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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

At a particular temperature, \(K_{\mathrm{p}}=1.00 \times 10^{2}\) for the reaction $$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \leftrightharpoons 2 \mathrm{HI}(g)$$ If 2.00 atm of \(\mathrm{H}_{2}(g)\) and 2.00 atm of \(\mathrm{I}_{2}(g)\) are introduced into a \(1.00-\mathrm{L}\) container, calculate the equilibrium partial pressures of all species.

The equilibrium constant \(K_{\mathrm{p}}\) for the reaction $$\mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{Cl}_{2}(g)$$ at \(700^{\circ} \mathrm{C}\) is \(0.76 .\) Determine the initial pressure of carbon tetrachloride that will produce a total equilibrium pressure of 1.20 \(\mathrm{atm}\) at \(700^{\circ} \mathrm{C} .\)

Consider the following reaction: $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ Amounts of \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}, \mathrm{H}_{2},\) and \(\mathrm{CO}_{2}\) are put into a flask so that the composition corresponds to an equilibrium position. If the CO placed in the flask is labeled with radioactive \(^{14} \mathrm{C}\) will \(^{14} \mathrm{C}\) be found only in \(\mathrm{CO}\) molecules for an indefinite period of time? Explain.

At \(35^{\circ} \mathrm{C}, K=1.6 \times 10^{-5}\) for the reaction $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$ If 2.0 moles of NO and 1.0 mole of \(\mathrm{Cl}_{2}\) are placed into a \(1.0-\mathrm{L}\) flask, calculate the equilibrium concentrations of all species.

Lexan is a plastic used to make compact discs, eyeglass lenses, and bullet- proof glass. One of the compounds used to make Lexan is phosgene \(\left(\mathrm{COCl}_{2}\right),\) an extremely poisonous gas. Phosgene decomposes by the reaction $$\mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)$$for which $K_{\mathrm{p}}=6.8 \times 10^{-9}\( at \)100^{\circ} \mathrm{C} .$ If pure phosgene at an initial pressure of 1.0 atm decomposes, calculate the equilibrium pressures of all species.
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