91Ó°ÊÓ

The equilibrium constant, often denoted as \( K \), is a vital concept in chemical equilibrium. It expresses the ratio of the concentration of the products to the concentration of the reactants, each raised to the power of their respective stoichiometric coefficients. In the context of gas-phase reactions, this ratio is based on partial pressures. The equilibrium constant provides valuable insight into the position of equilibrium in a chemical reaction. A larger \( K \) value indicates a greater concentration of products at equilibrium, signifying that the reaction favors the formation of products. Conversely, a smaller \( K \) value suggests a predominance of reactants, showing that the equilibrium does not substantially move towards the products. In the given problem, the equilibrium constant \( K \) was calculated using the pressures of \( \text{CO}_2 \) and \( \text{CO} \). The calculated value was \( 1.8 \, \text{atm} \), suggesting that the reaction at \( 1000 \, \text{K} \) moderately favors the formation of carbon monoxide from carbon dioxide.

Stoichiometry is a fundamental concept in chemistry that deals with measuring the quantities of reactants and products in a chemical reaction. It involves using the balanced chemical equation to determine the ratio in which substances react and are produced. For the given reaction: \[ \text{CO}_2(g) + C(s) \rightleftharpoons 2\text{CO}(g) \]the stoichiometric coefficients are vital for calculations. Each molecule of \( \text{CO}_2 \) produces two molecules of \( \text{CO} \). This 1:2 stoichiometric relationship is crucial in determining the pressure changes in equilibrium calculations. When the pressure of \( \text{CO}_2 \) decreases by \( x \, \text{atm} \) at equilibrium, the pressure of \( \text{CO} \) increases by \( 2x \, \text{atm} \). Stoichiometry helps in calculating these pressure changes, enabling us to write an expression for the total pressure which was used to solve for \( x \).

Partial pressure is a term that describes the contribution each gas in a mixture of gases makes to the total pressure. It is directly related to the concentration of that gas in the mixture. In the context of the provided exercise, we were initially given that the partial pressure of \( \text{CO}_2 \) was 0.5 atm. As the reaction progresses towards equilibrium, the partial pressures of the gases change. The change in partial pressures is calculated based on the stoichiometric ratios and the total equilibrium pressure. In this problem, determining the individual partial pressures of \( \text{CO} \) and \( \text{CO}_2 \) allowed for the proper calculation of the equilibrium constant \( K \). Using partial pressures in the \( K \) expression is standard practice for gas-phase reactions, since it directly relates to the concentrations of gases.

Gas-phase reactions are chemical processes that involve reactants and products in the gaseous state. These reactions can be particularly sensitive to changes in conditions like temperature and pressure, as gases typically vary significantly under different conditions. For gas-phase reactions, equilibrium calculations often involve partial pressures, as seen in the given exercise. The reaction between \( \text{CO}_2 \) and graphite to produce \( \text{CO} \) occurs in the gas phase, and its behavior in terms of equilibrium follows the laws of gases. Understanding the principles of gas-phase reactions is crucial for correctly evaluating how reactants transform into products and how equilibrium states are achieved. Variations in pressure and temperature can shift the equilibrium position, affecting the quantities of products and reactants at equilibrium. By thoroughly understanding how to apply these concepts, one can predict and control the outcomes of gas-phase reactions, as demonstrated by the calculation of the equilibrium constant in this example.