Your advisor, Dr. Gettowerk, has given you the task of making a 1-liter of a sol

Question

Your advisor, Dr. Gettowerk, has given you the task of making a 1-liter of a solution with a calcium ion activity {Ca2+} of 1.3 × 104 M, and he wants you to make it in three different ways: one solution made in distilled water, one in 0.05 M KCl, and one in 0.1 M MgCl2. How much CaCl2 do you need to add to 1-L of water (or the appropriate salt solution) to make each solution and achieve the desired activity? Assume that all of the salts completely dissociate. Use the Davies equation for activity coefficients.

Explanation / Answer

Molar concentration and activity are related by:

a = f*C

Here f is activity coefficient

Please refer to the formulas for ionic strength and Davies equation.

I am providing solutions after putting values into those equations.

In order to calculate the activity coefficients using Davies equatioj, we first need to know the Ionic strength I.

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Distilled water:

Ionic Strength, I = 0

Using the Davies equation, we get:

Activity coefficient for Ca2+ in distilled water = 1

So, moles of CaCl2 required = 1.3 * 10-4

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0.05M KCl:

Ionic Strength, I = 0.050

Using the Davies equation, we get:

Activity coefficient for Ca2+ in 0.05M KCl = 0.462

So, moles of CaCl2 required = 1.3/0.462 * 10-4 = 2.81 * 10-4

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0.1M MgCl2:

Ionic Strength, I = 0.250

Using the Davies equation, we get:

Activity coefficient for Ca2+ in 0.1M MgCl2 = 0.304

So, moles of CaCl2 required = 1.3/0.304 * 10-4 = 4.27 * 10-4

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