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Ch.14 - Chemical Kinetics
Tro - Chemistry: A Molecular Approach 4th Edition
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Tutti i libri di testoTro 4th EditionCh.14 - Chemical KineticsProblema 54d
Capitolo 14, Problema 54d

This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms.
d. If the initial concentration of AB is 0.250 M, and the reaction mixture initially contains no products, what are the concentrations of A and B after 75 s?

Guida verificata passo dopo passo
1
Identify the order of the reaction. Since a plot of \( \frac{1}{[\text{AB}]} \) versus time is a straight line, the reaction is second-order with respect to AB.
Use the second-order integrated rate law: \( \frac{1}{[\text{AB}]} = kt + \frac{1}{[\text{AB}]_0} \), where \( k \) is the rate constant, \( t \) is time, and \( [\text{AB}]_0 \) is the initial concentration.
Substitute the given values into the integrated rate law: \( \frac{1}{[\text{AB}]} = 0.55 \times 75 + \frac{1}{0.250} \).
Solve for \( [\text{AB}] \) to find the concentration of AB at 75 seconds.
Since the reaction is \( \text{AB} \rightarrow \text{A} + \text{B} \), the change in concentration of AB is equal to the increase in concentration of A and B. Calculate \( [\text{A}] = [\text{B}] = [\text{AB}]_0 - [\text{AB}] \).

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Rate Law and Reaction Order

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For the reaction AB → A + B, the straight line plot of 1/[AB] versus time indicates that the reaction is second-order with respect to AB. This means that the rate of reaction is proportional to the square of the concentration of AB, which is crucial for determining how concentrations change over time.
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Rate Law Fundamentals

Integrated Rate Law for Second-Order Reactions

For a second-order reaction, the integrated rate law is given by 1/[AB] = kt + 1/[AB]₀, where k is the rate constant, t is time, and [AB]₀ is the initial concentration. This equation allows us to calculate the concentration of AB at any time, which can then be used to find the concentrations of the products A and B, since they are produced in a 1:1 ratio.
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Second-Order Reactions

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this case, for every mole of AB that reacts, one mole of A and one mole of B are produced. Therefore, knowing the change in concentration of AB allows us to directly calculate the concentrations of A and B after a given time, based on the initial concentration and the amount reacted.
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Stoichiometry Concept
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This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms.

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