The solubility of calcium sulfate dihydrate (CaSO4·2H2O) in water and various solutions is a complex phenomenon that depends on several factors, including temperature, ionic strength, and the presence of other ions in the solution. Understanding the relationship between the solubility of CaSO4 and temperature is crucial in various industrial and scientific applications, such as water treatment, mineral processing, and pharmaceutical formulations.
The Equilibrium Reaction and Solubility Product Constant (Ksp)
The solubility of CaSO4 in water is described by the following reversible reaction and equilibrium expression:
CaSO4(s) ↔ Ca2+ + SO4 2-
Ksp(CaSO4) = [Ca2+][SO4 2-] = 2.4 × 10-5 (at 25°C)
This equilibrium expression implies that the product of the calcium ion concentration and the sulfate ion concentration can be no larger than 2.4 × 10-5 in any aqueous solution at 25°C. The value of the solubility product constant (Ksp) varies with temperature, as the solubility of CaSO4 is temperature-dependent.
Temperature Dependence of CaSO4 Solubility in Water
The solubility of CaSO4 in water increases with increasing temperature. This can be attributed to the endothermic nature of the dissolution process, as described by the following thermodynamic relationship:
ΔH° = -RT ln(Ksp)
Where:
– ΔH° is the standard enthalpy change of the dissolution reaction
– R is the universal gas constant
– T is the absolute temperature
– Ksp is the solubility product constant
As the temperature increases, the value of Ksp increases, indicating that the solubility of CaSO4 also increases. This is because the higher kinetic energy of the ions at higher temperatures overcomes the electrostatic attractions, allowing more ions to dissociate and enter the solution.
The following table shows the solubility of CaSO4 in water at different temperatures:
| Temperature (°C) | Solubility (g/100 mL) |
|---|---|
| 25 | 0.20 |
| 50 | 0.28 |
| 100 | 1.70 |
As can be seen, the solubility of CaSO4 in water increases significantly as the temperature rises from 25°C to 100°C, with the solubility at 100°C being almost 8.5 times higher than at 25°C.
The Common Ion Effect and Solubility in Salt Solutions
The solubility of CaSO4 in salt solutions can be significantly different from that in pure water due to the common ion effect and the influence of ionic strength.
The Common Ion Effect
The common ion effect occurs when a solution contains a common ion (in this case, the sulfate ion, SO4 2-) from another source, such as a dissolved salt. The presence of this common ion shifts the equilibrium of the CaSO4 dissolution reaction to the left, reducing the solubility of CaSO4.
For example, the solubility of CaSO4 in a 0.1 M Na2SO4 solution is lower than that in pure water due to the common ion effect. The additional sulfate ions from the Na2SO4 salt suppress the dissociation of CaSO4, leading to a decrease in the solubility.
Ionic Strength and Solubility
In contrast, the solubility of CaSO4 in a NaCl solution increases with increasing NaCl concentration. This is due to the increase in ionic strength, which weakens the electrostatic interactions between the ions in the solution, allowing more CaSO4 to dissociate and enter the solution.
The solubility of CaSO4 in multicomponent aqueous solutions can be modeled using the Pitzer equation, which takes into account the interactions between ions in the solution, including the common ion effect and ionic strength.
Numerical Examples and Calculations
To illustrate the temperature dependence of CaSO4 solubility, let’s consider the following examples:
- Calculate the solubility of CaSO4 in water at 50°C, given that the Ksp at 50°C is 3.14 × 10-5.
Using the Ksp expression:
Ksp = [Ca2+][SO4 2-]
Solubility = √(Ksp) = √(3.14 × 10-5) = 0.0056 M
Converting to g/100 mL:
Molar mass of CaSO4·2H2O = 172.17 g/mol
Solubility = 0.0056 M × (172.17 g/mol) × (100 mL/1 L) = 0.96 g/100 mL
- Determine the change in solubility of CaSO4 in a 0.1 M Na2SO4 solution compared to pure water at 25°C.
In pure water at 25°C, the solubility of CaSO4 is 0.20 g/100 mL.
In a 0.1 M Na2SO4 solution, the common ion effect reduces the solubility.
The new Ksp value can be calculated using the equilibrium expression:
Ksp = [Ca2+][SO4 2-]
[SO4 2-] = 0.1 M (from the Na2SO4 solution)
[Ca2+] = Ksp / [SO4 2-] = (2.4 × 10-5) / 0.1 = 2.4 × 10-4 M
Solubility = [Ca2+] × (172.17 g/mol) × (100 mL/1 L) = 0.041 g/100 mL
The solubility in the 0.1 M Na2SO4 solution is approximately 0.041 g/100 mL, which is significantly lower than the solubility in pure water (0.20 g/100 mL) due to the common ion effect.
These examples demonstrate how the solubility of CaSO4 can be calculated and compared in different scenarios, taking into account the effects of temperature and the presence of other ions in the solution.
Conclusion
The solubility of calcium sulfate (CaSO4) is a complex phenomenon that is strongly influenced by temperature and the composition of the surrounding solution. Understanding the relationship between CaSO4 solubility and temperature, as well as the effects of the common ion and ionic strength, is crucial in various industrial and scientific applications.
By applying the principles of equilibrium chemistry and thermodynamics, we can accurately predict and model the solubility of CaSO4 in different scenarios, enabling better control and optimization of processes involving this important compound.
References
- http://www1.udel.edu/chem/munson/chem445/Exp3.pdf
- https://pubs.acs.org/doi/10.1021/acs.jced.0c00052
- https://alpha.chem.umb.edu/chemistry/ch313/caso4%20exp%20Fall%202011.pdf
- https://pubs.acs.org/doi/10.1021/acs.jced.9b00112
- https://www.researchgate.net/publication/280096290_A_Thermodynamic_Model_of_CaSO4_Solubility_in_Multicomponent_Aqueous_Solutions
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