Use the standard Gibbs free energies of formation in Appendix \(2 \mathrm{~A}\) to calculate \(\Delta G^{\circ}\) for each of the following reactions at \(25^{\circ} \mathrm{C}\). Comment on the spontaneity of each reaction under standard conditions at \(25^{\circ} \mathrm{C}\). (a) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) \rightarrow \mathrm{NH}_{3}\) (g) \(+\mathrm{HCl}(\mathrm{g})\) (b) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{D}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{D}_{2}\) (g) \(+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{NO}_{2}\) (g) \(\rightarrow \mathrm{NO}\) (g) \(+\mathrm{N}_{2} \mathrm{O}\) (g) (d) \(2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+3 \mathrm{O}_{2}\) (g) \(\longrightarrow 2 \mathrm{CO}_{2}\) (g) \(+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

In the fascinating world of Chemical Thermodynamics, we explore the energy changes associated with chemical reactions and phase transitions. It's a branch of physical chemistry that deals with the relationships between heat, work, temperature, and chemical potential. The laws of thermodynamics govern how and when these processes can occur and they guide us in predicting the direction and extent of chemical reactions.

For instance, the first law, often known as conservation of energy, tells us that energy can neither be created nor destroyed in an isolated system. The second law introduces the concept of entropy, a measure of disorder, stating that the total entropy of an isolated system can only increase over time. This is crucial because it implies that energy conversions are never 100% efficient due to energy dispersal as heat. These laws help us understand why certain reactions release heat (exothermic) while others absorb it (endothermic), and provides insight into how energy is transferred and transformed in chemical processes. By applying the principles of chemical thermodynamics, we can predict the feasibility and spontaneity of chemical reactions which is essential in various fields such as material science, biochemistry, and engineering.

Ever wondered what makes a chemical reaction go on its own without any outside help? The secret lies in the concept of Reaction Spontaneity. A spontaneous reaction is one that occurs naturally under certain conditions without external intervention. Spontaneity is dictated not just by energy changes, but also by the changes in entropy, or disorder, in the system. It's a blend of these two factors, known as Gibbs free energy, represented by the symbol \( G \).

For a process at constant temperature and pressure, if the change in Gibbs free energy \( \Delta G \) is negative, the process is spontaneous. This signifies that the system moves towards equilibrium by decreasing its free energy and increasing its entropy. Conversely, if \( \Delta G > 0 \), the process is non-spontaneous and needs energy input to proceed. Furthermore, if \( \Delta G = 0 \), the system is in equilibrium and no net change occurs. Understanding reaction spontaneity is not only crucial for predicting the behavior of chemical reactions in a lab but also for industrial processes where controlling reaction conditions can lead to better yields and more efficient use of resources.

The Standard Gibbs Free Energies of Formation are a collection of vital thermodynamic properties relevant to many areas of chemistry. Represented by \( \Delta G^\circ_f \), these are the energy changes when 1 mole of a compound forms from its constituent elements in their standard states. The 'standard state' refers to the most stable form of an element or compound at 1 bar of pressure and a specified temperature, usually 25°C (298 K).

Calculating \( \Delta G^\circ \) for a reaction can be quite simple; you take the sum of the standard Gibbs free energies of formation for all the products and subtract the sum for all the reactants. This allows us to gauge the energy profile of a chemical reaction and predict its spontaneity. However, it's also important to recognize that these values are only truly applicable under standard conditions. In reality, the actual Gibbs free energy change would vary with different conditions such as temperature and pressure. These concrete values are essential for scientists and engineers who design chemical processes and want to maximize efficiency.

Imagine a tug-of-war between chemical reactions where neither side wins - that's Chemical Equilibrium for you! In layman terms, it's a state where the rate of the forward reaction equals the rate of the reverse reaction. Consequently, the concentrations of products and reactants remain constant over time, but it's critical to acknowledge that it's a dynamic equilibrium - reactions don't just stop, they continue occurring in both directions continuously.

At equilibrium, the Gibbs free energy is at its lowest, meaning that the system has no tendency to change until an external force is applied. The position of the equilibrium is characterized by the equilibrium constant \( K \), which is a function of the concentrations (or pressures) of reactants and products at equilibrium for a particular reaction at a specific temperature. The concept of equilibrium is deeply interwoven with the spontaneity of reactions: if a reaction reaches equilibrium before the conversion of all reactants to products, it might be product-favored (spontaneous) or reactant-favored (non-spontaneous), based on the value of \( K \). Comprehending chemical equilibrium is indispensable, it explains phenomena such as acidity, solubility, and the functioning of our very own body's metabolic pathways.