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?
Ch.14 - Chemical Kinetics
Chapter 14, Problem 28e
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?
Verified step by step guidance1
Step 1: Understand the rate law for the reaction. The rate law for a reaction is an equation that shows how the rate of a reaction depends on the concentrations of the reactants. In this case, the rate law is given by Rate = k[A][B]^0[C]^2, where k is the rate constant, [A], [B], and [C] are the concentrations of the reactants A, B, and C, respectively.
Step 2: Understand the order of reaction. The order of a reaction with respect to a particular reactant is the power to which its concentration in the rate equation is raised. In this case, the reaction is first order in A, zero order in B, and second order in C.
Step 3: Calculate the new rate when the concentrations of all three reactants are tripled. According to the rate law, if the concentration of A is tripled, the rate will triple because the reaction is first order in A. If the concentration of B is tripled, the rate will not change because the reaction is zero order in B. If the concentration of C is tripled, the rate will increase by a factor of 3^2 = 9 because the reaction is second order in C.
Step 4: Multiply the changes in the rate due to each reactant to find the total change in the rate. In this case, the total change in the rate is 3 (from A) * 1 (from B) * 9 (from C) = 27.
Step 5: Therefore, when the concentrations of all three reactants are tripled, the rate of the reaction increases by a factor of 27.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rate Law
The rate law of a reaction expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is determined by the reaction order with respect to each reactant, which indicates how the rate is affected by changes in concentration. For example, a first-order reaction in a reactant means that doubling its concentration will double the reaction rate.
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Rate Law Fundamentals
Reaction Order
Reaction order refers to the exponent to which the concentration of a reactant is raised in the rate law. It can be zero, first, second, or higher, indicating how the rate of reaction changes with varying concentrations. In the given reaction, A is first order, B is zero order, and C is second order, meaning that only the concentrations of A and C will affect the rate when their concentrations change.
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Effect of Concentration Changes
When the concentrations of reactants are changed, the overall rate of the reaction can be calculated by substituting the new concentrations into the rate law. For the given reaction, if the concentrations of A, B, and C are all tripled, the rate will change according to the orders: the rate will increase by a factor of 3 (for A) and 9 (for C), while B remains unchanged, leading to a total factor of 27 for the rate change.
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Related Practice
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. (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?
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?
Textbook Question
Consider the following reaction:
2 NO(g) + 2 H2(g) → N2(g) + 2 H2O(g)
(b) If the rate constant for this reaction at 1000 K is 6.0 × 104 M-2 s-1, what is the reaction rate when [NO] = 0.035 M and [H2] = 0.015 M?
(c) What is the reaction rate at 1000 K when the concentration of NO is increased to 0.10 M, while the concentration of H2 is 0.010 M?