Question

In a flask, colourless \(\mathrm{N}_{2} \mathrm{O}_{4}\) is in equilibrium with brown coloured \(\mathrm{NO}_{2}\) At equilibrium, when the flask is heated at \(373 \mathrm{~K}\), the brown colour deepens and on cooling it becomes less coloured. The change in enthalpy for this reaction is (a) negative (b) positive (c) zero (d) unpredictable

Short answer

The change in enthalpy for the reaction is (b) positive.

Step-by-step solution

Identify the type of reaction

The given scenario describes a chemical equilibrium between colorless \( \mathrm{N}_{2} \mathrm{O}_{4} \) and brown colored \( \mathrm{NO}_{2} \). The deepening of the brown color upon heating indicates that the equilibrium is shifting towards the production of more \( \mathrm{NO}_{2} \).

Apply Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. In this case, heating the system causes the equilibrium to shift towards the endothermic reaction, which in this case is the formation of \( \mathrm{NO}_{2} \) from \( \mathrm{N}_{2} \mathrm{O}_{4} \).

Determine the sign of enthalpy change

Since applying heat shifts the reaction towards the production of more \( \mathrm{NO}_{2} \), the reaction that forms \( \mathrm{NO}_{2} \) must absorb heat, meaning it is endothermic. Therefore, the enthalpy change for the reaction, which is the heat absorbed or released, is positive for an endothermic reaction.

Key concepts

Le Chatelier's Principle

Imagine a seesaw in perfect balance. Now, if you were to add weight to one side, the seesaw would tilt to adjust to this new change. Similarly, Le Chatelier's Principle describes how a chemical reaction at equilibrium adjusts to disturbances.

In our textbook problem, we observed the equilibrium between colorless N₂O₄ and brown NO₂. When we introduce heat (akin to adding weight to our metaphorical seesaw), we see a shift in the balance towards more brown NO₂ formation.

This illustrates Le Chatelier's Principle in action: the system tries to cool down by favoring the reaction that absorbs heat - in this case, the endothermic formation of NO₂. By understanding this principle, students can predict how changes like temperature, pressure, or concentration will affect the position of equilibrium in chemical reactions.

Enthalpy Change

To delve deeper into what's happening on a molecular level, we encounter the concept of enthalpy change, denoted as ΔH. Enthalpy is a measure of the total heat content in a chemical system under constant pressure. When a reaction occurs, energy is either released or absorbed, leading to a change in enthalpy.

The sign of ΔH tells us about the nature of the reaction: negative ΔH (exothermic reactions) means energy is released, while positive ΔH (endothermic reactions) indicates energy absorption. In the case of the N₂O₄ to NO₂ reaction, the problem states that heating deepens the brown color, signaling that the reaction is absorbing heat. Hence, the enthalpy change is positive, signifying an endothermic process.

Endothermic Reactions

Building upon the understanding of enthalpy change, in endothermic reactions, reactants absorb energy from their surroundings, usually in the form of heat. This is akin to sponges soaking up water.

These reactions often have products that contain higher energy than the reactants because the absorbed energy is stored within the chemical bonds. In our example, as the system absorbs heat (energy from the surroundings), more NO₂ forms because it's an endothermic process.

Moreover, not only does the reaction's direction change with temperature, but the color change also serves as an indicator. The deepening of the brown hue means we're seeing more NO₂ due to the endothermic reaction 'pulling' heat into itself as it forms more NO₂ molecules.