Second-Order Reactions

The rate for second-order reactions depends either on two reactants raised to the first power or a single reactant raised to the second power. We will examine a reaction that is the latter type: C → D. The differential rate law can be written:

Rate of reaction = – [latex] frac{Delta [C]}{Delta t} [/latex] = [latex] extit{k}[C]{}^{2} [/latex]

The integrated rate law can be written in the form of a straight line as:

[latex] frac{1}{{[C]}_t} [/latex] = [latex] extit{k}t + frac{1}{{[C]}_0} [/latex]

Therefore, if the reaction is second order, a plot of 1/[C]_t versus t will produce a straight line with a slope that corresponds to the rate constant, k, and a y-intercept that corresponds to the inverse of the initial concentration, 1/[C]₀ (Figure 1.1 “1/[C]t vs. Time, Second-Order Reaction”).

Figure 1.1:  1/[C]t vs. Time, Second-Order Reaction

The graph shows a plot of 1/[C]_t versus time for a second-order reaction.