Our atmosphere is composed primarily of nitrogen and oxygen,...

Our atmosphere is composed primarily of nitrogen and oxygen, which coexist at $25{ }^{\circ} \mathrm{C}$ without reacting to any significant extent. However, the two gases can react to form nitrogen monoxide according to the reaction: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ a. Calculate $\Delta G^{\circ}$ and $K_{\mathrm{p}}$ for this reaction at $298 \mathrm{~K}$. Is the reaction spontaneous? b. Estimate $\Delta G^{\circ}$ at $2000 \mathrm{~K}$. Does the reaction become more spontaneous as temperature increases?

Our atmosphere is composed primarily of nitrogen and oxygen, which coexist at $25{ }^{\circ} \mathrm{C}$ without reacting to any significant extent. However, the two gases can react to form nitrogen monoxide according to the reaction:
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$
a. Calculate $\Delta G^{\circ}$ and $K_{\mathrm{p}}$ for this reaction at $298 \mathrm{~K}$. Is the reaction spontaneous?
b. Estimate $\Delta G^{\circ}$ at $2000 \mathrm{~K}$. Does the reaction become more spontaneous as temperature increases?

Key Concepts

Gibbs-Helmholtz Equation

This equation relates the Gibbs free energy change with temperature and enthalpy changes, allowing for the calculation of ?G at different temperatures from known standard values. It is a key tool for understanding how temperature influences the thermodynamic favorability of a reaction, by quantitatively connecting the free energy and enthalpy variations with temperature.

Reaction Spontaneity

Reaction spontaneity is defined by whether the change in Gibbs free energy (?G) is negative or positive. A negative ?G indicates that the reaction is spontaneous under the given conditions, meaning it can proceed without needing external energy input. This concept is fundamental in thermodynamics to determine if a reaction will occur naturally.

Standard Gibbs Free Energy Change (?G°)

This concept represents the change in Gibbs free energy when a reaction occurs under standard conditions (usually 1 bar for gases, 1 M for solutes, and a specified temperature, typically 298 K). It serves as an indicator of the reaction's thermodynamic favorability under those specific conditions, with negative values signifying spontaneous processes and positive values indicating non-spontaneous reactions.

Equilibrium Constant (Kp)

Kp is the equilibrium constant expressed in terms of partial pressures for gaseous reactions. It quantifies the ratio of the products’ pressures to the reactants’ pressures at equilibrium. The relationship ?G° = -RT ln Kp links the equilibrium constant directly to the thermodynamics of the reaction, showing how the position of equilibrium is influenced by the free energy change.

Temperature Dependence of Reaction Free Energy

The Gibbs free energy change (?G) is temperature-dependent. As temperature varies, the balance between enthalpy and entropy contributions changes, which can alter the spontaneity of a reaction. Tools such as the Gibbs-Helmholtz equation are used to estimate how ?G changes with temperature, aiding in the prediction of reaction behavior under different thermal conditions.

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