Question

For the reaction: \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\) at a given temperature, the equilibrium amount of \(\mathrm{CO}_{2}(\mathrm{~g})\) can be increased by (a) Adding a suitable catalyst (b) Adding an inert gas (c) Decreasing the volume of the container (d) Increasing the amount of \(\mathrm{CO}(\mathrm{g})\)

Short answer

Increasing the amount of \(\mathrm{CO}(\mathrm{g})\) (option d) increases \(\mathrm{CO}_{2}(\mathrm{~g})\).

Step-by-step solution

Analyze the Effect of Catalysts

Catalysts do not affect the equilibrium position of a reaction; they only increase the rate of the reaction by lowering the activation energy. Thus, adding a catalyst will not increase the amount of \( \mathrm{CO}_{2}(\mathrm{~g}) \) in equilibrium.

Consider the Addition of an Inert Gas

Adding an inert gas at constant volume does not change the partial pressures of the reactants or products, so it does not shift the equilibrium or affect the amount of \( \mathrm{CO}_{2}(\mathrm{~g}) \).

Evaluate the Effect of Decreasing the Volume

Decreasing the volume of the container increases the total pressure. According to Le Chatelier's principle, the system will shift to the side with fewer moles of gas to reduce pressure. Both sides of the reaction have 2 moles of gas (\(\mathrm{CO} + \mathrm{H}_{2}\) and \(\mathrm{CO}_{2} + \mathrm{H}_{2}\)), so a change in volume will not shift the equilibrium.

Determine the Effect of Increasing \(\mathrm{CO}(\mathrm{g})\)

Increasing the concentration of \(\mathrm{CO}(\mathrm{g})\) will shift the equilibrium to the right to consume the added \(\mathrm{CO}(\mathrm{g})\), according to Le Chatelier's principle. This will result in an increased production of \(\mathrm{CO}_{2}(\mathrm{~g})\).

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle offers a way to predict how a chemical equilibrium will respond to changes in concentration, temperature, or pressure. It tells us that if a system at equilibrium is subjected to a change in these conditions, the system will adjust by shifting its position to counteract the change and re-establish equilibrium.

Let's consider an increase in concentration as in our original exercise. Increasing the concentration of a reactant, such as CO(g), shifts the equilibrium towards the products. This is because the system tries to decrease the concentration of the added substance by converting it into products, thereby re-establishing equilibrium.

This principle applies similarly to temperature and pressure changes and helps predict how the system will adapt, ensuring a deeper understanding and better control in both laboratory and industrial chemical processes.

Catalysts in Chemistry

Catalysts are substances that speed up chemical reactions without being consumed in the process. They work by providing an alternative pathway for the reaction, which has a lower activation energy than the non-catalyzed pathway.

However, it's crucial to note that catalysts do not alter the equilibrium position of a chemical reaction. They simply help the reaction reach equilibrium faster. This means, in equilibrium reactions like the one in our exercise, a catalyst will not increase the concentration of CO2(g), but it does ensure the reaction reaches its equilibrium state more rapidly.

• By lowering the activation energy, catalysts effectively increase the rate at which equilibrium is achieved.
• They do not favor either the forward or reverse reaction more than the other, hence the equilibrium position remains unchanged.
• In industrial applications, catalysts are invaluable for improving efficiency without affecting yield.

Understanding catalysts helps in grasping why reaction speed changes but the amount of product at equilibrium does not.

Effect of Pressure on Equilibrium

When discussing pressure's effect on equilibrium, Le Chatelier’s principle again plays a key role. When the pressure of a system is changed by altering the volume of the container, the equilibrium will shift towards the side with fewer moles of gas to counteract the increase in pressure.

In the example given,

• Both sides of the reaction have two moles of gas (0(g) + H2O(g) ⇌ CO2(g) + H2(g)).
• This implies a change in pressure due to volume change will not favor either side because the number of gas moles remains equal.

Recognizing when pressure changes have no effect makes it easier to predict reaction behavior.

For reactions where the number of moles on each side is unequal, pressure changes can significantly shift the equilibrium, either favoring the formation of fewer moles of products or reactants.