Chemistry

Problem

A student plotted the measured half-life of reactant A (in seconds) versus the initial concentration

[A]_0

(in

\text{mol}\,\text{L}^{-1}

). The data produced a straight line through the origin with a slope of

35\,\text{s}\,\text{M}^{-1}

. Which value of the rate constant

k

is most consistent with the graph? a)

0.020\,\text{M}\,\text{s}^{-1}

0.014\,\text{M}\,\text{s}^{-1}

0.029\,\text{M}\,\text{s}^{-1}

0.0070\,\text{M}\,\text{s}^{-1}

Intuitive explanation

The shape of the half-life vs. initial concentration plot tells you the reaction order. For a first-order reaction, $t_{1/2}$ is independent of $[A]_0$ (horizontal line); for second-order, $t_{1/2} = \frac{1}{k[A]_0}$ (a line through the origin with slope $\frac{1}{k}$ ). Since your graph is a straight line through the origin, you're dealing with second-order kinetics—now just extract $k$ from the slope using the relationship between half-life and rate constant.

Intuitive explanation

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