Problem 130 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(\mathrm{NaNO}_{3}(\mathrm{~d}=2.0 \mathrm{~g} / \mathrm{cc})\) is heated in a closed vessel of \(100 \mathrm{ml}\), oxygen is liberated and \(\mathrm{NaNO}_{2}\) \((\mathrm{d}=1.5 \mathrm{~g} / \mathrm{cc})\) is left behind as per the reaction : \(2 \mathrm{NaNO}_{3}(\mathrm{~s}) \rightleftharpoons 2 \mathrm{NaNO}_{2}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g})\). At equilibrium, the volumes of \(\mathrm{NaNO}_{3}\) left and \(\mathrm{NaNO}_{3}\) left and \(\mathrm{NaNO}_{2}\) produced are very small and can be neglected. Which of the following is a correct statement about this equilibrium? (a) Addition of \(30 \mathrm{~g}\) of \(\mathrm{NaNO}_{3}\) favours reverse reaction. (b) Addition of \(30 \mathrm{~g}\) of \(\mathrm{NaNO}_{2}\) favours forward reaction. (c) Increasing temperature favours reverse reaction. (d) None of these.

Step-by-Step Solution

Answer

(d) None of these.

Step 1: Understand the Reaction

The given reaction is \(2\, \text{NaNO}_3 (s) \rightleftharpoons 2\, \text{NaNO}_2 (s) + \text{O}_2 (g)\). It describes a decomposition where solid sodium nitrate decomposes to solid sodium nitrite and gaseous oxygen.

Step 2: Identify the Equilibrium Conditions

Since the problem states that the volumes of \(\text{NaNO}_3\) and \(\text{NaNO}_2\) can be ignored at equilibrium, it implies the equilibrium is dominated by the oxygen gas produced.

Step 3: Assess the Effect of Adding Sodium Nitrate

Increasing the amount of \(\text{NaNO}_3\) solid does not directly affect the equilibrium position of the reaction because adding a solid reactant generally doesn't shift the equilibrium in a gaseous reaction.

Step 4: Assess the Effect of Adding Sodium Nitrite

Increasing \(\text{NaNO}_2\), the product solid, does not affect the equilibrium position either because the reaction is primarily influenced by the gases, unless it affects the concentration of \(\text{O}_2\).

Step 5: Assess the Effect of Temperature on Equilibrium

If more heat (increased temperature) is provided, assuming the reaction is endothermic going forward (since it produces a gas), increasing temperature generally favors the forward reaction, thus producing more \(\text{O}_2\). This contradicts option (c) with it favoring the reverse reaction.

Step 6: Conclusion

Based on the reasoning that neither addition of solids affects the gaseous equilibrium and increasing temperature favors the forward reaction, none of the given statements (a), (b), or (c) hold true for the equilibrium condition.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium that helps predict how a change in conditions can affect the equilibrium state of a chemical system.
When a system at equilibrium is subjected to a change, such as temperature, pressure, or concentration, the system shifts in the direction that counteracts this change.
In the given reaction of sodium nitrate (\( ext{NaNO}_3 \)) decomposition, adding more of the solid reactant or product does not affect the position of the equilibrium.
This is because solids have a fixed concentration in a given volume and do not appear in the equilibrium expression for gases.
However, any change in the concentration of gaseous components, like the oxygen gas produced, can shift the equilibrium.
Thus, Le Chatelier's Principle highlights that disturbances to a system at equilibrium cause it to shift in a way that minimizes the effect of the disturbance, maintaining balance.

Effect of Temperature on Equilibrium

Temperature changes can significantly affect the equilibrium of a chemical reaction by altering the reaction rates and the equilibrium constant, denoted as \( K \).
In reactions where heat is absorbed (endothermic), an increase in temperature favors the formation of products as the system shifts to absorb the additional heat.
Conversely, in exothermic reactions, increasing temperature generally favors the reactants.For the reaction \( 2 \text{NaNO}_3 (s) \rightleftharpoons 2 \text{NaNO}_2 (s) + \text{O}_2 (g) \), the assumption that the forward reaction is endothermic leads to the prediction that increasing temperature will favor more oxygen gas production.
This contradicts the choice suggesting that increasing temperature favors the reverse reaction, which would decrease \( \text{O}_2 \).
Therefore, knowing whether a reaction is endothermic or exothermic helps determine how its equilibrium shifts with temperature changes.

Solid and Gas Phase Equilibrium

In chemical reactions involving solids and gases, it is essential to understand how different phases affect equilibrium.
Solids do not affect the equilibrium positions because their concentrations remain constant and have minimal volume impact in a reaction system.
Gas-phase components, however, play a significant role in determining the equilibrium state since their concentrations are variable with changes in volume and pressure.
In the sodium nitrate decomposition example, the major contributor to equilibrium is the production of gaseous oxygen, making it pivotal in shifting the balance. Equilibrium in solid-gas reactions allows us to focus mainly on the gas components when predicting and analyzing changes in the reaction environment.
This guides chemists in altering conditions to favor desired reaction outcomes, such as maximizing gas production without needing to consider solid phase changes.