Consider the system A(g) ⇌B(g) at 25^∘ C a. Assuming that GA^∘=8996 J / mol and GB^∘=11,718 J /

Consider the system A(g) ⇌B(g) at 25^∘ C a. Assuming that...

Consider the system $$\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)$$ at $25^{\circ} \mathrm{C}$ a. Assuming that $G_{\mathrm{A}}^{\circ}=8996 \mathrm{J} / \mathrm{mol}$ and $G_{\mathrm{B}}^{\circ}=11,718 \mathrm{J} / \mathrm{mol},$ calculate the value of the equilibrium constant for this reaction. b. Calculate the equilibrium pressures that result if 1.00 mole of $\mathrm{A}(g)$ at 1.00 atm and 1.00 mole of $\mathrm{B}(g)$ at 1.00 atm are mixed at $25^{\circ} \mathrm{C} .$ c. Show by calculations that $\Delta G=0$ at equilibrium.

Consider the system
$$\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)$$
at $25^{\circ} \mathrm{C}$
a. Assuming that $G_{\mathrm{A}}^{\circ}=8996 \mathrm{J} / \mathrm{mol}$ and $G_{\mathrm{B}}^{\circ}=11,718 \mathrm{J} / \mathrm{mol},$ calculate the value of the equilibrium constant for this reaction.
b. Calculate the equilibrium pressures that result if 1.00 mole of $\mathrm{A}(g)$ at 1.00 atm and 1.00 mole of $\mathrm{B}(g)$ at 1.00 atm are mixed at $25^{\circ} \mathrm{C} .$
c. Show by calculations that $\Delta G=0$ at equilibrium.

Key Concepts

Ideal Gas Behavior in Equilibria

In gas-phase reactions, the ideal gas law provides a relationship between pressure, volume, temperature, and moles. When dealing with equilibrium in gaseous systems, it is essential to consider how partial pressures are distributed and how they relate to the equilibrium constant.

Gibbs Free Energy under Non-standard Conditions

This concept extends the idea of standard Gibbs free energy to any set of conditions, using the relation ?G = ?G° + RT ln Q. Here, Q is the reaction quotient, and this expression allows one to determine the direction and extent of a reaction based on current conditions relative to the standard state.

Reaction Equilibrium Condition

At equilibrium, the reaction has reached a state where the free energy change, ?G, becomes zero because the reaction quotient equals the equilibrium constant (Q = K). This indicates that there is no net change in the composition of the system.

Standard Gibbs Free Energy Change

This is the change in Gibbs free energy when reactants are converted to products under standard conditions. It is calculated by subtracting the standard free energy of the reactants from that of the products and is directly related to the equilibrium constant through the equation ?G° = -RT ln K.

Equilibrium Constant

The equilibrium constant quantifies the ratio of the concentrations or partial pressures of products to reactants at equilibrium. It is a measure of the extent of a reaction and is determined using the relation between the standard Gibbs free energy change and temperature.