The equilibrium constant for a chemical reaction is a measure of the extent to which the reactants are converted into products at equilibrium. It is denoted by the symbol K and is determined by the concentrations of the reactants and products.

In this case, we have the following equilibrium: 3C10 (aq) + 2C1 (aq) ⇌ C105(aq). The equilibrium constant for this reaction is given as 10 x 10.

To calculate the Gibbs free energy change (ΔG) for this reaction, we can use the equation ΔG = -RTlnK, where R is the gas constant and T is the temperature in Kelvin.

Given that RT = 2500 J/mol and the equilibrium constant (K) is 10 x 10, we can substitute these values into the equation to find the value of ΔG.

Calculating the Gibbs free energy change (ΔG):

ΔG = -RTlnK
ΔG = -(2500 J/mol)(ln(10 x 10))

Simplifying the equation:

ΔG = -(2500 J/mol)(ln(10^2))
ΔG = -(2500 J/mol)(2ln10)
ΔG = -5000 J/mol(ln10)

Now, we can calculate the value of ln10 using a calculator:

ln10 ≈ 2.3026

Substituting this value back into the equation:

ΔG = -5000 J/mol(2.3026)
ΔG ≈ -11513 J/mol

Therefore, the Gibbs free energy change (ΔG) for this reaction is approximately -11513 J/mol.

Explanation:

- The equilibrium constant (K) is a measure of the extent to which the reactants are converted into products at equilibrium.
- The Gibbs free energy change (ΔG) is a measure of the spontaneity of a reaction. A negative ΔG indicates that the reaction is spontaneous.
- The equation ΔG = -RTlnK relates the Gibbs free energy change to the equilibrium constant and temperature.
- By substituting the given values into the equation, we can calculate the value of ΔG.
- The negative value of ΔG (-11513 J/mol) indicates that the reaction is spontaneous at the given temperature.