Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 5 / b / iii / Solution

A and C: integrate $dx/x=-k{h}_{\mathrm{const}}dt$:using $h_{\mathrm{const}}=10^{-2}\mathrm{M}$ for A and $10^{-4}\mathrm{M}$ for C.

B: integrate $dx/x^2=-kdt$:For completeness, unbuffered unequal initial concentrations obey $h=x+\delta$, $\delta =h_0-x_0$, and the exact expression isIt approaches the equimolar second-order expression as $\delta \to 0$ and the excess-hydroxide exponential when depletion is negligible.

The unequal-concentration expression is the unequal-concentration second-order integration formula.