Question

A graph between $log{t}_{\frac{1}{2}}$ and $log\left[A_0\right]$ for a reaction at $27{}^{\circ }C$ is given above. From the graph, which of the following statement(s) is/are correct?
($t_{\frac{1}{2}}$= Half-life ; $\left[A_o\right]$ = Initial concentration)

• A. The unit of k (rate constant) is the same as the rate of the reaction
• B. The half-life is directly proportional to $\left[A_o\right]$
• C. The half-life is independent of $\left[A_o\right]$
• D. The slope of the graph between $\left[A_t\right]$ and $t$ is $–k$

Answer 1

Answer: (A), (B), (D)

The correct options are
A The unit of k (rate constant) is the same as the rate of the reaction
B The half-life is directly proportional to $\left[A_o\right]$
D The slope of the graph between $\left[A_t\right]$ and $t$ is $–k$

The rate of the reaction is independent of the initial concentration of the reactant in a zero order reaction. Hence, the rate constant and the rate of the reaction have the same units.

For a zero order reaction,
$\left[A_t\right]=\left[A_o\right]-kt$
$t_{\frac{1}{2}}=\frac{\left[A_o\right]}{2k}$
$\Rightarrow log{t}_{\frac{1}{2}}=-log2k+log\left[A_o\right]$