Three different transformations of concentration–time data for the same elementary reaction are described below.
• Plot I: Concentration of reactant Z (in M) on the y-axis vs. time (in s) on the x-axis is a straight line with a negative slope.
• Plot II: Natural logarithm of the concentration of Z on the y-axis vs. time on the x-axis is a straight line with a negative slope.
• Plot III: Reciprocal of the concentration of Z on the y-axis vs. time on the x-axis is a straight line with a positive slope.
Assume the reaction is elementary and involves Z as the only species whose concentration changes measurably during the time interval shown.
(a) Identify which of the three plots (I, II, or III) indicates that the reaction is second order with respect to Z. Justify your answer in terms of the mathematical relationship between the plotted variables.
(b) Identify which of the three plots indicates that the reaction has a rate that is independent of the concentration of Z. Explain your reasoning.
(c) For a reaction that is first order in Z, describe how the half-life depends on the initial concentration of Z, citing evidence from the appropriate plot above.