= Pseudo-first-order reaction
In a <second-order reaction> $\mathrm A+\mathrm B\longrightarrow\mathrm P$ with <rate law> $-d[\mathrm A]/dt=k_2[\mathrm A][\mathrm B]$, a large excess of B can keep $[\mathrm B]\approx[\mathrm B]_0$ during the observation window. Then
$$
-\frac{d[\mathrm A]}{dt}\approx k_1[\mathrm A],\qquad k_1=k_2[\mathrm B]_0,\qquad
[\mathrm A](t)\approx[\mathrm A]_0e^{-k_1t}.
$$
This is a <pseudo-first-order reaction>: the approximate <first-order reaction> describes that window, while changing the excess B <concentration> changes $k_1$. Its units are $\mathrm{s^{-1}}$, distinct from the <second-order reaction> <rate constant> $k_2$. For one-to-one <stoichiometry>, the maximum fractional depletion of B is $[\mathrm A]_0/[\mathrm B]_0$; an original $100:1$ initial excess bounds its change by $1\%$. A twofold excess permits $50\%$ depletion and does not provide the same control.<Glossary of Terms Used in Physical Organic Chemistry (IUPAC Recommendations 1994): N and O entries by International Union of Pure and Applied Chemistry>[Glossary of Terms Used in Physical Organic Chemistry, IUPAC Recommendations 1994, entry “order of reaction”: constant B, observed coefficient and pseudo-first-order coefficient]{ref}
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