Problem 4 - A Complete Resource Book in Chemistry for JEE Main

Question

In the reaction \(\mathrm{BaO}_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{BaO}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g})\) \(\Delta \mathrm{H}=\) tve. In equilibrium condition, pressure of \(\mathrm{O}_{2}\) depends on (a) increase mass of \(\mathrm{BaO}_{2}\) (b) increase mass of \(\mathrm{BaO}\) (c) temperature of equilibrium (d) mass of \(\mathrm{BaO}_{2}\) and \(\mathrm{BaO}\) both

Step-by-Step Solution

Answer

(c) temperature of equilibrium

Step 1: Understanding Reaction and Heat Exchange

The given reaction is \( \mathrm{BaO}_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{BaO}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \). The enthalpy change \( \Delta \mathrm{H} \) is positive, meaning the reaction is endothermic. In an endothermic reaction, heat is absorbed from the surroundings to proceed in the forward direction.

Step 2: Equilibrium Pressure Dependence

At equilibrium, the pressure of \( \mathrm{O}_{2} \) is determined by the equilibrium constant \( K_p \), which is only affected by temperature for a gaseous equilibrium. The masses of solids, \( \mathrm{BaO}_{2} \) and \( \mathrm{BaO} \), do not affect the pressure of gases at equilibrium.

Step 3: Effect of Temperature Change

As the reaction is endothermic, increasing the temperature will shift the equilibrium to the right according to Le Chatelier's Principle, increasing the pressure of \( \mathrm{O}_{2} \) as more is produced. Conversely, decreasing the temperature will shift the equilibrium to the left, reducing \( \mathrm{O}_{2} \) pressure.

Step 4: Conclusion

Given the options, the only factor that affects the equilibrium pressure of \( \mathrm{O}_{2} \) is (c) temperature of equilibrium. Changes in the mass of \( \mathrm{BaO}_{2} \) or \( \mathrm{BaO} \) do not alter the pressure of the gaseous component.

Key Concepts

Equilibrium Constant

In chemical reactions, the equilibrium constant (\( K_p \) for pressure, \( K_c \) for concentration) helps understand how reactants and products distribute when a reaction reaches equilibrium. For a system at equilibrium, the rate at which the reactants turn into products is equal to the rate that products convert back into reactants. This balance is characterized by the equilibrium constant which remains unchanged unless the temperature is altered.

For the reaction \(\mathrm{BaO}_{2}(\mathrm{s}) \rightleftharpoons \mathrm{BaO}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g})\), only the gaseous component \(\mathrm{O}_2\) affects the equilibrium pressure. Changes to \(\mathrm{BaO}_2\) or \(\mathrm{BaO}\) masses as solids do not affect \( K_p \) since solids are not included in the expression.

• Only temperature changes can affect the equilibrium constant.
• When temperature increases or decreases, \( K_p \) changes, affecting how concentrations or pressures of the reactive species adjust.

Endothermic Reaction

An endothermic reaction is one where the system absorbs heat from its surroundings as it progresses. This means that energy is required to break the bonds of reactants more than it is released when new products form. The positive enthalpy change (\(\Delta H\)) indicates energy is taken in.

In the example with \(\mathrm{BaO}_{2}\), the breakdown into \(\mathrm{BaO}\) and \(\mathrm{O}_2\) absorbs energy, consistent with its endothermic nature. Recognizing a reaction as endothermic is crucial because it tells us how equilibrium will respond to temperature changes.

• When heat is added (increased temperature), it shifts equilibrium towards the products to absorb extra heat.
• Conversely, a decline in temperature would shift the equilibrium toward reactants, as the system sees fit to release heat.

Pressure of Gases at Equilibrium

In reactions involving gases at equilibrium, the pressure of gases can shift when conditions change, but not due to the masses of any solid components involved in the reaction. The example with \(\mathrm{O}_2\) production from \(\mathrm{BaO}_2\) decomposition helps clarify this.

Le Chatelier’s Principle outlines how the system responds to changes to maintain equilibrium. If \(\mathrm{O}_2\) pressure increases or decreases due to a change in volume, for instance, the equilibrium will adjust to counteract this change. However, in an endothermic reaction, the pressure is directly tied to temperature since it alone influences \( K_p \).

• Increasing the temperature of an endothermic reaction raises \(\mathrm{O}_2\) pressure by shifting equilibrium forward.
• Pressure changes of gas components are solely linked to temperature in reactions without volume changes or additional gases introduced.