Consider the tabulated data showing the initial rate of a reaction (A → products) at several different concentrations of A. What is the order of the reaction? Write a rate law for the reaction including the value of the rate constant, k.

Verified step by step guidance

1. Step 1: Understand the rate law equation. The rate law for a reaction A → products is generally expressed as rate = k[A]^n, where k is the rate constant, [A] is the concentration of reactant A, and n is the order of the reaction with respect to A.
2. Step 2: Analyze the data. Look at how the initial rate changes as the concentration of A changes. This will help determine the order of the reaction.
3. Step 3: Determine the order of the reaction. If the rate doubles when the concentration of A doubles, the reaction is first order (n=1). If the rate quadruples, the reaction is second order (n=2). If the rate remains unchanged, the reaction is zero order (n=0).
4. Step 4: Write the rate law. Once the order n is determined, substitute it into the rate law equation: rate = k[A]^n.
5. Step 5: Calculate the rate constant k. Use one set of data from the table to solve for k by substituting the known values of rate and [A] into the rate law equation.

Key Concepts

Reaction Order

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 reactants. For example, a first-order reaction means that doubling the concentration of the reactant will double the rate of reaction, while a second-order reaction means that doubling the concentration will quadruple the rate.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentrations of its reactants. It is typically written in the form Rate = k[A]^n, where k is the rate constant, [A] is the concentration of reactant A, and n is the order of the reaction with respect to A. The rate law can be determined experimentally by analyzing how changes in concentration affect the reaction rate.

Rate Constant (k)

The rate constant, k, is a proportionality factor in the rate law that is specific to a given reaction at a specific temperature. It reflects the speed of the reaction; a larger k indicates a faster reaction. The value of k can be determined from experimental data and is influenced by factors such as temperature and the presence of catalysts.