Determine the enthalpy of formation of \(\mathrm{B}_{2} \mathrm{H}_{6}(g)\) in \(\mathrm{kJ} / \mathrm{mol}\) of the following reaction. $$ \mathrm{B}_{2} \mathrm{H}_{6}(g)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{B}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) $$ Given : \(\Delta_{r} H^{\circ}=-1941 \cdot \mathrm{kJ} / \mathrm{mol} ; \quad \Delta H_{f}^{\circ}\left(\mathrm{B}_{2} \mathrm{O}_{3}, s\right)=-1273 \mathrm{~kJ} / \mathrm{mol}\) \(\mathrm{W}_{f}^{\circ}\left(\mathrm{H}_{2} \mathrm{O}, g\right)=-241.8 \mathrm{~kJ} / \mathrm{mol}\) (a) \(-75.6\) (b) \(+7 \overline{5} .6\) (c) \(-57.4\) (d) \(-28.4\)

Understanding Hess's Law is fundamental when tackling enthalpy of formation problems in chemical thermodynamics. It states that the total enthalpy change during a chemical reaction is the same, regardless of the number of stages in which the reaction occurs. This is a powerful concept because it allows us to use known enthalpy values for individual reactions to calculate unknown ones, like in the given exercise.

In the context of our exercise, we apply Hess's Law by breaking down the reaction into a series of hypothetical steps whose enthalpies are known, facilitating the calculation of the enthalpy of formation for a compound. For instance, the enthalpy of formation for \(\mathrm{B}_2 \mathrm{H}_6(g)\) can be deduced if we have the enthalpy for the overall reaction and the enthalpies of formation for all other products and reactants.

The calculation of enthalpy change allows chemists to predict the heat exchange associated with a chemical reaction. When determining the enthalpy of formation for \(\mathrm{B}_2 \mathrm{H}_6(g)\), we must consider both the reactants and products within the chemical reaction provided.

By writing the enthalpy change of the reaction as the difference between the sum of the enthalpies of formation of products and reactants, we can establish a formula that incorporates Hess's Law. In this exercise, we organized our known data and applied arithmetic to deduce the missing enthalpy value. It's imperative to account for the stoichiometry of the reaction, as the quantity of reactants and products can significantly affect the final enthalpy change calculation.

Chemical thermodynamics is the study of the energy and heat associated with chemical reactions and physical changes. One of its core components is enthalpy, a measure of the heat content in a system at constant pressure.

The enthalpy of formation is a specific type of enthalpy change and refers to the heat change that occurs when one mole of a substance is formed from its elements at their standard states. Through problems such as the one presented, students engage with chemical thermodynamics by learning to compute these changes. This is vital for predicting reaction spontaneity and feasibilities in real-world scenarios, ranging from industrial processes to environmental change predictions.

The Indian Institutes of Technology Joint Entrance Examination (IIT JEE) is a highly competitive exam among aspiring engineering undergraduates. Chemistry is one of the critical subjects in this exam, covering topics like chemical thermodynamics and enthalpy calculations.

For IIT JEE aspirants, mastering problems involving Hess's Law and enthalpy of formation is essential. The exam requires a deep understanding of concepts, accuracy, and speed in problem-solving. Therefore, solving exercises similar to the provided one is an excellent practice, as it trains students to quickly grasp the concepts and apply their knowledge efficiently under exam conditions.