Given experimental rate data for a reaction, how would you determine the rate law and the order with respect to reactant A?

• A. Plot rate vs time.
• B. Compare equilibrium constants.
• C. Use the average rate over time.
• D. Use the initial-rate method; compare rates for different [A]; determine n from log(rate1/rate2) = n log([A]1/[A]2).

Answer: (D)

Determining how the rate depends on the amount of A is done by examining how the rate changes when you change the initial concentration of A, using the initial-rate method. If the rate law is rate = k [A]^n for a reaction that depends on a single reactant, then the rate observed early in the reaction (when [A] is still close to its initial value) reflects that dependence without the complications of changing concentrations as the reaction proceeds.

Take two experiments with different initial concentrations [A]1 and [A]2 and their corresponding initial rates rate1 and rate2. Since rate ∝ [A]^n, the ratio rate1/rate2 = ([A]1/[A]2)^n. By taking logs, you get log(rate1/rate2) = n log([A]1/[A]2). This allows you to solve for n, the order with respect to A, from the slope of the log-log relationship or directly from the ratio equation if you know the concentrations and rates.

This approach is preferred because it directly links the measured rates to the concentration of A, without the confounding effects of changing concentrations over time. Other options either don’t isolate how rate scales with [A] (plotting rate vs time looks at the time course rather than the concentration dependence), rely on equilibrium information (not about kinetics), or use an average rate that smooths out the instantaneous dependence on [A] and loses essential information. The initial-rate method with varying [A] and a log-ratio analysis cleanly reveals the exponent n.