The congruent dissolution of langbeinite can be represented by the following equation:
K2Mg2(SO4)3(s) ⇌ 2K+(aq) + Mg2+(aq) + 3SO42-(aq)
The ΔG°R for this reaction can be calculated using the standard Gibbs free energy of formation (ΔG°f) values of the reactants and products. The standard Gibbs free energy change for the reaction can be calculated using the equation:
ΔG°R = ΣnΔG°f(products) - ΣnΔG°f(reactants)
where n is the stoichiometric coefficient of each species in the balanced chemical equation.
The standard Gibbs free energy of formation values for K2Mg2(SO4)3(s), K+(aq), Mg2+(aq), and SO42-(aq) are -3812.7, 0, -466.9, and -909.3 kJ/mol, respectively.
Using the stoichiometric coefficients in the balanced equation, we get:
ΔG°R = [2(0) + 1(-466.9) + 3(-909.3)] - (-3812.7)
ΔG°R = 1976.2 kJ/mol
Since ΔG°R is positive, the reaction is non-spontaneous under standard conditions. However, the actual value of ΔG for the reaction will depend on the concentrations of the species in solution and the temperature, according to the equation:
ΔG = ΔG° + RTln(Q)
where Q is the reaction quotient, R is the gas constant, and T is the temperature in Kelvin. If Q is less than K (the equilibrium constant), ΔG will be negative and the reaction will proceed spontaneously in the forward direction.