A reaction in which A, B, and C react to form products is zero order in A, one-half order in B, and second order in C. a. Write a rate law for the reaction.

Verified step by step guidance

1. Identify the general form of the rate law: \( \text{Rate} = k[A]^m[B]^n[C]^p \).
2. Determine the order of reaction with respect to each reactant: \( m = 0 \) for A, \( n = \frac{1}{2} \) for B, and \( p = 2 \) for C.
3. Substitute the orders into the rate law expression: \( \text{Rate} = k[A]^0[B]^{1/2}[C]^2 \).
4. Simplify the expression by noting that any concentration raised to the power of zero is 1: \( \text{Rate} = k[B]^{1/2}[C]^2 \).
5. The final rate law for the reaction is \( \text{Rate} = k[B]^{1/2}[C]^2 \).

Key Concepts

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by the concentration of that reactant. For example, a zero-order reaction means the rate is independent of the concentration of that reactant, while a first-order reaction means the rate is directly proportional to its concentration.

Rate Law

The rate law is an equation that relates the rate of a chemical reaction to the concentrations of the reactants, each raised to a power corresponding to its order in the reaction. It is typically expressed in the form: Rate = k[A]^m[B]^n[C]^p, where k is the rate constant, and m, n, and p are the orders of the reactants A, B, and C, respectively. Understanding the rate law is crucial for predicting how changes in concentration affect the reaction rate.

Rate Constant (k)

The rate constant, denoted as k, is a proportionality factor in the rate law that is specific to a given reaction at a specific temperature. It reflects the intrinsic speed of the reaction and is influenced by factors such as temperature and the presence of catalysts. The value of k can vary with the order of the reaction and is essential for calculating the rate of the reaction under different conditions.