How is a rate law for a system with two reactants determined experimentally?

• A. Vary concentrations and fit to rate = k[A]^m[B]^n
• B. Use stoichiometric coefficients directly
• C. Use equilibrium data to infer rate constants
• D. Assume rate is independent of concentrations

Answer: (A)

The main idea is that the rate law is an empirical relationship showing how the reaction rate depends on the concentrations of the reactants, determined by experiments that vary those concentrations and observe the effect on rate. For a system with two reactants, you test how the rate changes when you change one concentration at a time while keeping the other constant, and then again for the other reactant. The rate is expressed as rate = k [A]^m [B]^n, where the exponents m and n are the orders with respect to each reactant and are determined from the data, not from the balanced equation.

In practice, you can determine m by varying [A] (with [B] fixed) and measuring the rate; plotting log(rate) versus log([A]) gives a straight line whose slope is m. Do the same with [B] (holding [A] constant) to find n. The rate constant k comes from plugging the measured rate and concentrations back into the rate law. This approach works even if m and n are fractional or not equal to the stoichiometric coefficients, because they reflect the actual mechanism’s rate-determining steps, which governs how sensitive the rate is to each concentration. Equilibrium data don’t reveal these kinetic dependencies, and assuming independence from concentration would only describe a zero-order scenario, which is not generally correct.