Consider the following reaction at 800 . K : N2(g)+3 F2(g) ⟶2 NF3(g) An equilibrium mixture con

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Consider the following reaction at 800 . K : N2(g)+3 F2(g)...

Consider the following reaction at $800 . \mathrm{K}$ : $$\mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)$$ An equilibrium mixture contains the following partial pressures: $P_{\mathrm{N}_{2}}=0.021 \mathrm{~atm}, P_{\mathrm{F}_{2}}=0.063 \mathrm{~atm}, P_{\mathrm{NF}_{3}}=0.48 \mathrm{~atm} .$ Calculate $\Delta G^{\circ}$ for the reaction at $800 . \mathrm{K}$.

Consider the following reaction at $800 . \mathrm{K}$ :
$$\mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)$$
An equilibrium mixture contains the following partial pressures:
$P_{\mathrm{N}_{2}}=0.021 \mathrm{~atm}, P_{\mathrm{F}_{2}}=0.063 \mathrm{~atm}, P_{\mathrm{NF}_{3}}=0.48 \mathrm{~atm} .$ Calculate
$\Delta G^{\circ}$ for the reaction at $800 . \mathrm{K}$.

Key Concepts

Relationship Between ?G° and the Equilibrium Constant

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 universal gas constant and T is the temperature in Kelvin. This equation allows for the quantification of the reaction’s thermodynamic favorability by linking the observed equilibrium composition directly to the free energy change.

Chemical Equilibrium

Chemical equilibrium is the state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentrations (or partial pressures for gases) of the reactants and products remain constant over time, even though both reactions are still occurring. This concept is crucial for determining the equilibrium properties such as the equilibrium constant and ultimately the thermodynamic parameters like ?G°.

Partial Pressures

Partial pressures refer to the pressure contributed by each gas in a mixture, assuming that each gas behaves ideally. They are used to express the relative amounts of gases present, and in the context of equilibrium, they can be used to formulate expressions for the equilibrium constant (Kp) for reactions involving gases.

Equilibrium Constant (Kp)

The equilibrium constant for a gaseous reaction, denoted as Kp, is expressed in terms of the partial pressures of the reactants and products raised to the power of their stoichiometric coefficients. Kp quantifies the position of equilibrium and is fundamental in relating the observable partial pressures in the system to the thermodynamic properties of the reaction.

Standard Gibbs Free Energy Change (?G°)

The standard Gibbs free energy change, ?G°, indicates the spontaneity of a reaction under standard state conditions. It is a thermodynamic potential that represents the maximum reversible work that a system can perform at constant temperature and pressure. A negative ?G° implies a spontaneous process under standard conditions, whereas a positive ?G° suggests non-spontaneity.

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