Question

For a first order chemical reaction,

• A. the product formation rate is independent of reactant concentration.
• B. the time taken for the completion of half of the reaction $(t_{1/2})$ is 69.3% of the rate constant $(k)$
• C. the dimension of Arrhenius pre-exponential factor is reciprocal of time.
• D. the concentration vs time plot for the reactant should be linear with a negative slope

Answer 1

Answer: (C)

Arrhenius equation for rate constant, $k$ is $k=A{e}^{-E_a/R{T}_{}}$ where A is the pre-exponential factor. Since, $e^{-E_a/R{T}_{}}$ is dimensionless, dimension of $A=k$.
For first order reaction, dimension of $k=time{s}^{-1}$
$\therefore$ Also same for $A$.
As for the other options,
For a first order reaction, the product formation rate is directly proportional to reactant concentration, half-life $=\frac{0.693}{k}$
or $69.3\%$ of $(\frac{1}{k})$, and concentration of reactant changes with time by the equation ${\left[A\right]}_t={\left[A\right]}_0^{e^{-kt}}$ which shows exponential decreases, not linear.