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Chapter 15: Problem 14

Consider the reaction \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D} .\) Assume that both the forward reaction and the reverse reaction are elementary processes and that the value of the equilibrium constant is very large. (a) Which species predominate at equilibrium, reactants or products? (b) Which reaction has the larger rate constant, the forward or the reverse? Explain.

Short Answer

Expert verified
(a) At equilibrium, products (C and D) predominate due to the very large value of the equilibrium constant. (b) The forward reaction (A + B -> C + D) has the larger rate constant, as K = k_forward / k_reverse, and a large K indicates a larger k_forward compared to k_reverse.

Step by step solution

01

(a) Identifying the predominant species at equilibrium

The equilibrium constant (K) for a given reaction is defined as the ratio of the concentrations of products to reactants at equilibrium. Since we are given that the equilibrium constant is very large, it means that the concentration of products (C and D) is much higher than the concentration of reactants (A and B) at equilibrium. Therefore, the products (C and D) predominate at equilibrium.
02

(b) Understanding the relationship between equilibrium constant and rate constants

The equilibrium constant (K) is related to the rate constants of the forward (k_forward) and reverse (k_reverse) reactions by the following equation: K = k_forward / k_reverse. This equation tells us that if the equilibrium constant is very large, the forward rate constant must be much larger than the reverse rate constant since K is the ratio of k_forward to k_reverse.
03

(b) Determining which reaction has the larger rate constant

Based on our understanding of the relationship between the equilibrium constant and the rate constants, we can conclude that the forward reaction (A + B -> C + D) has the larger rate constant since K is very large. This means that the forward reaction is faster than the reverse reaction, ultimately leading to a higher concentration of products (C and D) at equilibrium.

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Most popular questions from this chapter

At \(100^{\circ} \mathrm{C}, K_{c}=0.078\) for the reaction $$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$$ In an equilibrium mixture of the three gases, the concentrations of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) and \(\mathrm{SO}_{2}\) are \(0.108 \mathrm{M}\) and \(0.052 \mathrm{M}\), respectively. What is the partial pressure of \(\mathrm{Cl}_{2}\) in the equilibrium mixture?

Consider the reaction \(\mathrm{IO}_{4}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\mathrm{H}_{4} \mathrm{IO}_{6}^{-}(a q) ; K_{c}=3.5 \times 10^{-2} .\) If you start with \(25.0 \mathrm{~mL}\) of a \(0.905 \mathrm{M}\) solution of \(\mathrm{NaIO}_{4}\), and then dilute it with water to \(500.0 \mathrm{~mL}\), what is the concentration of \(\mathrm{H}_{4} \mathrm{IO}_{6}^{-}\) at equilibrium?

The equilibrium \(2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\) is estab- lished at \(500 \mathrm{~K}\). An equilibrium mixture of the three gases has partial pressures of 0.095 atm, 0.171 atm, and 0.28 atm for \(\mathrm{NO}, \mathrm{Cl}_{2},\) and \(\mathrm{NOCl}\), respectively. (a) Calculate \(K_{p}\) for this reaction at \(500.0 \mathrm{~K}\). (b) If the vessel has a volume of \(5.00 \mathrm{~L}\) calculate \(K_{c}\) at this temperature.

For the reaction \(\mathrm{I}_{2}+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{IBr}(g), K_{c}=280\) at \(150^{\circ} \mathrm{C}\). Suppose that \(0.500 \mathrm{~mol}\) IBr in a 2.00 - \(\mathrm{L}\) flask is allowed to reach equilibrium at \(150^{\circ} \mathrm{C}\). What are the equilibrium concentrations of \(\mathrm{IBr}, \mathrm{I}_{2}\), and \(\mathrm{Br}_{2}\) ?

A sample of nitrosyl bromide (NOBr) decomposes according to the equation $$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ An equilibrium mixture in a \(5.00-\mathrm{L}\) vessel at \(100{ }^{\circ} \mathrm{C}\) contains \(3.22 \mathrm{~g}\) of \(\mathrm{NOBr}, 3.08 \mathrm{~g}\) of \(\mathrm{NO},\) and \(4.19 \mathrm{~g}\) of \(\mathrm{Br}_{2}\) (a) Calculate \(K_{c}\) (b) What is the total pressure exerted by the mixture of gases? (c) What was the mass of the original sample of NOBr?
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