Consider the 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

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.

Step 2: Analyze the data provided. Look at how the initial rate of the reaction changes as the concentration of A changes. This will help determine the order of the reaction.

Step 3: Determine the reaction order. If the rate doubles when [A] doubles, the reaction is first order (n=1). If the rate quadruples when [A] doubles, the reaction is second order (n=2). If the rate remains unchanged when [A] changes, the reaction is zero order (n=0).

Step 4: Write the rate law. Once the order n is determined, write the rate law as rate = k[A]^n.

Step 5: Calculate the rate constant k. Use one set of data (concentration and rate) to solve for k in the rate law equation.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 and provides insight into the mechanism of the reaction.

Rate Constant (k)

The rate constant, k, is a proportionality factor in the rate law that is specific to a particular reaction at a given 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.

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Related Practice

Textbook Question

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.

Textbook Question

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. c. By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant)? d. By what factor does the reaction rate change if [B] is doubled? e. By what factor does the reaction rate change if [C] is doubled? f. By what factor does the reaction rate change if [C] is doubled (and the other reactant concentrations are held constant)?

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Textbook Question

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.