91Ó°ÊÓ

The concept of the equilibrium constant, denoted as \( K_c \), is crucial for understanding chemical equilibria. It provides a quantitative measure of the position of equilibrium in a reversible reaction. In simple terms, \( K_c \) reflects how much product and reactant are present when the system has reached equilibrium. If \( K_c \) is large, it suggests a lot of products at equilibrium; if small, more reactants remain.

For the reaction \( \mathrm{CO(g)} + \mathrm{H}_2\mathrm{O(g)} \rightleftharpoons \mathrm{CO}_2\mathrm{(g)} + \mathrm{H}_2\mathrm{(g)} \), the given equilibrium constant is \( 2.64 \times 10^{-3} \) at 2300 K. This value tells us that, at equilibrium, the system will have a much larger concentration of reactants compared to products. These calculations revolve around the balanced equation, as \( K_c \) is derived directly from it.

To calculate \( K_c \), use the expression:\[ K_c = \frac{[\text{CO}_2][\text{H}_2]}{[\text{CO}][\text{H}_2\text{O}]} \]Here, brackets represent molar concentrations of the respective gases at equilibrium.

The reaction quotient, \( Q \), is a tool used to determine the direction in which a reversible reaction will proceed to reach equilibrium. Like the equilibrium constant, \( Q \) is calculated using the same expression as \( K_c \), but with initial or non-equilibrium concentrations:

\[ Q = \frac{[\text{CO}_2][\text{H}_2]}{[\text{CO}][\text{H}_2\text{O}]} \]

By comparing \( Q \) to \( K_c \):

• If \( Q < K_c \), the system will shift to the right, forming more products.
• If \( Q > K_c \), the system will shift to the left, forming more reactants.
• If \( Q = K_c \), the system is at equilibrium.

In our scenario, initially, \( [\text{CO}_2] = 0 \) M and \( [\text{H}_2] = 0 \) M, thus \( Q = 0 \), which is less than \( K_c \), indicating that the reaction will produce more CO2 and H2 to reach equilibrium.

Le Chatelier's Principle is a fundamental concept in chemistry used to predict the behavior of a system at equilibrium when it is subjected to an external change, such as concentration, temperature, or pressure. This principle states that if a system at equilibrium is disturbed, the system will adjust itself to counteract the disturbance and restore a new equilibrium.

In the exercise above, when additional 1.00 mol of CO and \( \text{H}_2\text{O} \) are added, the system is no longer in equilibrium. According to Le Chatelier's Principle, the system will respond by shifting the equilibrium to the right, producing more \( \text{CO}_2 \) and \( \text{H}_2 \), to reduce the effect of the increase in reactants.

This adjustment continues until a new equilibrium is established, where the concentrations align with the constant \( K_c \). This highlights how dynamic equilibria can adjust to changes, always striving to maintain balance.