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Chapter 14: Problem 111

Consider the potential energy diagrams for two types of reactions \(\mathrm{A} \rightleftharpoons \mathrm{B}\). In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant? (d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture.

Short Answer

Expert verified
(a) A catalyst would increase both the forward and reverse rates of the reaction. (b) A catalyst would not affect the energies of the reactant and product, it only lowers the activation energy. (c) An increase in temperature would cause the equilibrium constant to increase for endothermic reactions and decrease for exothermic reactions. (d) Since the equilibrium constant is only influenced by temperature and catalysts only change the rate at which equilibrium is achieved but not the energies of the reactants or products, the equilibrium constant remains unchanged when a catalyst is added.

Step by step solution

01

Understand the Effect of a Catalyst on Reaction Rates

A catalyst increases both the forward and reverse rates of a reaction by decreasing the activation energy required. That is to say, a catalyst speeds up the rates of the forward and reverse reactions equally, without preferring one direction over the other.
02

Understand the Effect of a Catalyst on Energies of Reactants and Products

A catalyst does not affect the energies of the reactants or products. It only lowers the activation energy, which is the energy barrier that must be overcome for the reaction to occur. The energies of the reactants and products, and thus the ΔG of the reaction, remain the same.
03

Understand the Effect of Temperature on Equilibrium Constant

An increase in temperature will affect the equilibrium constant depending on the endothermicity or exothermicity of the reaction. For an endothermic reaction (ΔH > 0), increasing temperature will increase the equilibrium constant (K), shifting the equilibrium to the right towards the products. For an exothermic reaction (ΔH < 0), increasing temperature will decrease the equilibrium constant, shifting the equilibrium to the left towards the reactants.
04

Prove That the Equilibrium Constant Remains Unchanged When a Catalyst is Added

The equilibrium constant (K) is only influenced by temperature. It is defined by the ratio of the concentrations of the products to the reactants, each raised to a power equal to the coefficient in the balanced chemical equation. Adding a catalyst doesn't affect this ratio at equilibrium because catalysts do not change the energies of the reactants or products, they only change the rate at which equilibrium is achieved. Hence, the equilibrium constant remains unchanged when a catalyst is added.

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Most popular questions from this chapter

Give an example of a multiple equilibria reaction.

Explain Le Châtelier's principle. How can this principle help us maximize the yields of reactions?

Consider the following reaction at \(1600^{\circ} \mathrm{C}\). $$\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)$$ When 1.05 moles of \(\mathrm{Br}_{2}\) are put in a 0.980 - \(\mathrm{L}\) flask, 1.20 percent of the \(\mathrm{Br}_{2}\) undergoes dissociation. Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.

Consider the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ At \(430^{\circ} \mathrm{C},\) an equilibrium mixture consists of 0.020 mole of \(\mathrm{O}_{2}, 0.040\) mole of \(\mathrm{NO},\) and 0.96 mole of \(\mathrm{NO}_{2}\). Calculate \(K_{P}\) for the reaction, given that the total pressure is 0.20 atm.

The vapor pressure of mercury is \(0.0020 \mathrm{mmHg}\) at \(26^{\circ} \mathrm{C}\). (a) Calculate \(K_{\mathrm{c}}\) and \(K_{P}\) for the process \(\mathrm{Hg}(l) \rightleftharpoons \mathrm{Hg}(g) .\) (b) A chemist breaks a thermometer and spills mercury onto the floor of a laboratory measuring \(6.1 \mathrm{~m}\) long, \(5.3 \mathrm{~m}\) wide, and \(3.1 \mathrm{~m}\) high. Calculate the mass of mercury (in grams) vaporized at equilibrium and the concentration of mercury vapor in \(\mathrm{mg} / \mathrm{m}^{3}\). Does this concentration exceed the safety limit of \(0.05 \mathrm{mg} / \mathrm{m}^{3} ?\) (Ignore the volume of furniture and other objects in the laboratory.)
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