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Chapter 13: Problem 15

Suppose a reaction has the equilibrium constant \(K=1.3 \times 10^{8} .\) What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached? Is this reaction likely to be a good source of the products?

Short Answer

Expert verified
The given equilibrium constant, \(K = 1.3 \times 10^8\), is significantly greater than 1, indicating that the reaction is product-favored. At equilibrium, the concentration of products will be much greater than that of reactants. Therefore, this reaction is likely to be a good source of the products.

Step by step solution

01

Understand the meaning of the equilibrium constant

The equilibrium constant (K) is a dimensionless value that helps us determine the extent of a reaction at equilibrium, i.e., the relative concentrations of products and reactants. A reaction can be written in the form: \(aA + bB \rightleftharpoons cC + dD\) At equilibrium, the constant K is defined as: \[K = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b}\] Where [A], [B], [C], and [D] are the molar concentrations of the reactants (A and B) and products (C and D) at equilibrium. If K >> 1, the reaction is product-favored, meaning the concentration of products is much greater than that of reactants at equilibrium. If K << 1, the reaction is more reactant-favored.
02

Interpret the given equilibrium constant

In this exercise, we are given the equilibrium constant as \(K = 1.3 \times 10^8\). This value is significantly greater than 1, meaning the reaction is product-favored. Once equilibrium is reached, the concentration of products will be much greater than that of reactants.
03

Determine the suitability of the reaction as a product source

Since K >> 1, the reaction is product-favored, and the concentration of products at equilibrium will be much greater than that of reactants. This indicates the system would likely be a good source of the products. The large value of K suggests that the products are largely favored, so if the reactants were introduced into the system, the equilibrium would shift to produce more products.

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Most popular questions from this chapter

In a solution with carbon tetrachloride as the solvent, the compound \(\mathrm{VCl}_{4}\) undergoes dimerization: $$2 \mathrm{VCl}_{4} \rightleftharpoons \mathrm{V}_{2} \mathrm{Cl}_{8}$$ When 6.6834 g \(\mathrm{VCl}_{4}\) is dissolved in 100.0 \(\mathrm{g}\) carbon tetrachloride, the freezing point is lowered by \(5.97^{\circ} \mathrm{C}\) . Calculate the value of the equilibrium constant for the dimerization of \(\mathrm{VCl}_{4}\) at this temperature. (The density of the equilibrium mixture is \(1.696 \mathrm{g} / \mathrm{cm}^{3},\) and \(K_{\mathrm{f}}=29.8^{\circ} \mathrm{C} \mathrm{kg} / \mathrm{mol}\) for \(\mathrm{CCl}_{4} . )\)

Predict the shift in the equilibrium position that will occur for each of the following reactions when the volume of the reaction container is increased. a. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) b. \(\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\) c. \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) d. \(\mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)\) e. \(\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\)

Le Chatelier's principle is stated (Section 13.7\()\) as follows: "If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change." The system \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) is used as an example in which the addition of nitrogen gas at equilibrium results in a decrease in \(\mathrm{H}_{2}\) concentration and an increase in \(\mathrm{NH}_{3}\) concentration. In the experiment the volume is assumed to be constant. On the other hand, if \(\mathrm{N}_{2}\) is added to the reaction system in a container with a piston so that the pressure can be held constant, the amount of \(\mathrm{NH}_{3}\) actually could decrease and the concentration of \(\mathrm{H}_{2}\) would increase as equilibrium is reestablished. Explain how this can happen. Also, if you consider this same system at equilibrium, the addition of an inert gas, holding the pressure constant, does affect the equilibrium position. Explain why the addition of an inert gas to this system in a rigid container does not affect the equilibrium position.

At a particular temperature, 12.0 moles of \(\mathrm{SO}_{3}\) is placed into a 3.0 -L rigid container, and the \(\mathrm{SO}_{3}\) dissociates by the reaction $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$At equilibrium, 3.0 moles of \(\mathrm{SO}_{2}\) is present. Calculate \(K\) for this reaction.

In which direction will the position of the equilibrium $$2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g)$$ be shifted for each of the following changes? a. \(\mathrm{H}_{2}(g)\) is added. b. \(\mathrm{I}_{2}(g)\) is removed. c. \(\operatorname{HI}(g)\) is removed. d. In a rigid reaction container, some Ar(g) is added. e. The volume of the container is doubled. f. The temperature is decreased (the reaction is exothermic).
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