At an instant the concentration of reactant A in a reaction following the rate law $r=k[A{]}^2$ is $0.15\mathrm{M}$. The instantaneous rate of reaction is $0.045\mathrm{M},{\mathrm{s}}^{-1}$. Find the rate constant $k$ (in ${\mathrm{M}}^{-1},{\mathrm{s}}^{-1}$).

Step-by-step solution

1. Write the given rate law: $r=k[A{]}^2$.
2. Insert the numerical values: $r=0.045\mathrm{M},{\mathrm{s}}^{-1}$, $[A]=0.15\mathrm{M}$.
3. Calculate $[A{]}^2=(0.15{)}^2=0.0225{\mathrm{M}}^2$.
4. Solve for $k$: $k=r/[A{]}^2=0.045/0.0225=2.0{\mathrm{M}}^{-1},{\mathrm{s}}^{-1}$.
5. Thus the rate constant is $2.0{\mathrm{M}}^{-1},{\mathrm{s}}^{-1}$.

Concept tested: Rate law of an elementary reaction

Published 6 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked