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Chapter 15: Problem 63

How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant (b) removal of a product, (c) decrease in the volume, (d) decrease in the temperature, (e) addition of a catalyst?

Short Answer

Expert verified
In summary, for a gas-phase exothermic reaction, the value of the equilibrium constant (K) is affected only by changes in temperature. A decrease in temperature will result in a decrease of the equilibrium constant value. The removal or addition of reactants, products, or catalysts, and changes in volume do not affect the equilibrium constant value.

Step by step solution

01

1. Understanding the equilibrium constant

The equilibrium constant (K) is a value that is related to the rate constants for the forward and reverse reactions in a chemical system at equilibrium. It is calculated as the ratio of the product concentrations to the reactant concentrations, with each concentration raised to the power of its respective coefficient in the balanced chemical equation. For a general exothermic reaction, represented as: \(aA + bB \rightleftharpoons cC + dD \) The equilibrium constant is given by: \(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\) Now, let's see how the different changes in the system affect the equilibrium constant.
02

2. Effect of removal of a reactant (a)

Removing a reactant will decrease its concentration in the system. According to Le Chatelier's principle, the system will shift to counteract the disturbance and restore the equilibrium. In this case, the system will shift towards the reactants to increase the concentration of the removed reactant. However, the equilibrium constant value remains unaffected as it is only dependent on the temperature of the system.
03

3. Effect of removal of a product (b)

Similarly, removing a product will decrease its concentration in the system. Again, according to Le Chatelier's principle, the system will shift to counteract the disturbance. In this case, the system will shift towards the products to increase the concentration of the removed product. The equilibrium constant value remains unaffected as it depends only on the temperature.
04

4. Effect of decrease in volume (c)

A decrease in volume will increase the pressure of the system. According to Le Chatelier's principle, the system will respond by shifting in the direction that reduces pressure. In this case, it will shift towards the side with fewer moles of gas. However, the equilibrium constant value remains unaffected as it depends only on the temperature.
05

5. Effect of decrease in temperature (d)

Since the reaction is exothermic, a decrease in temperature will favor the forward reaction, as it releases heat to the surroundings. As a result, the equilibrium will shift towards the products. This change in temperature will affect the equilibrium constant value. In this case, decreasing the temperature will cause the equilibrium constant value to decrease as well.
06

6. Effect of addition of a catalyst (e)

Adding a catalyst to the system will increase the rate of both the forward and reverse reactions without affecting the equilibrium concentrations of the reactants or products. As a result, the system will reach equilibrium more quickly, but the equilibrium constant value will remain unaffected. In summary, the value of the equilibrium constant for a gas-phase exothermic reaction is only affected by changes in temperature (decreasing temperature will decrease the equilibrium constant). Removal or addition of reactants, products, or catalysts, and changes in volume do not affect the equilibrium constant value.

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Most popular questions from this chapter

Consider \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g),\) \(\Delta H=-904.4 \mathrm{~kJ} .\) How does each of the following changes affect the yield of \(\mathrm{NO}\) at equilibrium? Answer increase, decrease, or no change: (a) increase \(\left[\mathrm{NH}_{3}\right] ;(\mathbf{b})\) increase \(\left[\mathrm{H}_{2} \mathrm{O}\right] ;(\mathrm{c})\) decrease \(\left[\mathrm{O}_{2}\right]\) (d) decrease the volume of the container in which the reaction occurs; (e) add a catalyst; (f) increase temperature.

Can the equilibrium constant ever be a negative number? Explain.

Suppose that the gas-phase reactions \(\mathrm{A} \longrightarrow \mathrm{B}\) and \(\mathrm{B} \longrightarrow \mathrm{A}\) are both elementary processes with rate constants of \(4.7 \times 10^{-3} \mathrm{~s}^{-1}\) and \(5.8 \times 10^{-1} \mathrm{~s}^{-1}\), respectively. (a) What is the value of the equilibrium constant for the equilibrium \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g) ?\) (b) Which is greater at equilibrium, the partial pressure of \(\mathrm{A}\) or the partial pressure of \(\mathrm{B}\) ? Explain.

(a) How does a reaction quotient differ from an equilibrium constant? (b) If \(Q_{c}

Consider the following equilibrium for which \(\Delta H<0\) $$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$ How will each of the following changes affect an equilibrium mixture of the three gases: (a) \(\mathrm{O}_{2}(g)\) is added to the system; (b) the reaction mixture is heated; (c) the volume of the reaction vessel is doubled; (d) a catalyst is added to the mixture; (e) the total pressure of the system is increased by adding a noble gas; (f) \(\mathrm{SO}_{3}(g)\) is removed from the system?
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