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.

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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. Look at how the initial rate changes as the concentration of A changes. This will help determine the order of the reaction.

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).

Step 4: Write the rate law. Once the order n is determined, substitute it into the rate law equation: rate = k[A]^n.

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.

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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 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.

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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

The tabulated data were collected for this reaction: CH₃Cl(g) + 3 Cl₂(g) → CCl₄( g) + 3 HCl(g)

Write an expression for the reaction rate law and calculate the value of the rate constant, k. What is the overall order of the reaction?

Textbook Question

Indicate the order of reaction consistent with each observation. a. A plot of the concentration of the reactant versus time yields a straight line. Indicate the order of reaction consistent with each observation b. The reaction has a half-life that is independent of initial concentration. c. A plot of the inverse of the concentration versus time yields a straight line.