Problem 51 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction \(\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) \(\Delta_{\mathrm{r}} \mathrm{H}=-170.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) Which of the following statements is not true? (a) addition of \(\mathrm{CH}_{4}(\mathrm{~g})\) or \(\mathrm{O}_{2}(\mathrm{~g})\) at equilibrium will cause a shift to the right (b) the reaction is exothermic (c) at equilibrium, the concentrations of \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}\) (l) are not equal (d) the equilibrium constant for the reaction is given by \(\mathrm{K}_{\mathrm{P}}=\frac{\left[\mathrm{CO}_{2}\right]}{\left[\mathrm{CH}_{4}\right]\left[\mathrm{O}_{2}\right]}\)

Step-by-Step Solution

Answer

Statement (d) is not true.

Step 1: Analyze Statement (a)

According to Le Châtelier's Principle, adding more reactants (\(\mathrm{CH}_4\) or \(\mathrm{O}_2\)) to a system at equilibrium will cause the equilibrium to shift to the right to produce more products. This statement is true, as the system will favor the forward reaction to re-establish equilibrium.

Step 2: Evaluate Statement (b)

The reaction is given as \(\Delta_{\mathrm{r}} \mathrm{H}=-170.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\), which indicates that the reaction releases heat. Reactions that release heat are classified as exothermic. Therefore, statement (b) is true.

Step 3: Assess Statement (c)

In the reaction, one mole of \(\mathrm{CO}_2\) is produced for every two moles of \(\mathrm{H}_2\mathrm{O}\). At equilibrium, these quantities will differ, usually, based on stoichiometry, making this statement true.

Step 4: Verify Statement (d)

The equilibrium constant \(\mathrm{K}_{\mathrm{P}}\) for a gaseous reaction is expressed in terms of the partial pressures of the gases involved. Since water is a liquid, it is not included in the expression. Therefore, the correct expression should be \(\mathrm{K}_{\mathrm{P}}=\frac{P_{\mathrm{CO}_2}}{P_{\mathrm{CH}_4}(P_{\mathrm{O}_2})^2}\). Statement (d) uses the incorrect expression, so it is not true.

Key Concepts

Le Châtelier's Principle

Le Châtelier's Principle is a key concept in chemistry which helps us understand how a chemical equilibrium reacts to changes in concentration, temperature, or pressure. Imagine a see-saw in perfect balance. When you add weight to one side, it will tip over to regain balance by shifting in the opposite direction. This is similar to chemical reactions. When a system at equilibrium is disturbed, it will shift in a direction that counteracts the disturbance.

For example, if we increase the concentration of reactants like methane (\(\mathrm{CH}_4\)) and oxygen (\(\mathrm{O}_2\)), the system responds by favoring the forward reaction. This is to produce more carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)) and re-establish equilibrium.

• This principle helps predict the behavior of a reaction when conditions change.
• It's important for understanding how to maximize the yield of desired products in industrial processes.

By applying this principle, chemists can effectively manipulate reaction conditions to achieve the best possible outcomes.

Exothermic Reactions

Exothermic reactions are those which release energy, usually in the form of heat. This is indicated by a negative enthalpy change (\(\Delta_{r} H\)). For the chemical reaction example presented, the enthalpy change is \(-170.8 \, \text{kJ} \, \text{mol}^{-1}\), confirming it is exothermic. This means heat is a product of the reaction.

Exothermic reactions are common in everyday life, such as combustion and the metabolism of food. For the reaction given, burning methane produces carbon dioxide and water, releasing significant heat energy.

• These reactions are typically spontaneous and can continue without continuous energy input.
• They play a vital role in industries such as energy generation and manufacturing.

Understanding the exothermic nature of reactions helps in designing safety protocols and ensuring efficiency in energy usage.

Equilibrium Constant

The equilibrium constant, denoted as \(K_{P}\) when dealing with gases, provides insight into the extent of a reaction at equilibrium. It is mathematically described using the partial pressures of the gaseous reactants and products. In our example, the equilibrium constant expression should be \(K_{P}=\frac{P_{\mathrm{CO}_{2}}}{P_{\mathrm{CH}_{4}}(P_{\mathrm{O}_{2}})^2}\).

This expression reflects how changes in the concentrations of reactant or product gases affect the equilibrium. The equilibrium constant is a fixed value at a given temperature, independent of initial concentrations:

• If \(K_{P} > 1\), the products are favored at equilibrium.
• If \(K_{P} < 1\), the reactants are favored.

Understanding \(K_{P}\) is essential for predicting how changes in conditions can shift the equilibrium of a system. It also facilitates the calculation of unknown concentrations when the reaction reaches equilibrium.