Problem 39 - A Complete Resource Book in Chemistry for JEE Main

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 \(\mathrm{CO}(\mathrm{g})\)

Step-by-Step Solution

Answer

Increasing the amount of \(\mathrm{CO}(\mathrm{g})\) will increase the equilibrium amount of \(\mathrm{CO}_{2}\).

Step 1: Identify equilibrium expression

The reaction is \[\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}\mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})\]At equilibrium, the reaction is governed by the equilibrium expression: \[K_c = \frac{[\mathrm{CO}_{2}][\mathrm{H}_2]}{[\mathrm{CO}][\mathrm{H}_{2}O]}\] where \([\ldots]\) denotes concentration of each species.

Step 2: Analyze the effect of adding a catalyst

A catalyst increases the rate of reaction but does not affect the position of equilibrium. Therefore, adding a catalyst in this case will not change the equilibrium amount of \( \mathrm{CO}_{2} \).

Step 3: Analyze the effect of adding an inert gas

Adding an inert gas at constant volume does not change reactant or product concentrations, thus it will not affect the equilibrium concentrations. Hence, it will not change the equilibrium amount of \( \mathrm{CO}_{2} \).

Step 4: Analyze the effect of decreasing the container volume

Decreasing the volume of the container increases the pressure. Since the number of moles of gas on each side of the chemical equation is equal (2 moles of gas on both sides), the position of equilibrium is not affected by volume change. Therefore, it does not change the equilibrium amount of \( \mathrm{CO}_{2} \).

Step 5: Analyze the effect of increasing \(\mathrm{CO}(\mathrm{g})\) amount

Increasing the concentration of \(\mathrm{CO}(\mathrm{g})\) shifts the equilibrium to the right, favoring the production of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_2\), according to Le Chatelier's principle. Thus, this will increase the equilibrium amount of \(\mathrm{CO}_{2}\).

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that predicts how a system at equilibrium will respond to changes in concentration, pressure, or temperature. The principle states that when a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium will shift to counteract the effect of the disturbance and restore equilibrium.

In simple terms, if you add more of a reactant or product, the system will shift to decrease the added component. If you remove a substance, the system will try to replace it. For example, in our exercise, increasing the concentration of \(\mathrm{CO}(\mathrm{g})\) results in a shift of the equilibrium position to the right, producing more \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_2(\mathrm{g})\).

Le Chatelier's Principle is a handy tool to predict which direction a reaction will move when subjected to external changes. It's important to note that this principle applies to changes in concentration, pressure (via volume changes), and temperature.

Equilibrium Constant (Kc)

The Equilibrium Constant, denoted as \(K_c\), is a numerical value that characterizes the position of equilibrium for a reversible chemical reaction at a given temperature. It provides the ratio of the concentrations of products to reactants, each raised to the power of their stoichiometric coefficients, at equilibrium.

The expression for the equilibrium constant for the given reaction \[ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}\mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \]
can be written as:

\[K_c = \frac{[\mathrm{CO}_{2}][\mathrm{H}_2]}{[\mathrm{CO}][\mathrm{H}_{2}O]}\]

A large \(K_c\) value indicates that, at equilibrium, the formation of products is favored. A small \(K_c\) implies that reactants are favored at equilibrium. \(K_c\) values are specific to each reaction and only change with temperature; they remain constant with shifts in concentration or changes in pressure.

Reaction Quotient

The Reaction Quotient, \(Q_c\), is very similar to the equilibrium constant, \(K_c\), with the difference being that \(Q_c\) is calculated using the concentrations of reactants and products at any point in time, not necessarily at equilibrium. It is given by the same expression as \(K_c\):

\[Q_c = \frac{[\mathrm{CO}_{2}][\mathrm{H}_2]}{[\mathrm{CO}][\mathrm{H}_{2}O]}\]

By comparing \(Q_c\) with \(K_c\), one can predict the direction in which the reaction will proceed to reach equilibrium:

• If \(Q_c < K_c\), the reaction will proceed in the forward direction to form more products.
• If \(Q_c > K_c\), the reaction will proceed in the reverse direction to form more reactants.
• If \(Q_c = K_c\), the system is at equilibrium.

Evaluating the reaction quotient is especially helpful when you have initial concentrations and want to know where the system is relative to its equilibrium state.

Catalysts in Reactions

Catalysts play a crucial role in increasing the speed at which reactions reach equilibrium by providing an alternative reaction pathway with a lower activation energy. However, it's important to note that catalysts do not alter the position of equilibrium or the equilibrium constant.

In the context of our exercise, adding a catalyst will hasten the rate at which equilibrium is achieved for the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}\mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})\). But it will not affect the concentrations of the reactants and products at equilibrium. Therefore, the equilibrium amount of \(\mathrm{CO}_{2}\) would remain unchanged.

Catalysts are extensively used in various industries to enhance the efficiency of chemical processes without being consumed in the reaction.