Integrated Rate Equations

Zero Order Reactions

The Differential Rate Equation

A zero order reaction means that the rate of the reaction is proportional to the zero power of the concentration of reactants. Consider the reaction $R \rightarrow P$:

$Rate = -\frac{d[R]}{dt} = k[R]^0$

First Order Reactions

The Differential Form

In a first order reaction, the rate is proportional to the first power of the concentration of the reactant ($R \rightarrow P$).

$Rate = -\frac{d[R]}{dt} = k[R]$

Problem. The initial concentration of $N_2O_5$ in the following first order reaction $N_2O_5(g) \rightarrow 2 NO_2(g) + 1/2 O_2(g)$ was $1.24 \times 10^{-2} \text{ mol L}^{-1}$ at 318 K. The concentration of $N_2O_5$ after 60 minutes was $0.20 \times 10^{-2} \text{ mol L}^{-1}$. Calculate the rate constant of the reaction at 318 K.