Question

Make a graph of [A] versus time for zero-, first-, and second-order reactions. From these graphs, compare successive half-lives.

Short answer

For a zero-order reaction, the plot of concentration of reactant vs time is a straight line (linear) with a negative slope and non-zero intercept.

For a first-order reaction, the plot of concentration of reactant vs time is an exponential curve withthe concentration of the reactant decreasing exponentially with time.

For a second-order reaction, the plot of concentration of reactant vs time is an exponential curve with the concentration of the reactant decreasing exponentially with time.

Step-by-step solution

Analyzing the graph of [A] versus time for zero-, first-, and second-order reactions.

For a zero-order reaction, the plot between the concentration of reactant vs time is found to be a straight line (linear) having a negative slope and an intercept that is not zero.

For a first-order reaction, the plot of concentration of reactant vs time is an exponential curve in which the concentration of the reactant decreases exponentially with time.

In the case of a second-order reaction, the plot of concentration of reactant vs time is found to be an exponential curve where the concentration of the reactant decreases exponentially with time.

Determining the half-life reactions for zero-, first-, and second-order reactions by analyzing their respective graphs.

For zero order reaction, according to the graph, the half-life period corresponds to $t_{1/2}=\frac{{\left[\text{A}\right]}_0}{2k}$. Thus, for a zero-order reaction, the half-life period is directly proportional to the initial concentration.

For the first-order reaction, according to the graph, the half-life period corresponds to $t_{1/2}=\frac{0.693}{k}$. Thus, for first-order reactions, the half-life period is independent of the initial concentration.

For a second-order reaction, according to the graph, the half-life period corresponds to $t_{1/2}=\frac{1}{k{\text{A}}_0}$. Thus, for first-order reactions, the half-life period is inversely proportional to the initial concentration of reactants.