What happens to \(\Delta G^{\circ}\) (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased? (a) \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)\) (c) \(\mathrm{HgO}(s) \longrightarrow \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\)

Understanding chemical equilibrium is fundamental for studying reactions, as it represents a state where the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of the reactants and products remain constant over time. However, this does not mean the reactants and products are present in equal amounts but are at a stable ratio.

Le Chatelier's Principle helps us predict how a system at equilibrium reacts to external changes, such as pressure, temperature, or concentration. If we increase the partial pressure of a gaseous reactant or product in a system, the equilibrium will shift to counteract that change. This shift can result in the production of more products or reactants, depending on which direction the equilibrium moves. It's like a see-saw that will tilt to one side if weight is added, trying to balance itself back.

Gibbs free energy (ΔG) is pivotal for understanding the spontaneity of reactions. It's a thermodynamic quantity representing the maximum amount of work obtainable from a process at constant temperature and pressure. When ΔG is negative, a process or reaction will proceed spontaneously in the forward direction, and when it's positive, the reaction is non-spontaneous and may require energy to proceed.

The relationship between ΔG and the reaction conditions is dictated by the equation ΔG = ΔG^{circ} + RT ln(Q), where ΔG^{circ} is the Gibbs free energy change under standard conditions, R is the gas constant, T is the temperature, and Q is the reaction quotient. How the equilibrium shifts due to changes in partial pressures can affect Q and subsequently ΔG, either encouraging or discouraging the process's spontaneity.

Determining whether a reaction will occur spontaneously, without an outside energy source, is a critical concept in chemistry. A spontaneous reaction is characterized by a natural tendency to occur under specific conditions and is heavily related to the concept of Gibbs free energy.

When the Gibbs free energy (ΔG) of a reaction is negative, it indicates that the reaction can occur spontaneously, making it more likely to proceed until equilibrium is reached. It's important to understand that 'spontaneous' does not imply that the reaction will happen quickly, only that it will happen without external input if given enough time. Factors such as temperature, pressure, and concentration play significant roles in this, influencing how the materials react and how far a reaction goes towards completion.

The concept of partial pressure is crucial when dealing with gases, as it represents the pressure that a gas would exert if it occupied the entire volume alone in a mixture of gases. It's directly proportional to the concentration of the gas in the mixture, meaning that any change in partial pressure will affect the equilibrium position of a gaseous reaction.

When we talk about changing the partial pressure of oxygen in a reaction, we're looking at how this adjustment influences the equilibrium of the reaction. An increase in the partial pressure of a reactant, in this case oxygen, typically drives the equilibrium toward the products, while an increase in the partial pressure of a product pushes the equilibrium toward the reactants. This interplay with equilibrium is tied closely to Le Chatelier's Principle and guides the conditions required for optimal production of desired substances in industrial chemical processes.