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 \(100^{\circ} \mathrm{C}\) the brown colour deepens and on cooling it becomes less coloured. The change in enthalpy, \(\Delta H\), for the system is (a) negative (b) positive (c) zero (d) undefined

Chemical equilibrium is a state in which the rate of the forward reaction equals the rate of the reverse reaction, meaning that the concentrations of reactants and products remain constant over time, although both reactions are still occurring. This balance can be represented by a reversible arrow in chemical equations (
\( A + B \rightleftharpoons C + D \)
).

Le Chatelier's Principle plays a crucial role in understanding how this balance can be disturbed. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. In the context of our exercise, when temperature is increased, the equilibrium system of colourless \(\mathrm{N}_2\mathrm{O}_4\) and brown \(\mathrm{NO}_2\) responds to restore balance by favoring the endothermic reaction that absorbs heat – thus, more \(\mathrm{NO}_2\) is formed, deepening the brown color observed.

Endothermic reactions are chemical processes that absorb energy from their surroundings, typically in the form of heat. This energy is necessary to break the bonds of the reactants, so the reaction will not proceed unless this energy is provided.

Visual signs, like the deepening of the brown color in the equilibrium of \(\mathrm{N}_2\mathrm{O}_4\) and \(\mathrm{NO}_2\), can indicate that a reaction is endothermic. In practice, endothermic reactions need a continuous input of energy to keep the reaction going, which could be in the form of thermal energy, as illustrated in the problem. As Le Chatelier's Principle suggests, increasing the temperature causes the endothermic reaction to be more favorable to absorb the excess heat, which is exactly why more \(\mathrm{NO}_2\) is produced when the flask is heated.

The change in enthalpy, designated by \(\Delta H\), represents the total heat change in a system during a chemical reaction at constant pressure. A positive \(\Delta H\) value signifies an endothermic reaction, indicating that the reaction absorbs heat from the surroundings. Conversely, an exothermic reaction has a negative \(\Delta H\), meaning it releases heat.

In the given exercise, the darkening of the brown color on heating implies that the system absorbs heat, pointing to a positive \(\Delta H\). This concept is crucial in the study of thermodynamics, as it helps chemists understand and predict how the equilibrium will shift in response to temperature changes or other external conditions. Knowing whether a reaction is endothermic or exothermic is essential for controlling industrial chemical processes and even for everyday cooking!