Rate constant ($k$)

A rate constant is the coefficient in a specified rate law, held fixed under specified conditions. It can describe an empirical overall chemical reaction, as well as an elementary reaction. Fixed temperature matters: changing temperature can change $k$, even for the same chemical reaction. See IUPAC Gold Book: order of reaction and rate constants and IUPAC Gold Book: rate coefficient.

For $v=k[\mathrm{A}{]}^n$, dimensional consistency requiresA zero-order reaction therefore uses $\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}$; a first-order reaction uses ${\mathrm{s}}^{-1}$; a second-order reaction uses $\mathrm{L}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{s}}^{-1}$. Comparing bare numerical values of $k$ across different orders of reaction is meaningless without their units and concentrations. Even for the same order of reaction, state whether $k$ multiplies the normalized reaction rate $v$ or a particular reactant disappearance rate: a stoichiometric coefficient can change that convention.