Use data from Appendix C to calculate the equilibrium...

Use data from Appendix $C$ to calculate the equilibrium constant, $K,$ and $\Delta G^{\circ}$ at 298 K for each of the following reactions: $$ \begin{array}{l}{\text { (a) } \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)} \\ {\text { (b) } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g)}\end{array} $$

Use data from Appendix $C$ to calculate the equilibrium constant, $K,$ and $\Delta G^{\circ}$ at 298 K for each of the following reactions:
$$
\begin{array}{l}{\text { (a) } \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)} \\ {\text { (b) } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g)}\end{array}
$$

Key Concepts

Thermodynamic Data

Thermodynamic data, such as standard free energies of formation, enthalpies, and entropies of substances, are essential for calculating ?G° for reactions. This data is typically compiled in reference tables or appendices and is used to determine the overall energy change for a reaction under standard state conditions, enabling the evaluation of both equilibrium constants and reaction spontaneity.

Relationship between ?G° and K

The relationship between the standard Gibbs free energy change (?G°) and the equilibrium constant (K) is given by the equation ?G° = -RT ln K, where R is the gas constant and T is the temperature in Kelvin. This equation allows one to determine the favorability of a reaction based on its equilibrium constant, linking thermodynamic stability with reaction conditions.

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. At equilibrium, the reaction does not stop, but the dynamic process maintains a steady state, which is described quantitatively by the equilibrium constant.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that quantifies the ratio of the concentrations (or partial pressures for gases) of the products to that of the reactants, each raised to the power of their stoichiometric coefficients at equilibrium. It provides insight into the position of equilibrium and indicates whether the products or reactants are favored under a given set of conditions.

Standard Gibbs Free Energy (?G°)

Standard Gibbs free energy (?G°) is the change in Gibbs free energy for a reaction when all reactants and products are in their standard states, typically at 1 bar pressure for gases and 1 M concentration for solutions. This thermodynamic quantity is fundamental in predicting whether a reaction is spontaneous under standard conditions; a negative ?G° indicates a spontaneous reaction.

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