Predict whether each of the following equilibria will shift toward products or reactants with a temperature increase. (a) \(\mathrm{N}_{2} \mathrm{O}_{4}(g)=2 \mathrm{NO}_{2}(g), \Delta H^{\circ}=+57 \mathrm{~kJ}\) (b) \(\mathrm{X}_{2}(\mathrm{~g})=2 \mathrm{X}(\mathrm{g})\), where \(\mathrm{X}\) is a halogen (c) \(\mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g})=\mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{~g}), \Delta \mathrm{H}^{+}=-161 \mathrm{~kJ}\) (d) \(\mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\), \(\Delta H^{\circ}=-90 \mathrm{~kJ}\)

Understanding chemical equilibrium is critical for anyone studying chemistry. It refers to a state where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products. This dynamic equilibrium is not a static situation; instead, reactions continue to occur, but with no overall effect on the concentrations.

For instance, consider the reaction \( N_2O_4(g) \leftrightarrow 2 NO_2(g) \) in our exercise. At equilibrium, the breakdown of \( N_2O_4 \) to form \( NO_2 \) molecules occurs at the same rate as the formation of \( N_2O_4 \) from \( NO_2 \) molecules. However, if we change the conditions, such as temperature, pressure, or concentrations, the equilibrium will shift to re-establish itself according to Le Chatelier's Principle.

Reactions can be categorized based on their energy changes as either endothermic or exothermic. Endothermic reactions absorb energy from their surroundings, typically in the form of heat, and are characterized by a positive enthalpy change (\(\Delta H > 0\)). On the other hand, exothermic reactions release energy into their surroundings, with a negative enthalpy change (\(\Delta H < 0\)).

When a reaction absorbs heat, like our example \( N_2O_4(g) \leftrightarrow 2 NO_2(g) \) with \(\Delta H^\circ = +57 \text{kJ}\), introducing additional heat (increasing temperature) will shift the equilibrium towards the products to consume this extra heat. Conversely, for an exothermic reaction such as \( Ni(s) + 4 CO(g) \leftrightarrow Ni(CO)_4(g) \) with \(\Delta H^+ = -161 \text{kJ}\), adding heat will shift the equilibrium towards the reactants.

Le Chatelier's Principle plays a key role when it comes to equilibrium shifts due to temperature changes. It essentially states that if an external condition (like temperature) is changed, the equilibrium will shift in a direction that tends to reduce that change.

When the temperature of an endothermic reaction is increased, the equilibrium shifts towards the products to absorb the added heat. Conversely, when the temperature of an exothermic reaction is increased, the equilibrium shifts towards the reactants to release the heat. This understanding helps us predict the behavior of a given reaction when it undergoes temperature changes, as showcased in the step by step solution for our exercise.

Thermochemistry is the study of energy and heat associated with chemical reactions and physical changes in matter. It is a branch of thermodynamics that focuses on the heat evolved or absorbed in chemical processes. The enthalpy change (\(\Delta H\)) of a reaction indicates whether the reaction is endothermic or exothermic, and it is a crucial concept in understanding reaction energetics.

For example, reaction (d) \( CO_2(g) + 2 NH_3(g) \leftrightarrows CO(NH_2)_2(s) + H_2O(g) \) with \(\Delta H^\circ = -90 \text{kJ}\) releases energy; hence it's exothermic. Thermochemistry allows us to quantify these energy changes and predict how changes in temperature will affect the equilibrium in terms of shifting towards reactants or products.