Consider the following equilibrium: N₂O₄(g) ⇌ 2 NO₂(g) Thermodynamic data on these gases are given in Appendix C. You may assume that ΔH° and ΔS° do not vary with temperature. (a) At what temperature will an equilibrium mixture contain equal amounts of the two gases?

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this case, the equilibrium expression can be used to relate the concentrations of N2O4 and NO2 at a given temperature, allowing for the determination of conditions under which equal amounts of both gases are present.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions and the position of equilibrium. The change in Gibbs Free Energy (ΔG) is related to the enthalpy (ΔH) and entropy (ΔS) of the system, and at equilibrium, ΔG equals zero. This relationship is crucial for determining the temperature at which equal concentrations of N2O4 and NO2 exist.

Van 't Hoff Equation

The Van 't Hoff equation relates the change in the equilibrium constant (K) of a reaction to the change in temperature. It is expressed as ln(K2/K1) = -ΔH°/R(1/T2 - 1/T1), where R is the gas constant. This equation is essential for calculating the temperature at which the equilibrium concentrations of N2O4 and NO2 are equal, as it allows for the determination of K at different temperatures.