A reaction in which A, B, and C react to form products is first order in A, second order in B, and zero 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 (and the other reactant concentrations are held constant)? e. By what factor does the reaction rate change if [C] is doubled? f. By what factor does the reaction rate change if the concentrations of all three reactants are doubled?

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Identify the rate law for the reaction. Since the reaction is first order in A, second order in B, and zero order in C, the rate law can be expressed as: \( \text{Rate} = k[A]^1[B]^2[C]^0 \).

Recognize that a zero order in C means that changes in the concentration of C do not affect the rate of the reaction.

Focus on the effect of doubling [A] while keeping [B] and [C] constant. Substitute the new concentration of A into the rate law: \( \text{New Rate} = k(2[A])^1[B]^2[C]^0 \).

Simplify the expression for the new rate: \( \text{New Rate} = 2k[A][B]^2 \).

Compare the new rate to the original rate: \( \text{New Rate} = 2 \times \text{Original Rate} \). Therefore, the reaction rate doubles when [A] is doubled.

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Key Concepts

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

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. It indicates how the rate of reaction is affected by the concentration of that reactant. In this case, the reaction is first order in A, second order in B, and zero order in C, meaning that the rate depends linearly on [A], quadratically on [B], and is independent of [C].

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically written 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 reaction with respect to each reactant. For the given reaction, the rate law can be expressed as Rate = k[A]^1[B]^2[C]^0, highlighting how changes in concentrations affect the overall reaction rate.

Effect of Concentration Change on Reaction Rate

When the concentration of a reactant is changed, the reaction rate changes according to its order. For a first-order reactant, doubling the concentration will double the rate, while for a second-order reactant, it will quadruple the rate. In this scenario, since [A] is doubled and it is first order, the reaction rate will also double, while the concentrations of B and C remain constant.

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Textbook Question

A reaction in which A, B, and C react to form products is first order in A, second order in B, and zero order in C.

a. Write a rate law for the reaction.

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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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