A reaction follows the rate law $r = k [A]^{2}$ . If the concentration of $A$ is $0.10 M$ at a certain instant and the instantaneous rate of reaction is $0.020 M, s^{- 1}$ , find the rate constant $k$ .

easy 1 mark Class 12 · Chemistry · Chemical Kinetics

Answer

k = 2.0 \times 1 0^{2}, M^{- 1}, s^{- 1}

The correct answer is $k = 2.0 \times 1 0^{2}, M^{- 1}, s^{- 1}$ — Step 5: Include the units: $k$ has units of $M^{- 1}, s^{- 1}$ . Hence $k = 2.0 \times 1 0^{2}, M^{- 1}, s^{- 1}$ .

Step-by-step solution

Step 1: Write the given rate law $r = k [A]^{2}$ .
Step 2: Substitute $r = 0.020 M, s^{- 1}$ and $[A] = 0.10 M$ into the equation: $0.020 = k (0.10)^{2}$ .
Step 3: Simplify $(0.10)^{2} = 0.01$ . The equation becomes $0.020 = k \times 0.01$ .
Step 4: Solve for $k$ by dividing both sides by $0.01$ : $k = 0.020/0.01 = 2.0$ .
Step 5: Include the units: $k$ has units of $M^{- 1}, s^{- 1}$ . Hence $k = 2.0 \times 1 0^{2}, M^{- 1}, s^{- 1}$ .

Common mistake: Treating

k

as having units of

s^{- 1}

instead of

M^{- 1} s^{- 1}

Concept tested: Determination of rate constant from rate law

Published 2 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

A reaction follows the rate law r=k[A]2. If the concentration of A is 0.10 M at a certain instant and the instantaneous rate of reaction is 0.020 M,s−1, find the rate constant k.

Step-by-step solution

Related questions

A reaction follows the rate law $r = k [A]^{2}$ . If the concentration of $A$ is $0.10 M$ at a certain instant and the instantaneous rate of reaction is $0.020 M, s^{- 1}$ , find the rate constant $k$ .