Debye-Huckel Limiting Law for Mean Activity Coefficient

The Debye-Huckel limiting law is an equation used to calculate the mean activity coefficient for ions in a solution. The equation is:

log γ± = -0.509 z₁z₂ √(I)/T

where γ± is the mean activity coefficient, z₁ and z₂ are the charges on the ions, I is the ionic strength of the solution, and T is the temperature in Kelvin.

Calculating the Mean Activity Coefficient for K₂SO₄

Given:

Molality of K₂SO₄ = 0.010 mol/kg
Temperature (T) = 25°C = 298 K

Ionic strength (I) can be calculated using the formula:

I = 1/2 ∑mi zi²

where mi is the molality of the ion and zi is the charge on the ion.

For K₂SO₄, the ions are K⁺ and SO₄²⁻. The molality of K⁺ is 0.010 mol/kg and the molality of SO₄²⁻ is also 0.010 mol/kg. The charges on K⁺ and SO₄²⁻ are +1 and -2 respectively.

Therefore, the ionic strength of the solution is:

I = 1/2 [(0.010 mol/kg) x (1²) + (0.010 mol/kg) x (2²)] = 0.035 mol/kg

Substituting the values in the Debye-Huckel equation, we get:

log γ± = -0.509 (1) (-2) √(0.035 mol/kg)/298 K = -0.508

γ± = 10^(-0.508) = 0.943

Therefore, the mean activity coefficient for the ions in an aqueous solution of K₂SO₄ with a molality of 0.010 mol/kg at 25°C is 0.943.

Conclusion

The Debye-Huckel limiting law can be used to calculate the mean activity coefficient for ions in a solution. The ionic strength of the solution can be calculated using the molality and charges of the ions. Substituting the values in the equation, we can calculate the mean activity coefficient for the ions. In this case, the mean activity coefficient for K₂SO₄ was calculated to be 0.943.