Which of the following value of \(\Delta H_{f}^{\circ}\) represent that the product is least stable? (a) \(-94.0 \mathrm{kcal} \mathrm{mol}^{-1}\) (b) \(-231.6 \mathrm{kcal} \mathrm{mol}^{-1}\) (c) \(+21.4 \mathrm{kcal} \mathrm{mol}^{-1}\) (d) \(+64.8 \mathrm{kcal} \mathrm{mol}^{-1}\)

When it comes to understanding the stability of chemical compounds, the standard enthalpy of formation, denoted as \(\Delta H_{f}^{\circ}\), is a crucial concept. It refers to the change in enthalpy that occurs when one mole of a compound is formed from its elements under standard conditions, which are typically 1 bar pressure and 298.15 K (25°C). The standard states of the elements are their forms as they exist under these conditions.

Compounds with negative \(\Delta H_{f}^{\circ}\) values are generally more stable because their formation releases energy, suggesting that the bonds formed in the product are stronger than those in the reactants. Conversely, a positive \(\Delta H_{f}^{\circ}\) implies that the compound requires an input of energy to form. This energy absorption is indicative of weaker chemical bonds in the product compared to the reactants, thus signifying a less stable compound.

The magnitude of the \(\Delta H_{f}^{\circ}\) value gives insight into the relative stability of different compounds. A larger negative value means a more stable compound, as it releases more energy upon formation. Similarly, a larger positive value points to a less stable compound. Understanding this concept is essential for predicting reaction spontaneity and the feasibility of synthesizing various chemicals.

An exothermic reaction is one in which energy, typically in the form of heat, is released to the surroundings. This release of energy occurs because the total energy of the products is lower than that of the reactants, symbolizing a decrease in potential energy during the reaction.

In an exothermic reaction, the \(\Delta H_{f}^{\circ}\) value will be negative. This is because the formation of products from reactants has resulted in a net release of energy. The concept of enthalpy, represented by the symbol H, signifies the total heat content of a system. The negative sign of \(\Delta H\) highlights that the system has lost enthalpy.

Examples of exothermic reactions include combustion reactions like the burning of wood or fossil fuels, and many everyday chemical reactions such as rusting of iron. Exothermic reactions are often more spontaneous than endothermic ones because they result in a lower-energy, more stable state.

In contrast to exothermic reactions, endothermic reactions absorb energy from the surroundings. This absorption of energy takes place because the products of an endothermic reaction contain more potential energy than the reactants. During such a reaction, energy is taken in, typically in the form of heat, to break existing bonds in the reactants and form new bonds in the products.

These reactions are characterized by a positive \(\Delta H_{f}^{\circ}\) value, indicating that the process requires an input of energy for the reaction to proceed. An endothermic reaction essentially requires more energy to break the bonds of the reactants than is released when the new bonds in the products are formed.

Common examples of endothermic processes include photosynthesis, the evaporation of water, and the cooking of an egg. These reactions often require an external source of energy, such as light or heat, to continue. Understanding the energy changes involved in chemical reactions is vital for applications in chemical engineering, environmental science, and energy technology.