(a) Calculate the reaction Gibbs free energy of \(\mathrm{I}_{2}(\mathrm{~g}) \rightarrow\) \(2 \mathrm{I}(\mathrm{g})\) at \(1200 . \mathrm{K}(K=6.8)\) when the partial pressures of \(\mathrm{I}_{2}\) and \(\mathrm{I}\) are \(0.13\) bar and \(0.98\) bar, respectively. (b) What is the spontaneous direction of the reaction? Explain briefly.

Chemical equilibrium is the state of a reversible chemical reaction where the rates of the forward and reverse reactions are equal, leading to no overall change in the concentrations of reactants and products over time. It's a dynamic balance, not a static one, as molecules continuously react, converting in both directions.

At equilibrium, the ratio of the concentrations of products to reactants remains constant, which is numerically expressed by the equilibrium constant, denoted as 'K'. It's important to note that different reactions at the same temperature will have unique equilibrium constants. In the exercise, the equilibrium constant, 'K', is given as 6.8 at 1200 K for the reaction involving iodine. The concept of equilibrium is essential when talking about reaction spontaneity and the reaction quotient since it serves as a point of reference.

Reaction spontaneity refers to whether a chemical reaction would occur without any additional input of energy. This is different from the rate of the reaction - spontaneous reactions can still be slow. The spontaneity of a reaction can be understood by considering Gibbs free energy, symbolized as \( \Delta G \).

A spontaneous reaction is indicated by a negative \( \Delta G \) value, meaning the reaction can proceed in the forward direction without external work. On the other hand, a positive \( \Delta G \) suggests that the reaction is not spontaneous and will not occur under the existing conditions without an input of energy.

In the textbook example, by calculating the Gibbs free energy and observing its sign, students can determine whether the reaction of \( \mathrm{I}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{I}(\mathrm{g}) \) is spontaneous at the given temperature and partial pressures. This directly relates to the fundamental concepts of thermodynamics and is an important factor for chemical reactions and processes.

The reaction quotient (Q) is a measure that compares the relative amounts of products and reactants present during a reaction at any point in time. It is calculated in the same way as the equilibrium constant (K), but it is not limited to just the conditions at chemical equilibrium.

The value of Q provides a snapshot of a reaction's progress and offers insight into which direction the reaction will proceed to reach equilibrium. If \( Q < K \) the reaction will move forward towards the products to reach equilibrium. If \( Q > K \) the reaction will proceed in the reverse direction, converting products back into reactants.

In the step-by-step exercise provided, by calculating the reaction quotient (Q) using the given partial pressures, and comparing it with the equilibrium constant (K), students can assess the status of the reaction regarding its equilibrium position. This analysis supports the determination of the Gibbs free energy change (\(\Delta G\)) and ultimately the spontaneity of the reaction.