Question

For the reaction \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) at a certain temperature, \(K_{\text {eq }}\) is 1 . At equilibrium which of the following would you expect to find? (a) only \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) (b) mostly \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\) (c) about equal concentrations of \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\), compared to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\) (d) mostly \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\) (e) only \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\) Explain your answer briefly.

Short answer

You would expect to find about equal concentrations of CO and H2O, compared to CO2 and H2 (option c) because K_eq is 1.

Step-by-step solution

Understanding the Equilibrium Constant

The equilibrium constant, denoted as K_eq, of a reaction gives the ratio of the concentration of the products to reactants at equilibrium. When K_eq is 1, it means that the concentrations of the products and reactants are in equal measure at equilibrium.

Analyzing the Reaction

For the given reaction \( \mathrm{CO}(g) + \mathrm{H}_2 \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_2(g) + \mathrm{H}_2(g) \), since K_eq is equal to 1, it indicates that there will be comparable amounts of reactants and products at equilibrium.

Eliminating Incorrect Answers

Since the K_eq is 1 and suggests comparable amounts of both reactants and products, we can eliminate options (a), (d), and (e) which suggest an unequal balance of either reactants or products only.

Choosing the Correct Option

Between options (b) and (c), since K_eq is equal to 1, option (c) is correct because it suggests about equal concentrations of \( \mathrm{CO} \) and \( \mathrm{H}_2 \mathrm{O} \), compared to \( \mathrm{CO}_2 \) and \( \mathrm{H}_2 \) which aligns with the meaning of a K_eq value of 1.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. It’s important to understand that this doesn’t mean the reactants and products are present in equal amounts; rather, their concentrations have stabilized in a fixed proportion that doesn’t change.

For the reaction \(\mathrm{CO}(g) + \mathrm{H}_2 \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_2(g) + \mathrm{H}_2(g)\), reaching chemical equilibrium means that the rates at which \(\mathrm{CO}\) and \(\mathrm{H}_2\mathrm{O}\) are converted into \(\mathrm{CO}_2\) and \(\mathrm{H}_2\) are exactly balanced by the rates at which \(\mathrm{CO}_2\) and \(\mathrm{H}_2\) revert back to \(\mathrm{CO}\) and \(\mathrm{H}_2\mathrm{O}\).

At equilibrium, even though the concentrations remain constant, it is crucial to realize that the actual reactions are still occurring; they are dynamic and ongoing. This dynamic state is characterized by the equilibrium constant \(K_{\text{eq}}\), which in this particular reaction is given as 1, indicating a particular ratio of product to reactant concentration that will be maintained.

Reaction Quotient

The reaction quotient, \(Q\), is a measure that tells us how far away a system is from reaching equilibrium. It is calculated using the same formula as the equilibrium constant \(K_{\text{eq}}\), but instead of using the concentrations at equilibrium, \(Q\) uses the current concentrations of the reactants and products at any given point in time.

To understand its significance, let’s compare \(Q\) with \(K_{\text{eq}}\). If \(Q < K_{\text{eq}}\), the forward reaction is favored, and the concentrations of products will increase until equilibrium is reached. Conversely, if \(Q > K_{\text{eq}}\), the reverse reaction is favored, and the concentrations of reactants will increase until equilibrium is again established.

In our given reaction, if we started with arbitrary concentrations of reactants and products, we could calculate \(Q\) to predict which direction the reaction will proceed to reach equilibrium. However, since we know \(K_{\text{eq}} = 1\), at equilibrium, the value of \(Q\) will also be 1, indicating that the concentrations of reactants and products are in the exact ratio required to maintain equilibrium.

Le Chatelier's Principle

Le Chatelier's principle provides insight into how a chemical system at equilibrium responds to external changes, such as changes in concentration, pressure, or temperature. According to this principle, if a system at equilibrium is subjected to a disturbance, it will adjust itself in a way that counteracts the disturbance and establishes a new equilibrium.

For instance, if we added more \(\mathrm{CO}\) to the system in our example, Le Chatelier's principle predicts that the equilibrium would shift to the right, favoring the production of \(\mathrm{CO}_2\) and \(\mathrm{H}_2\) in order to reduce the concentration of \(\mathrm{CO}\). Similarly, if we were to decrease the volume of the container (which increases pressure), the equilibrium would shift towards the side with fewer gas molecules.

Le Chatelier's principle is a valuable tool in predicting the behavior of a system when unforeseen changes occur. It helps to understand not only how equilibrium can be restored, but also how the changes can be leveraged, for example, to increase the yield of a desired product in industrial chemical reactions.