Final answer:
The ΔG (kJ/mol) for the given reaction at 25 Celsius can be calculated using the equation ΔG = ΔG° + RTln(Q), where Q is the reaction quotient calculated using the initial concentrations of Mg2+ and PO43−. Given the ΔG° value of 137.0 kJ/mol, the value of ΔG for the reaction is -97.2 kJ/mol.
Step-by-step explanation:
The ΔG (kJ/mol) for a reaction at 25 Celsius can be calculated using the equation:
ΔG = ΔG° + RTln(Q)
where ΔG° is the standard Gibbs free energy change, R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient.
In this case, the given reaction is:
Mg3(PO4)2 (s) ⇄ 3 Mg2+ (aq) + 2 PO43− (aq)
To calculate ΔG, we need to know the value of Q, which can be calculated using the initial concentrations of Mg2+ and PO43− in solution.
Q = [Mg2+]3[PO43−]2
Q = (0.65 M)3(0.43 M)2 = 0.011 M5
Given that ΔG° = 137.0 kJ/mol, R = 8.314 J/(mol⋅K), and T = 298 K, we can calculate the value of ΔG.
ΔG = 137.0 kJ/mol + (8.314 J/(mol⋅K) × 298 K × ln(0.011 M5)) = -97.2 kJ/mol
Therefore, the value of ΔG for the reaction at 25 Celsius is -97.2 kJ/mol.