Textbook Question
A reaction A + B → C obeys the following rate law: Rate = k[B]2. (b) What are the reaction orders for A and B? What is the overall reaction order?
Ch.14 - Chemical Kinetics
Chapter 14, Problem 28b,c,d,f
Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?
Verified step by step guidance1
Identify the rate law for the reaction. Since the reaction is first order in A, zero order in B, and second order in C, the rate law can be expressed as: , where k is the rate constant.
For part (b), consider the effect of doubling [A]. Since the reaction is first order in A, doubling [A] will double the rate. This is because the rate is directly proportional to the concentration of A raised to the first power.
For part (c), consider the effect of tripling [B]. Since the reaction is zero order in B, changing the concentration of B does not affect the rate. Therefore, tripling [B] will have no effect on the rate.
For part (d), consider the effect of tripling [C]. Since the reaction is second order in C, tripling [C] will increase the rate by a factor of , which is 9. This is because the rate is proportional to the square of the concentration of C.
For part (f), consider the effect of cutting the concentrations of all three reactants in half. The rate will change by a factor of , which simplifies to . This means the rate will decrease by a factor of 0.125.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Order of Reaction
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 that reactant. For example, a first-order reaction in A means that if the concentration of A is doubled, the rate of reaction will also double, while a zero-order reaction in B indicates that changes in B's concentration do not affect the rate.
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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]^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 reactants A, B, and C, respectively. Understanding the rate law is crucial for predicting how changes in concentration will affect the reaction rate.
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Effect of Concentration Changes
The effect of changing reactant concentrations on the reaction rate can be determined using the rate law. For instance, if a reactant is first-order, doubling its concentration will double the rate; for zero-order, the rate remains unchanged regardless of concentration changes. In the case of second-order reactions, tripling the concentration will increase the rate by a factor of nine, illustrating how different orders lead to varying impacts on the reaction rate.
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Related Practice
Textbook Question
A reaction A + B → C obeys the following rate law: Rate = k[B]2. (c) What are the units of the rate constant?
Textbook Question
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.
Textbook Question
Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (e) By what factor does the rate change when the concentrations of all three reactants are tripled?
Textbook Question
The decomposition reaction of N2O5 in carbon tetrachloride is 2 N2O5 → 4 NO2 + O2. The rate law is first order in N2O5. At 64°C the rate constant is 4.82 × 10-3 s-1. (a) Write the rate law for the reaction.
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Textbook Question
The decomposition reaction of N2O5 in carbon tetrachloride is 2 N2O5 → 4 NO2 + O2. The rate law is first order in N2O5. At 64°C the rate constant is 4.82 × 10-3 s-1. (c) What happens to the rate when the concentration of N2O5 is doubled to 0.0480 M? (d) What happens to the rate when the concentration of N2O5 is halved to 0.0120 M?