Methanol can be prepared from carbon monoxide and hydrogen at high temperature and pressure in the presence of a suitable catalyst. (a) Write the expression for the equilibrium constant \(\left(K_{c}\right)\) for the reversible reaction \(2 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) \quad \Delta H=-90.2 \mathrm{kJ}\) (b) What will happen to the concentrations of \(\mathrm{H}_{2}, \mathrm{CO},\) and \(\mathrm{CH}_{3} \mathrm{OH}\) at equilibrium if more \(\mathrm{H}_{2}\) is added? (c) What will happen to the concentrations of \(\mathrm{H}_{2}, \mathrm{CO},\) and \(\mathrm{CH}_{3} \mathrm{OH}\) at equilibrium if CO is removed? (d) What will happen to the concentrations of \(\mathrm{H}_{2}, \mathrm{CO},\) and \(\mathrm{CH}_{3} \mathrm{OH}\) at equilibrium if \(\mathrm{CH}_{3} \mathrm{OH}\) is added? (e) What will happen to the concentrations of \(\mathrm{H}_{2}, \mathrm{CO},\) and \(\mathrm{CH}_{3} \mathrm{OH}\) at equilibrium if the temperature of the system is increased?

Le Chatelier's Principle is a fundamental concept in chemistry that helps predict the effect of changing conditions on a chemical equilibrium. When a system at equilibrium is disturbed by a change in temperature, pressure, volume, or concentration, the system will adjust to counteract the change and re-establish equilibrium.

For example, increasing the concentration of reactants or decreasing the concentration of products will typically shift the equilibrium towards the product side, as the system attempts to use up the added reactants or replenish the removed products. Conversely, increasing the concentration of products or removing reactants shifts the equilibrium towards the reactants to offset the disturbance.

This principle is vividly illustrated in the production of methanol where modifications to reactant and product concentrations cause shifts in the equilibrium position to re-balance the system. Understanding how to apply Le Chatelier's Principle is essential for controlling chemical reactions in industrial processes and laboratory settings.

The equilibrium constant, represented by the symbol \(K_c\), is a ratio that reflects the concentrations of products and reactants at chemical equilibrium. The expression for \(K_c\) is based on a balanced chemical equation and is calculated by dividing the product of the concentrations of the products, each raised to the power of its coefficient, by the product of the concentrations of the reactants, similarly raised. The value of \(K_c\) is constant at a given temperature for a reversible reaction.

\[K_c = \frac{\text{[Products]}^{\text{coefficients}}}{\text{[Reactants]}^{\text{coefficients}}}\]
It's important to note that \(K_c\) does not involve solids or pure liquids as their concentrations do not change. In the methanol synthesis example, an increase in the value of \(K_c\) indicates a reaction favoring methanol production, while a decrease suggests a shift towards the reactants. This helps predict which way the equilibrium will shift under different conditions, which is essential for optimizing chemical processes.

The reaction quotient, denoted \(Q_c\), serves as a predictive tool for the direction of a reaction's shift towards equilibrium. It is calculated using the same formula as the equilibrium constant \(K_c\), but with the initial concentrations of the reactants and products rather than their equilibrium concentrations.

\[Q_c = \frac{\text{[Products]}^{\text{coefficients}}}{\text{[Reactants]}^{\text{coefficients}}}\]
By comparing \(Q_c\) to \(K_c\), one can determine the reaction's direction. If \(Q_c < K_c\), the reaction will proceed forward to produce more products. If \(Q_c > K_c\), the reaction will go in the reverse direction to generate more reactants. When \(Q_c = K_c\), the system is at equilibrium. This quantitative analysis, in light of Le Chatelier's Principle, empowers students and chemists to predict and control the outcomes of reactions.

Exothermic reactions are chemical processes that release energy, usually in the form of heat, to the surroundings. These reactions are characterized by having negative enthalpy changes \(\Delta H\), indicating that the energy of the products is lower than the energy of the reactants. In the context of equilibrium, the concept of exothermicity has significant implications.

According to Le Chatelier's Principle, an increase in temperature for an exothermic reaction will result in a shift of the equilibrium towards the reactants to absorb the added heat. Consequently, for the methanol-producing reaction shown in the exercise, a temperature increase will cause a decrease in methanol concentration as the equilibrium adjusts in favor of the reverse reaction.

This relationship between temperature and equilibrium is crucial in industrial applications where controlling the amount of produced substances is vital. Chemical engineers must carefully manage temperatures to optimize yields in exothermic processes like methanol production.