If the \(\Delta G^{\circ}\) for a reaction is \(-4.5 \mathrm{kcal} / \mathrm{mol}\) at \(298 \mathrm{~K}\), what is the \(K_{\text {eq }}\) for this reaction? What is the change in entropy of this reaction if \(\Delta H^{\circ}=-3.2 \mathrm{kcal} / \mathrm{mol}\) ?

The equilibrium constant, denoted as K_eq, is a number that expresses the ratio of the concentrations of the products to the reactants for a reversible chemical reaction at equilibrium. The value of K_eq provides insight into the position of the equilibrium. If K_eq is much greater than 1, the reaction favors the formation of products. Conversely, if it is much less than 1, the reaction favors the reactants.

Calculating K_eq involves using the Gibbs Free Energy change (abla G^ablacircn) of the reaction. The formula that connects these two is abla G^ablacircn = -RT ln K_eqn, where R is the universal gas constant and T is the temperature in Kelvin. In our example, the equilibrium constant was found to be approximately 2920, indicating that at 298 K, the products are heavily favored at equilibrium.

In thermodynamics, entropy is a measure of the disorder or randomness in a system. Symbolized as S, entropy is an important factor in determining the spontaneity of a process. The second law of thermodynamics states that in an isolated system, entropy tends to increase over time.

Entropy also plays a crucial role in the Gibbs Free Energy formula: abla G^ablacircn = abla H^ablacircn - Tabla S^ablacircn. In this equation, T is the temperature, abla H^ablacircn is the change in enthalpy, and abla S^ablacircn is the change in entropy. A positive abla S^ablacircn value indicates increased disorder, while a negative value indicates increased order. The example provided shows a negative change in entropy, meaning the reaction results in a more ordered state.

Enthalpy, represented by H, is a measure of the total energy of a thermodynamic system, including internal energy and the product of pressure and volume. It reflects the heat transferred during a chemical reaction at constant pressure. The change in enthalpy (abla H^ablacircn) is an essential component in calculating Gibbs Free Energy.

The formula for Gibbs Free Energy requires knowing the change in enthalpy: abla G^ablacircn = abla H^ablacircn - Tabla S^ablacircn. Here, a negative abla H^ablacircn implies that the reaction releases heat and is exothermic, while a positive abla H^ablacircn means it absorbs heat and is endothermic. Our step-by-step solution reveals an exothermic process with abla H^ablacircn = -13388.8 J/mol, as the reaction releases energy to the surroundings.

Chemical thermodynamics is the area of chemistry that studies the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Gibbs Free Energy, entropy, and enthalpy are all fundamental concepts within this field.

The Gibbs Free Energy is particularly significant because it predicts the direction of chemical change and the extent to which a reaction will proceed. Our exercise shows the practical application of chemical thermodynamics in determining both the equilibrium constant and the change in entropy, highlighting the interconnectedness of these thermodynamic quantities and their importance in predicting reaction behavior.