Nitrogen dioxide, a pollutant in the atmosphere, can combine...

Nitrogen dioxide, a pollutant in the atmosphere, can combine with water to form nitric acid. One of the possible reactions is shown here. Calculate $\Delta G^{\circ}$ and $K_{p}$ for this reaction at $25^{\circ} \mathrm{C}$ and comment on the spontaneity of the reaction. $$3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)$$

Nitrogen dioxide, a pollutant in the atmosphere, can combine with water to form nitric acid. One of the possible reactions is shown here. Calculate $\Delta G^{\circ}$ and $K_{p}$ for this reaction at $25^{\circ} \mathrm{C}$ and comment on the spontaneity of the reaction.
$$3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)$$

Key Concepts

Chemical Equilibrium and Equilibrium Constant (K?)

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations (or pressures) of reactants and products. For reactions involving gases, the equilibrium constant is often expressed in terms of partial pressures (K?). This concept is fundamental in understanding the distribution of species in a reaction mixture at equilibrium.

Reaction Spontaneity

The spontaneity of a reaction is determined by its Gibbs free energy change. A negative ?G° implies that the reaction is energetically favorable and will spontaneously proceed under standard conditions, while a positive ?G° means that the reaction is non-spontaneous and requires an input of energy to proceed. This principle is central to predicting reaction behavior in chemical thermodynamics.

Gibbs Free Energy Change (?G°)

This concept represents the change in free energy when a reaction occurs under standard conditions. It is a vital thermodynamic quantity used to predict whether a reaction is spontaneous, with a negative ?G° indicating that the process can proceed without external energy input. The calculation often involves using standard free energies of formation for both reactants and products.

Relationship between ?G° and Equilibrium Constant

There is an important connection in thermodynamics between the change in Gibbs free energy under standard conditions and the equilibrium constant of a reaction. This is expressed by the equation ?G° = -RT ln K, which allows one to compute either ?G° or the equilibrium constant if the other is known. This relation bridges the gap between thermodynamic feasibility and the extent to which a reaction will proceed.

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