life at this temperature when

\left[ \mathrm { NO } _ { 2 } \right] _ { 0 }

= 0.45 mol L^-1 is ________ s.

Quizplus · Accepted Answer

The half-life for a second-order reaction is given by $ t_{1/2} = \frac{1}{k [A]_0} $. Substituting the given values, $ t_{1/2} = \frac{1}{1.64 \times 10^{-2} \times 0.45} \approx 1.4 \times 10^2 $ s.

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