Q.The rate of formation of a dimer in a second order reaction is $7.5\times10^{-3}\ \text{mol L}^{-1}\text{s}^{-1}$ at 0.05 mol $L^{-1}$ monomer concentration. Calculate the rate constant.

Step 1. A second order reaction in the monomer M has rate law $\text{Rate}=k[M]^2$; here 'rate of formation of the dimer' is taken directly as the reaction rate (the dimer's own stoichiometric coefficient is 1).

Step 2. Given: rate $=7.5\times10^{-3}\ \text{mol L}^{-1}\text{s}^{-1}$ at $[M]=0.05\ \text{mol L}^{-1}$.

Step 3. $k=\dfrac{\text{Rate}}{[M]^2}=\dfrac{7.5\times10^{-3}}{(0.05)^2}=\dfrac{7.5\times10^{-3}}{2.5\times10^{-3}}=3$. …

Substitute the given rate and monomer concentration directly into the second order rate law $\text{Rate}=k[\text{monomer}]^2$ an …

• Squaring the rate instead of the concentration, or forgetting to square $[M]$ at all before dividing. …