Question

A hydrothermal solution contains dissolved ions of Ca\(^{2+}\) and SO\(_4^{2-}\). If the Saturation Index (SI) of the solution is negative, which of the following statements is/are CORRECT if gypsum is added to the solution?

• A. Gypsum will precipitate from the solution
• B. Gypsum will dissolve in the solution
• C. The concentration of Ca\(^{2+}\) will increase and SO\(_4^{2-}\) will decrease in the solution
• D. The concentrations of both Ca\(^{2+}\) and SO\(_4^{2-}\) will increase in the solution

Hint:

Negative SI means undersaturated with respect to gypsum, so added gypsum dissolves, releasing Ca2+ and SO4(2-) together in a 1:1 ratio.

Answer 1

The Correct Option is B, D

Step 1: Recall what the Saturation Index tells us.
The Saturation Index of a mineral in a solution is defined as
\[ SI=\log_{10}\left(\frac{IAP}{K_{sp}}\right) \]
where \(IAP\) is the ion activity product of the mineral forming ions actually present in the solution, and \(K_{sp}\) is the solubility product of that mineral at equilibrium.
When \(SI>0\), the solution is supersaturated and the mineral tends to precipitate.
When \(SI=0\), the solution is exactly at equilibrium with the mineral.
When \(SI<0\), the solution is undersaturated, meaning it holds less of the dissolved ions than it is capable of holding, and it can take up, that is dissolve, more of the mineral.

Step 2: Apply this to the given solution.
We are told the Saturation Index of the solution with respect to gypsum is negative. This means the solution is undersaturated with respect to gypsum, \(CaSO_4\cdot 2H_2O\), and has room to dissolve more of it before reaching equilibrium.

Step 3: Work out what happens when gypsum is added.
Since the solution is undersaturated, adding solid gypsum to it will cause the gypsum to dissolve, moving the solution towards saturation. The dissolution reaction is
\[ CaSO_4\cdot 2H_2O \rightarrow Ca^{2+}+SO_4^{2-}+2H_2O \]
Every formula unit of gypsum that dissolves releases exactly one \(Ca^{2+}\) ion and one \(SO_4^{2-}\) ion into solution, in a fixed \(1:1\) ratio.

Step 4: Analyze option (A).
"Gypsum will precipitate from the solution" would require \(SI>0\), a supersaturated solution. Since \(SI\) is negative here, precipitation cannot happen, this statement is incorrect.

Step 5: Analyze option (B).
"Gypsum will dissolve in the solution" matches the reasoning in Step 3 exactly, an undersaturated solution takes up more of the mineral added to it. Correct.

Step 6: Analyze option (C).
"The concentration of \(Ca^{2+}\) will increase and \(SO_4^{2-}\) will decrease" cannot be right, because gypsum releases both ions together in equal amounts when it dissolves, so both go up together, neither one falls while the other rises. Incorrect.

Step 7: Analyze option (D).
"The concentrations of both \(Ca^{2+}\) and \(SO_4^{2-}\) will increase" matches the stoichiometry of the dissolution reaction in Step 3, both ions are added to solution together as gypsum dissolves. Correct.

Step 8: Final conclusion.
\[ \boxed{\text{Gypsum dissolves; both } Ca^{2+} \text{ and } SO_4^{2-} \text{ increase (options B and D)}} \]