(a) Calculate the reaction free energy of \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Hl}(\mathrm{g})\) at \(700 \mathrm{~K}\) when the concentrations of \(\mathrm{H}_{2}, \mathrm{I}_{2}\), and HI are \(0.026,0.33\), and \(1.84 \mathrm{~mol} \cdot \mathrm{L}^{-1}\), respectively. For this reaction, \(K_{c}=54\) at \(700 \mathrm{~K}\). (b) Indicate whether this reaction mixture is likely to form reactants, is likely to form products, or is at equilibrium.

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, resulting in no net change in the concentration of reactants and products over time. This state can be visually represented as a see-saw balanced in the middle, symbolizing that while reactants are continuously converting to products, and vice versa, the amounts remain constant.

At equilibrium, the system's properties, such as concentration, color, and pressure, will appear static because the forward and reverse reactions are in perfect sync. However, this doesn't mean the reactions have ceased; they are ongoing but in exact opposition, creating a dynamic but stable system.

The reaction quotient (Q) is a measure that tells us how far a reaction has processed toward equilibrium at a given moment. The formula for Q is based on the concentrations of the chemical species involved in the reaction at non-equilibrium conditions. For a general reaction given as \(aA + bB \rightarrow cC + dD\), the reaction quotient \(Q\) is defined as \(Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\), where the concentrations are those at the specific moment being assessed, not necessarily at equilibrium.

By calculating Q and comparing it to the equilibrium constant (Kc), we can predict the direction in which the reaction will proceed to reach equilibrium. If \(Q < K_c\), the reaction will proceed in the forward direction, forming more products. Conversely, if \(Q > K_c\), the system will shift to form more reactants.

Gibbs free energy (\(\Delta G\)) is a thermodynamic quantity that helps us understand whether a reaction will occur spontaneously at constant pressure and temperature. It's defined as the energy difference between the enthalpy of a system and the product of its entropy and temperature (\(\Delta G = \Delta H - T\Delta S\)).

A negative \(\Delta G\) value indicates the reaction occurs spontaneously, producing more products, while a positive value suggests the reaction is non-spontaneous and favors the formation of reactants. At equilibrium, \(\Delta G\) is zero, signifying there's no free energy change, as the system is in its most stable state. By understanding \(\Delta G\), we gain insight into the energetic favorability of a chemical process and its potential to do work.

The equilibrium constant (Kc) reflects the relative quantities of reactants and products at chemical equilibrium. Unlike Q, which applies at any moment, Kc specifically addresses the state where the reaction is balanced. Given for a reaction of the form \(aA + bB \rightarrow cC + dD\), Kc appears as \(K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\), where the concentrations are those at equilibrium.

Kc is a constant at a given temperature, meaning it's independent of initial concentrations. It provides valuable insight into the reaction's nature; a large Kc implies a product-favored reaction, while a small Kc indicates a reactant-favored reaction. In our exercise, a Kc of 54 at 700K suggests the formation of products is favored over reactants at equilibrium for the specific reaction.