A rate law used to determine the reaction rate from reactant concentrations and rate constants can be converted into rate laws demonstrating the dependence of reaction rate on reactant concentration and time.

These rate laws can be used to study how slowly or quickly a reactant is consumed, or how much time is necessary to reach half the concentration of a reactant.

To begin, examine the differential rate law, which expresses the reaction rate as a change in reactant concentration during a specific time interval. Integration of this law leads to the integrated rate law, which expresses the reaction rate as a relation between a reactant’s initial concentration and its concentration after a specific duration.

The integrated rate law is dependent on the overall reaction order and, hence, varies for each reaction type. However, irrespective of the overall order, all integrated rate laws take the form of a standard linear equation with distinct y, m, x, and b components, and can be plotted to generate a straight line.

In a zero-order integrated rate law, [A]_t is the reactant concentration at the time t, k is the rate constant, t is the time, and [A]₀ is the initial reactant concentration.

For a zero-order reaction, a plot of the reactant concentration as a function of time generates a straight line. The slope is the negative value of the rate constant, and the y-intercept is the initial reactant concentration.

In a first-order reaction, the natural log of reactant concentration plotted as a function of time gives a straight line. The slope corresponds to the negative value of the rate constant, while the y-intercept gives the natural log of the initial reactant concentration.

According to the second-order integrated rate law, a plot of the inverse of the reactant concentration versus time yields a straight line. The slope equates to the rate constant, and the y-intercept represents the inverse of the initial reactant concentration.

The overall reaction order can be identified using experimental kinetic data by plotting the different integrated rate laws. Only the plot with a linear graph corresponds to the correct overall reaction order. Subsequent analysis allows determining the rate constant and reactant concentration at any given time.