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 (1) adding a suitable catalyst (2) adding an inert gas (3) decreasing the volume of containcr (4) increasing the amount of \(\mathrm{CO}\)

Short answer

The equilibrium amount of \( \text{CO}_{2} \) can be increased by increasing the amount of \( \text{CO} \) (Option 4).

Step-by-step solution

Identify the Reaction and Concept

The reaction given is \(\text{CO}(\text{g}) + \text{H}_{2}\text{O}(\text{g}) \rightleftharpoons \text{CO}_{2}(\text{~g}) + \text{H}_{2}(\text{~g})\). This is an equilibrium reaction and can be analyzed using Le Chatelier's Principle, which states that a system at equilibrium will respond to a disturbance by shifting in the direction that counteracts the disturbance.

Analyze the Effect of a Catalyst

A catalyst speeds up the attainment of equilibrium but does not change the position of equilibrium. Therefore, adding a catalyst will not increase the amount of \(\text{CO}_{2}(\text{~g})\).

Analyze the Effect of Adding an Inert Gas

Adding an inert gas at constant volume increases the total pressure but does not change the partial pressures of the reactants or products. Therefore, the equilibrium position remains unchanged, and the amount of \(\text{CO}_{2}(\text{~g})\) does not increase.

Analyze the Effect of Decreasing the Volume of the Container

Decreasing the volume increases the pressure and the system will shift in the direction that decreases the number of moles of gas. Here, the reaction involves the same number of gas moles on both sides (2 reactants to 2 products). Hence, changing the volume has no effect on the equilibrium position.

Analyze the Effect of Increasing the Amount of CO

Increasing the amount of \( \text{CO} \) means increasing the concentration of one of the reactants. According to Le Chatelier’s Principle, the equilibrium will shift to the right to produce more products \( \text{CO}_{2} \) and \( \text{H}_{2} \) to counteract the change. Thus, increasing the amount of \( \text{CO} \) will increase the amount of \( \text{CO}_{2} \).

Key concepts

equilibrium reactions

Equilibrium reactions are a unique type of chemical reactions where the reactants and products are in a state of balance. When a system reaches equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentration of the reactants and products remains constant over time.
Le Chatelier's Principle helps predict how an equilibrium system will respond to various disturbances, like changes in concentration, temperature, or pressure. The principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system responds by counteracting the disturbance to re-establish equilibrium.
Understanding equilibrium reactions is crucial for solving many chemistry problems and understanding how reactions behave under different conditions.

effect of catalyst

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. Catalysts work by providing an alternative reaction pathway with a lower activation energy, which speeds up the reaction.
However, it is essential to remember that while a catalyst can speed up the attainment of equilibrium, it does not affect the position of equilibrium. This means that the concentrations of reactants and products at equilibrium remain unchanged in the presence of a catalyst.
So, for the exercise problem, adding a suitable catalyst will not increase the amount of \(\text{CO}_{2}(\text{~g})\). The catalyst simply helps the system reach equilibrium faster.

effect of inert gas

Inert gases, like helium or neon, are gases that do not participate in the chemical reaction. When added to a system at constant volume, an inert gas increases the total pressure but does not change the partial pressures of the reactants or products.
Because the partial pressures remain the same, the equilibrium position of the reaction does not change. This is why adding an inert gas to the reaction given in the exercise does not increase the amount of \(\text{CO}_{2}(\text{~g})\).
In general, inert gases can be useful in controlling reaction environments without affecting the reaction equilibrium.

effect of volume change

Changing the volume of the container holding a gaseous reaction mixture affects the reaction's equilibrium by changing the pressure. Le Chatelier's Principle states that the system will shift to counteract this change.
If the volume decreases (increasing pressure), the system shifts towards the side with fewer moles of gas. Conversely, increasing the volume (decreasing pressure) shifts to the side with more moles of gas.
In our exercise, the reaction involves equal moles of gas on both sides: \(\text{CO}(\text{g}) + \text{H}_{2}\text{O}(\text{g}) \rightleftharpoons \text{CO}_{2}(\text{~g}) + \text{H}_{2}(\text{~g})\). Therefore, changing the volume has no effect on the equilibrium position.

concentration changes

Changing the concentration of reactants or products in an equilibrium reaction causes the system to shift in a direction that minimizes that change, according to Le Chatelier's Principle.
For example, if we increase the concentration of \(\text{CO}\), the system will shift to the right to produce more products, \(\text{CO}_{2}\) and \(\text{H}_{2}\), to counteract the increased concentration of \(\text{CO}\).
This explains why in the exercise, increasing the amount of \(\text{CO}\) results in more \(\text{CO}_{2}\). Understanding how concentration changes affect equilibrium is key in manipulating reactions to obtain desired products.