Question

In a flask colourless \(\mathrm{N}_{2} \mathrm{O}_{4}\) is in cquilibrium with brown-coloured \(\mathrm{NO}_{2} . \Lambda \mathrm{t}\) cquilibrium when the flask is heated at \(100^{\circ}\) the brown colour decpens and on cooling it becomes less coloured. Now, the change in enthalpy \(\Delta H\) for the system is (1) Negative (2) Positive (3) Zero (4) none

Short answer

\(\Delta H\) is positive, as the reaction absorbs heat.

Step-by-step solution

Understanding the reaction and the color change

The reaction in question is the equilibrium between \(\text{N}_2\text{O}_4\) and \(\text{NO}_2\): \[ \text{N}_2\text{O}_4 (\text{colorless}) \rightleftharpoons 2\text{NO}_2 (\text{brown}) \] The flask's color intensity change indicates a shift in the reaction equilibrium.

Observing the temperature effect

When the temperature is increased to \100^\text{o}\text{C}\, the brown color deepens, meaning \(\text{NO}_2\) concentration increases. When cooling, the color fades indicating \(\text{N}_2\text{O}_4\) concentration becomes higher. This signifies temperature dependence of the reaction.

Applying Le Chatelier's Principle

According to Le Chatelier's Principle, if an equilibrium is subjected to a change in temperature, the system will adjust to counteract that change. If the equilibrium shifts toward the endothermic direction (product side, in this context), the reaction is endothermic (heat is absorbed).

Determining \(\text{\text{Δ} H}\)

Since heating increases the concentration of \(\text{NO}_2\), the reaction shifts to the right (endothermic direction). This implies the reaction absorbs heat, making the enthalpy change, \(\text{\text{Δ} H}\), positive.

Key concepts

Le Chatelier's Principle

In chemical reactions, equilibrium can shift under various conditions. Le Chatelier's Principle helps predict the direction of this shift. This principle states that if an external change, like temperature, pressure, or concentration, is applied to a system in equilibrium, the system adjusts to counteract the change.
For instance, in the equilibrium between \( \text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2 \), temperature plays a key role. If we heat the system, Le Chatelier's Principle indicates that the system will counteract the added heat by shifting the equilibrium in the endothermic direction (towards more \( \text{NO}_2 \)). This means the reaction absorbs heat and produces more brown-colored \( \text{NO}_2 \). When cooled, the reverse happens; the system shifts towards the exothermic direction (towards more \( \text{N}_2\text{O}_4 \)) to release the extra energy, and thus the solution appears less brown.

Endothermic Reaction

An endothermic reaction absorbs energy from its surroundings, typically in the form of heat. This energy absorption results in a positive change in enthalpy (\text{\text{Δ} H}). In the given reaction, \( \text{N}_2\text{O}_4 (\text{colorless}) \rightleftharpoons 2\text{NO}_2 (\text{brown}) \), the production of \( \text{NO}_2 \) is endothermic.
When the flask is heated, more \( \text{NO}_2 \) molecules are produced, evidenced by the deepening brown color. This confirms that the reaction absorbs heat (endothermic) and therefore, the enthalpy change (\text{\text{Δ} H}) is positive. Endothermic reactions are crucial in many biological processes and industrial applications, where energy absorption is essential to drive reactions to completion.

Equilibrium Shift

The concept of an equilibrium shift is crucial in understanding reversible reactions. A chemical equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction. Any change in conditions, like temperature, pressure, or concentration, will disturb this balance, causing the system to shift to a new equilibrium.
In the given example, the equilibrium between \( \text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2 \) shifts with temperature changes. Heating the system shifts the equilibrium to favor the production of \( \text{NO}_2 \) (endothermic direction), making the solution more brown. Conversely, cooling shifts the equilibrium towards \( \text{N}_2\text{O}_4 \) (exothermic direction), lightening the color.
Understanding equilibrium shifts is essential for predicting how a system will respond under various conditions. This knowledge is useful in chemical industry applications like optimizing reaction conditions to maximize product yield or minimize energy consumption.