what is the activity coefficient of SO4^2- when the ionic strength of a solution is .1?
To determine the activity coefficient of SO4^2- in a solution with an ionic strength of 0.1, we need to use an activity coefficient model such as the Debye-Hückel equation. The Debye-Hückel equation is an approximation that relates the activity coefficient to the ionic strength of a solution.
The equation is given by:
logγ± = -0.509*z^2*√(I)/(1 + 1.2*√(I))
Where:
- logγ± is the logarithm of the activity coefficient
- z is the charge of the ion (in this case, z = 2 for SO4^2-)
- I is the ionic strength of the solution
Using this equation, we can calculate the activity coefficient of SO4^2- in a solution with an ionic strength of 0.1.
Let's plug in the values:
logγ± = -0.509*(2^2)*√(0.1)/(1 + 1.2*√(0.1))
Simplifying the equation:
logγ± = -0.509*4*√(0.1)/(1 + 1.2*√(0.1))
logγ± = -2.036*√(0.1)/(1 + 1.2*√(0.1))
Now, we can calculate the value using a calculator or software:
logγ± ≈ -0.938
To get the activity coefficient, we can take the antilog (inverse logarithm) of the value:
γ± ≈ 0.10 (approximately)
Therefore, the activity coefficient of SO4^2- in a solution with an ionic strength of 0.1 is approximately 0.10.