Question

Consider the equilibrium \(\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\) \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\). (a) If the partial pressure of \(\mathrm{CO}_{2}\) is increased, what happens to the partial pressure of \(\mathrm{CH}_{4}\) ? (b) If the partial pressure of \(\mathrm{CH}_{4}\) is decreased, what happens to the partial pressure of \(\mathrm{CO}_{2}\); (c) If the concentration of \(\mathrm{CH}_{4}\) is increased, what happens to the equilibrium constant for the reaction? (d) If the concentration of \(\mathrm{H}_{2} \mathrm{O}\) is decreased, what happens to the concentration of \(\mathrm{CO}_{2}\) ?

Short answer

(a) The partial pressure of CH4 will increase. (b) The partial pressure of CO2 will increase. (c) The equilibrium constant K will remain unchanged. (d) The concentration of CO2 will increase.

Step-by-step solution

Analyzing the Effect of Increasing CO2 Pressure

To determine the effect of increasing the partial pressure of CO2 on the partial pressure of CH4, Le Chatelier's principle is used. The principle states that if a change is applied to a system at equilibrium, the system will adjust in such a way as to counteract that change. Increasing CO2 will shift the equilibrium to the left, increasing the partial pressure of CH4.

Analyzing the Effect of Decreasing CH4 Pressure

According to Le Chatelier's principle, decreasing the partial pressure of CH4 will shift the equilibrium to the right to counter the change, which will increase the partial pressure of CO2.

Assessing the Impact on Equilibrium Constant with Increased CH4 Concentration

The equilibrium constant, K, is solely dependent on the temperature for a given reaction. Changes in the concentration of reactants or products at constant temperature do not affect the value of K.

Predicting the Impact of Decreasing H2O Concentration on CO2 Concentration

Decreasing the concentration of H2O will drive the reaction to shift to the right according to Le Chatelier's principle, thereby increasing the concentration of CO2 to re-establish equilibrium.

Key concepts

Chemical Equilibrium

In the study of chemistry, the state of chemical equilibrium is fundamental when dealing with reactions. It refers to the point in a reaction at which the rate of the forward reaction equals the rate of the reverse reaction. At this juncture, the concentrations of the reactants and products remain constant over time, but it's crucial to note that reactions still occur; they're just in a state of dynamic balance.

Take, for example, the reaction of methane with oxygen to form carbon dioxide and water. If this system reaches equilibrium, it doesn't mean that methane and oxygen stop reacting. Instead, as methane and oxygen molecules collide and react to form carbon dioxide and water, an equal amount of carbon dioxide and water molecules convert back into methane and oxygen at the same time, keeping the overall concentrations stable.

Equilibrium Constant

The equilibrium constant, represented by K, is a value that expresses the ratio of the concentrations of the products to the reactants at equilibrium, each raised to the power of their respective coefficients in the balanced equation. Mathematically, for the reaction \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant \(K\) is defined by the expression \[K = \frac{{[C]^c [D]^d}}{{[A]^a [B]^b}}\].

The value of \(K\) is constant for a given reaction at a particular temperature and does not change unless the temperature changes. This means that irrespective of the initial amounts of reactants or products, the reaction will adjust itself until the same ratio defined by the equilibrium constant is achieved.

Reaction Quotient

The reaction quotient, or \(Q\), is a measurement that serves a similar function to the equilibrium constant but applies to any point in time during the reaction, not just at equilibrium. It's calculated exactly the same way as the equilibrium constant, using the current concentrations of the reactants and products.

By comparing the reaction quotient \(Q\) with the equilibrium constant \(K\), we can predict the direction in which the reaction will proceed to reach equilibrium. If \(Q < K\), the forward reaction is favored, and the reaction will proceed to the right. Conversely, if \(Q > K\), the reverse reaction is favored, and it will shift to the left. When \(Q = K\), the system is at equilibrium, and no net change will occur.

Partial Pressure

In the context of gases, the term partial pressure is used to describe the pressure that each gas in a mixture would exert if it alone occupied the entire volume of the mixture at the same temperature. Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.

Changing the partial pressure of one of the reactants or products in a gaseous equilibrium system will shift the equilibrium position according to Le Chatelier's principle. Increased partial pressure of a product will typically shift the equilibrium towards the reactants (to the left), and vice versa: a decrease in partial pressure of a reactant will shift the equilibrium towards the products (to the right). The changes in partial pressures will cause shifts until a new equilibrium point is established, where the pressures once again align with the equilibrium constant.