Calculate the equilibrium constant at \(25^{\circ} \mathrm{C}\) for each of the following reactions from the value of \(\Delta G^{\circ}\) given. (a) \(\mathrm{I}_{2}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{ICl}(g) \quad \Delta G^{\circ}=-10.88 \mathrm{kJ}\) (b) \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow 2 \mathrm{HI}(g) \quad \Delta G^{\circ}=3.4 \mathrm{kJ}\) (c) \(\mathrm{CS}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)+\mathrm{S}_{2} \mathrm{Cl}_{2}(g) \quad \Delta G^{\circ}=-39 \mathrm{kJ}\) (d) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g) \quad \Delta G^{\circ}=-141.82 \mathrm{kJ}\) (e) \(\mathrm{CS}_{2}(g) \longrightarrow \mathrm{CS}_{2}(l) \quad \Delta G^{\circ}=-1.88 \mathrm{kJ}\)

Grasping the concept of standard free energy change (HTML() G^HTML()oHTML())) is crucial for understanding chemical reactions and their spontaneity. This term represents the difference in free energy between reactants and products under standard conditions (1 bar, 298 K). A negative G^HTML()oHTML() indicates a spontaneous process, which tends to occur on its own without input of energy. Conversely, a positive G^HTML()oHTML() suggests that the reaction is non-spontaneous under standard conditions.
Knowing the G^HTML()oHTML() of a reaction allows you to predict not only the spontaneity but also the equilibrium position of a reaction. If G^HTML()oHTML() is zero, the system is at equilibrium, meaning the rates of the forward and reverse reactions are equal. Calculating the equilibrium constant (HTML()KHTML()eqHTML())) from this value involves using the relationship HTML()G^HTML()oHTML() = -RTtHTML()n KHTML()eqHTML(), where HTML()RHTML() is the universal gas constant and HTML()THTML() is the temperature in Kelvin.

Gibbs free energy (GHTML()) is a thermodynamic property used to describe the energy available in a system to do work at constant temperature and pressure. When we talk about a reaction's GHTML(), we're looking at the difference between the free energy of the products and the reactants. A negative G indicates that the products have less free energy than the reactants, which often translates to the reaction being spontaneous.
The GHTML() for a reaction can change with temperature, pressure, and concentration of reactants and products; by defining G^HTML()oHTML(), we focus on the specific case of standard conditions, which simplifies comparisons between different reactions. However, it's important to remember that 'standard' does not necessarily mean 'normal' conditions experienced in everyday life. It is simply a way to standardize the measurements.

The van't Hoff equation is a mathematical relation that links the equilibrium constant (HTML()KHTML()eqHTML())) of a chemical reaction with temperature (HTML()THTML()). This relationship is depicted as tHTML()n K = -HTML()G^HTML()oHTML()/(RT)HTML(). It is an equation of immense importance in chemical kinetics and thermodynamics as it allows the prediction of how HTML()KHTML()eqHTML() will change with temperature.
The van't Hoff equation is particularly useful because it offers insights into the temperature dependence of reaction equilibrium. For instance, as the temperature increases, the equilibrium constant for an exothermic reaction will decrease, implying the reaction is less likely to proceed spontaneously at higher temperatures. The equation also forms the foundation for understanding how catalysts affect reaction rates without changing the equilibrium position.

Chemical equilibrium is a state in which a chemical reaction and its reverse reaction occur at the same rate, leading to an unchanging concentration of reactants and products over time. It's important to understand that achieving equilibrium doesn't mean that reactants and products are present in equal amounts; rather, their ratios are constant, as given by the equilibrium constant (HTML()KHTML()eqHTML()).
The equilibrium constant is a dimensionless number that provides the ratio of product concentrations to reactant concentrations, each raised to the power of their respective stoichiometric coefficients in the balanced equation. A large HTML()KHTML()eqHTML() indicates a reaction mixture heavy with products, whereas a small HTML()KHTML()eqHTML(), one with more reactants. This constant is immensely valuable as it allows chemists to predict the extent of a reaction and formulate processes for optimal yields.

Converting temperature from Celsius to Kelvin is a basic but essential task in chemistry, as it aligns with the International System of Units (SI). The Kelvin scale is an absolute temperature scale, starting at absolute zero, whereas the Celsius scale is based on the properties of water, with 0°C as the freezing point and 100°C as the boiling point under standard atmospheric pressure.
To convert Celsius to Kelvin, one simply adds 273.15 to the Celsius temperature: HTML()T(K) = T(C^HTML()oHTML())) + 273.15HTML(). In calculations involving the equilibrium constant and Gibbs free energy, using Kelvin is crucial because it ensures that the values are positive and the equations are consistent with thermodynamic principles.