Calculate the Gibbs free energy of the reaction from mixing 50 mL each of 0.50 M AgNO3(aq) solution and 1 M of NaCl(aq) to form AgCl(s) at 25°. The Ksp of AgCl is 6.0 × 10—11 at 25 °C

To calculate the Gibbs free energy (ΔG) of the reaction, we first need to find the equilibrium constant (K) of the reaction. The reaction is:

AgNO3(aq) + NaCl(aq) -> AgCl(s) + NaNO3(aq)

Since AgCl is a solid, its concentration is not included in the equilibrium expression. The Ksp given is the solubility product constant for the dissolution of AgCl, which is the reverse of the reaction given. Therefore, the equilibrium constant for the reaction given is the reciprocal of the Ksp.

K = 1/Ksp = 1/(6.0 × 10^-11) = 1.67 × 10^10

Next, we use the formula for Gibbs free energy in terms of the equilibrium constant:

ΔG = -RT ln(K)

where R is the gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin. Convert the temperature from Celsius to Kelvin:

T = 25°C + 273.15 = 298.15 K

Substitute the values into the formula:

ΔG = -8.314 J/(mol·K) × 298.15 K × ln(1.67 × 10^10)

Calculate the natural logarithm:

ΔG = -8.314 J/(mol·K) × 298.15 K × 23.64

Finally, calculate the Gibbs free energy:

ΔG = -58,500 J/mol = -58.5 kJ/mol

So, the Gibbs free energy of the reaction is -58.5 kJ/mol.