Ch.14 - Chemical Kinetics

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.14 - Chemical Kinetics

Problem 127c

Chapter 14, Problem 127c

Consider the reversible, first-order interconversion of two molecules A and B: where k_f = 3.0⨉10-3 s^-1 is the rate constant for the forward reaction and kr = 1.0⨉10^-3 s^-1 is the rate constant for the reverse reaction. We'll see in Chapter 15 that a reaction does not go to completion but instead reaches a state of equilibrium with comparable concentrations of reactants and products if the rate constants k_f and k_r have comparable values.
(c) What are the relative concentrations of B and A when the rates of the forward and reverse reactions become equal?

Verified step by step guidance

Identify that the system is at equilibrium when the rates of the forward and reverse reactions are equal.

Write the rate expressions for the forward and reverse reactions: Rate_forward = k_f[A] and Rate_reverse = k_r[B].

Set the rate expressions equal to each other to represent the equilibrium condition: k_f[A] = k_r[B].

Rearrange the equation to solve for the ratio of concentrations: [B]/[A] = k_f/k_r.

Substitute the given rate constants into the equation: [B]/[A] = (3.0 \times 10^{-3} \text{ s}^{-1}) / (1.0 \times 10^{-3} \text{ s}^{-1}).

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Key Concepts

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

Equilibrium in Chemical Reactions

Equilibrium in a chemical reaction occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. At this point, the system is in a dynamic state where the conversion between reactants and products continues, but their concentrations remain unchanged over time.

Rate Constants (k_f and k_r)

Rate constants, denoted as k_f for the forward reaction and k_r for the reverse reaction, quantify the speed of each reaction. The values of these constants are crucial in determining the position of equilibrium; when k_f equals k_r, the system reaches equilibrium, and the concentrations of A and B can be calculated based on these constants.

Concentration Ratios at Equilibrium

At equilibrium, the ratio of the concentrations of products to reactants can be expressed using the rate constants. Specifically, the ratio of concentrations of B to A at equilibrium is given by the equation [B]/[A] = k_f/k_r. This relationship allows for the determination of relative concentrations when the rates of the forward and reverse reactions are equal.

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Related Practice

Textbook Question

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl^-). The products are chloride ion and hypoiodite ion (OI^-).

(d) Propose a mechanism that is consistent with the rate law, and express the rate constant in terms of the rate constants for the elementary steps in your mechanism. (Hint: Transfer of an H⁺ ion between H₂O and OCl^- is a rapid reversible reaction.)

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Textbook Question

Consider the reversible, first-order interconversion of two molecules A and B: where k_f = 3.0⨉10-3 s^-1 is the rate constant for the forward reaction and kr = 1.0⨉10^-3 s^-1 is the rate constant for the reverse reaction. We'll see in Chapter 15 that a reaction does not go to completion but instead reaches a state of equilibrium with comparable concentrations of reactants and products if the rate constants k_f and k_r have comparable values.

(a) What are the rate laws for the forward and reverse reactions?

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Textbook Question

(b) Draw a qualitative graph that shows how the rates of the forward and reverse reactions vary with time.

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Textbook Question

Assume that you are studying the first-order conversion ofa reactant X to products in a reaction vessel with a constantvolume of 1.000 L. At 1 p.m., you start the reactionat 25 °C with 1.000 mol of X. At 2 p.m., you find that0.600 mol of X remains, and you immediately increase thetemperature of the reaction mixture to 35 °C. At 3 p.m.,you discover that 0.200 mol of X is still present. You wantto finish the reaction by 4 p.m. but need to continue it untilonly 0.010 mol of X remains, so you decide to increase thetemperature once again. What is the minimum temperaturerequired to convert all but 0.010 mol of X to productsby 4 p.m.?

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Textbook Question

The half-life for the first-order decomposition of N2O4 is 1.3 * 10-5 s. N2O41g2S 2 NO21g2 If N2O4 is introduced into an evacuated flask at a pressure of 17.0 mm Hg, how many seconds are required for the pressure of NO2 to reach 1.3 mm Hg?

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Textbook Question

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H₃O⁺ by OH^-, which has a second-order rate constant of 1.3⨉10¹¹ M^-1 s^-1 at 25 °C. (a) If equal volumes of 2.0 M HCl and 2.0 M NaOH are mixed instantaneously, how much time is required for 99.999% of the acid to be neutralized?

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