Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (a) Write the rate law for the reaction.

Verified step by step guidance

1. insert step 1> Identify the order of the reaction with respect to each reactant. The problem states that the reaction is first order in A, zero order in B, and second order in C.
2. insert step 2> Recall that the rate law for a reaction is expressed as: \( \text{Rate} = k[A]^m[B]^n[C]^p \), where \( k \) is the rate constant, and \( m, n, \) and \( p \) are the orders of the reaction with respect to A, B, and C, respectively.
3. insert step 3> Substitute the given orders into the rate law expression: \( m = 1 \), \( n = 0 \), and \( p = 2 \).
4. insert step 4> Write the rate law using the substituted values: \( \text{Rate} = k[A]^1[B]^0[C]^2 \).
5. insert step 5> Simplify the rate law expression by removing any terms raised to the power of zero, as they equal 1: \( \text{Rate} = k[A][C]^2 \).

Key Concepts

Rate Law

The rate law of a chemical reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. It is typically formulated as an equation where the rate is proportional to the concentrations of the reactants raised to their respective orders. The order of a reactant indicates how the rate is affected by changes in its concentration.

Reaction Order

Reaction order refers to the exponent to which the concentration of a reactant is raised in the rate law. It can be determined experimentally and indicates the sensitivity of the reaction rate to changes in that reactant's concentration. In this case, the reaction is first order in A, zero order in B, and second order in C, meaning the rate depends linearly on A, is independent of B, and depends quadratically on C.

Units of Rate Constant

The units of the rate constant (k) in a rate law depend on the overall order of the reaction. For a reaction that is first order in A, zero order in B, and second order in C, the overall order is 3 (1 + 0 + 2). The units of k for this reaction would be M^-2 s^-1, where M is molarity, reflecting how the rate of reaction changes with the concentrations of the reactants.