## Solubility of Gypsum (CaSO4)

How much gypsum dissolves in water at 25°C?

We solve this task in two different ways: (i) by an analytical approach (with the “pocket calculator”) and (ii) numerically by running the whole gamut of chemical thermodynamics. The results will differ considerably, and we will explain why.

Analytical Approach

The reaction formula and its log K value (at 25°C) is given by:123

 (1) CaSO4  =  Ca+2 + SO4-2 log K = -4.58

The calculation rests upon two equations:

 (2) law of mass action:4 K  ≈  Ksp*  =  [Ca+2] · [SO4-2]  =  10-4.58 (3) charge balance: [Ca+2]  =  [SO4-2]

Inserting Eq.(3) into Eq.(2) yields the simple quadratic dependence:

 (4) K  =  [SO4-2]2

Since the dissolved amount of gypsum equals the value of [SO4], we immediately get the result:

 (5) ΔGypsum = K1/2 (6) ΔGypsum = (10-4.58)1/2 M (7) ΔGypsum = 10-2.29 M  =  5.12×10-3 M  =  5.12 mM

In words: The amount of 5.12 mmol gypsum dissolves in 1 liter of pure water. [Please note that Eq.(5), and the final result, are independent of the initial inventory of gypsum.] Numerical Approach with aqion

We start with pure water (button New) and switch to molar units (activate checkbox Mol). To open the mineral table click on Minerals, then enter the amount of 20 mmol/L gypsum.5

Run the calculation with Start, a first schematic overview appears. After click on next, the results are shown again in the output table. In the right column you find:

 pH = 7.07 Ca = 15.6 mM SO4 = 15.6 mM

According to this calculation, the amount of 15.4 mmol gypsum dissolves in 1 liter of pure water – it is three times more than in the calculation above!

Here, SO4 and Ca abbreviate the total concentrations:

 (8) [Ca]T = [Ca+2] + [CaSO4(aq)] + [CaHSO4+] + [CaOH+] (9) [SO4]T = [SO4-2] + [HSO4-] + [CaSO4(aq)] + [CaHSO4+]

The corresponding equilibrium speciation is listed in the table Ions:

 Ca+2 10.5 mM CaSO4(aq) 5.19 mM CaHSO4+ 3.2×10-6 mM CaOH+ 1.2×10-5 mM SO4-2 10.5 mM HSO4- 5.1×10-5 mM

In fact, there are only three major players: Ca+2, SO4-2 and CaSO4(aq). The last species is an aquoeous complex; it shoud not be confused with the mineral phase gypsum usually abbreviated with CaSO4(s).

Résumé

Both results differ considerably:

(10a) analytical approach (pocket calculator): 5.1 mM
(10b) numerical approach (chem. thermodynamics): 15.6 mM

The reasons for the deficiency of the analytical approach are:

• neglect of complexation (especially CaSO4(aq))
• neglect of activity corrections (at ionic strength I = 42 mM, γ = 0.48)

Remarks & Footnotes

1. The correct formula of gypsum is CaSO4:2H2O. To keep the notation straight, we use here the short form, CaSO4

2. Here and in the following, the shorter notation ‘log x’ is used for the decadic logarithm: log10 x.

3. Tables of Ksp values are given here

4. Here we approximate Ksp by the stoichiometric solubility product (Reminder: This is strictly valid for ideal solutions only, where ionic activities = concentrations).

5. The initial amount of gypsum should at least exceed the solubility limit. For eample, if you enter 3 mmol/L gypsum, it is far too little (the saturation index remains below zero).