Question

In what manner will increase of pressure affect the following equation: \(\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{~g})\) (a) Shift in the reverse direction (b) Shift in the forward direction (c) Increase in the yield of hydrogen (d) No effect

Short answer

(a) Shift in the reverse direction.

Step-by-step solution

Understanding the Reaction and the Effect of Pressure

The reaction is a gas-phase equilibrium involving solid carbon and gaseous water, carbon monoxide, and hydrogen. According to Le Chatelier's Principle, increasing pressure on a system at equilibrium will shift the equilibrium towards the side with fewer moles of gas.

Counting Moles of Gases on Each Side

The left side of the equilibrium, \( \mathrm{C}(\mathrm{s}) + \mathrm{H}_{2}\mathrm{O}(\mathrm{g}) \), has 1 mole of gas (\(\mathrm{H}_{2}\mathrm{O}\)) since carbon is a solid and isn't counted in the gas phase. The right side, \( \mathrm{CO}(\mathrm{g}) + \mathrm{H}_{2}(\mathrm{~g}) \), has 2 moles of gas (\(2\) moles: \(\mathrm{CO}\) and \(\mathrm{H}_2\)).

Analyzing the Effect of Pressure on the Equilibrium

Since increasing the pressure favors the side with fewer moles of gas, we compare the moles on each side. The left side (1 mole) has fewer moles of gas than the right side (2 moles). Thus, an increase in pressure will shift the reaction to the left, or in the reverse direction, to reduce the number of gas moles.

Key concepts

Gas-Phase Equilibrium

Gas-phase equilibrium refers to a state where the concentrations of reactants and products in a chemical reaction involving gases do not change over time. This balance occurs when the rate of the forward reaction, where reactants are converted into products, equals the rate of the reverse reaction, where products revert back to reactants. In a chemical equation, such as \[\mathrm{C} (\mathrm{s}) + \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g}) + \mathrm{H}_{2}(\mathrm{g})\], gas-phase equilibrium is reached involving gaseous water, carbon monoxide, and hydrogen, while carbon is a solid and does not directly participate in the gas phase dynamics.
The main aim in studying equilibrium is to understand how various factors like pressure, temperature, or concentration can shift the equilibrium, influencing the amount of products formed in the reaction.

Effect of Pressure on Equilibrium

The effect of pressure on equilibrium can be best explained using Le Chatelier's Principle. This principle states that if an external change such as pressure is applied to a system in equilibrium, the system will adjust itself to counteract the change and restore equilibrium.
When the pressure is increased, the equilibrium will shift towards the side with fewer moles of gas. This happens because by reducing the number of gas particles, the system decreases the pressure.

• In the given reaction, increasing the pressure would cause the equilibrium to favor the side with fewer gas moles, in this case, the left side where there is only 1 mole of gas.

Understanding how pressure affects equilibrium is crucial in industrial processes where gas reactions are common. It allows engineers to manipulate conditions to maximize product yield by shifting the equilibrium in the desired direction.

Moles of Gas in Equilibrium

The concept of moles of gas in equilibrium is essential for predicting how equilibrium will shift when external conditions such as pressure change. Moles refer to the quantity of substance involved in the reaction, and in the context of gas-phase reactions, it specifically pertains to the gaseous molecules.

• In the equation \(\mathrm{C} (\mathrm{s}) + \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g}) + \mathrm{H}_{2}(\mathrm{g})\), we focus on the gas molecules to determine equilibrium shifts.
• The left side has 1 mole of water vapor, whereas the right side has a total of 2 moles of gas, one from carbon monoxide and one from hydrogen.

This difference in moles between the two sides is critical in determining the effect of pressure changes on equilibrium, given that only gaseous components are considered when assessing these shifts.

Forward and Reverse Reactions in Equilibrium

In a chemical equilibrium, forward and reverse reactions occur simultaneously and at equal rates, maintaining the overall balance. The forward reaction converts reactants into products, while the reverse reaction converts those products back into reactants.
Equilibrium is dynamic, which means that even though concentrations remain constant, reactions continue to occur. Factors such as pressure can cause shifts in this dynamic balance:

• Increased pressure in the reaction \(\mathrm{C} (\mathrm{s}) + \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g}) + \mathrm{H}_{2}(\mathrm{g})\) would cause the reverse reaction to be favored as it results in fewer moles of gas.

By understanding the interplay between forward and reverse reactions, especially under changing conditions, it's possible to predict and control the outcome of chemical processes, optimizing them for industrial or laboratory purposes.