Consider the following rate law: rate = k[a]^n[b]^m. How are the exponents n and m determined?

• A. They are assigned based on the molecular weights of a and b.
• B. They are always equal to the coefficients of a and b in the balanced chemical equation.
• C. They are determined experimentally by measuring how the rate changes with concentration.
• D. They are determined by the stoichiometry of the overall reaction.

Answer: (C)

Verified step by step guidance

1. Understand that the rate law expresses how the rate of a reaction depends on the concentrations of reactants, typically written as \(\text{rate} = k[\text{A}]^n[\text{B}]^m\) where \(n\) and \(m\) are the reaction orders with respect to reactants A and B.
2. Recognize that the exponents \(n\) and \(m\) are not necessarily related to the coefficients in the balanced chemical equation or molecular weights; instead, they reflect the reaction mechanism and how changes in concentration affect the rate.
3. Determine \(n\) and \(m\) experimentally by measuring the initial rate of the reaction while varying the concentration of one reactant at a time, keeping others constant, and observing how the rate changes.
4. Use the method of initial rates: for example, if doubling the concentration of A while keeping B constant doubles the rate, then \(n = 1\); if the rate quadruples, then \(n = 2\), and so on.
5. Repeat this process for reactant B to find \(m\), and combine these experimentally determined orders to write the complete rate law.