How to Calculate Ksp from Temperature
Use the integrated van’t Hoff equation to estimate how a solubility product constant changes between two temperatures when you know a reference Ksp and the dissolution enthalpy.
Assumption: ΔH is approximately constant over the temperature range. For large temperature spans or concentrated systems, measured equilibrium data are better than a simple thermodynamic estimate.
Calculated Results
Ksp vs Temperature Chart
Expert Guide: How to Calculate Ksp from Temperature
If you want to know how to calculate Ksp from temperature, the key idea is that a solubility equilibrium behaves like any other equilibrium. When temperature changes, the equilibrium constant can change too. For a slightly soluble salt, that equilibrium constant is the solubility product constant, or Ksp. In practical chemistry, you usually do not calculate Ksp from temperature alone. You calculate the new Ksp at a different temperature by combining a known reference Ksp with a thermodynamic quantity, most often the enthalpy of dissolution, ΔH.
The standard approach is the integrated van’t Hoff equation. This relation tells you how an equilibrium constant changes between two temperatures. It is especially useful when you know the Ksp at one temperature and want to estimate it at another temperature without running a full experimental solubility study. That is exactly what the calculator above does.
What Ksp Means in Solubility Equilibria
Ksp describes the equilibrium established when a sparingly soluble ionic solid dissolves in water. For example, silver chloride dissolves according to:
The corresponding solubility product is:
Solids do not appear in the equilibrium expression because their activity is treated as constant. A larger Ksp generally means the compound is more soluble, although stoichiometry matters when you convert Ksp into molar solubility. Temperature can shift this balance because dissolution can be endothermic or exothermic. If a salt dissolves endothermically, heating often raises Ksp. If dissolution is exothermic, heating can lower Ksp.
The Main Equation Used to Calculate Ksp at a New Temperature
The most common equation for estimating Ksp at a second temperature is the integrated van’t Hoff expression:
Where:
- K1 is the known Ksp at the reference temperature.
- K2 is the Ksp you want to calculate.
- T1 and T2 must be in Kelvin.
- ΔH is the enthalpy of dissolution in J/mol.
- R is the gas constant, 8.314 J/mol·K.
Rearranging gives:
Step by Step Method
- Find a trusted reference Ksp at a known temperature, often 25°C or 298.15 K.
- Find the enthalpy of dissolution, ΔH, for the salt. Make sure the sign is correct.
- Convert both temperatures to Kelvin.
- Convert ΔH to J/mol if it is given in kJ/mol.
- Substitute all values into the van’t Hoff equation.
- Solve for K2 and interpret whether the solubility increased or decreased.
Worked Example
Suppose a compound has a reference Ksp of 1.80 × 10-10 at 25°C, and its dissolution enthalpy is +65.0 kJ/mol. You want the estimated Ksp at 35°C.
- Convert temperatures: 25°C = 298.15 K and 35°C = 308.15 K.
- Convert enthalpy: 65.0 kJ/mol = 65000 J/mol.
- Apply the formula:
ln(K2/1.80 × 10-10) = -(65000/8.314) × (1/308.15 – 1/298.15)
- Evaluate the temperature term. Because 1/T2 is smaller than 1/T1, the bracket becomes negative.
- With positive ΔH, the full right side becomes positive, meaning K2 is larger than K1.
This is the thermodynamic signature of an endothermic dissolution. A temperature increase favors dissolution, so Ksp rises. The calculator above automates the arithmetic and also charts the predicted trend over a range of temperatures.
Why Temperature Must Be in Kelvin
One of the most common student mistakes is plugging Celsius values directly into the equation. That causes a major error because the van’t Hoff equation uses absolute temperature. Always convert to Kelvin first:
- K = °C + 273.15
- K = (°F – 32) × 5/9 + 273.15
The calculator accepts Celsius, Kelvin, or Fahrenheit, then converts internally to Kelvin before it computes Ksp.
Interpreting the Sign of ΔH
The sign of ΔH determines the direction of the temperature effect:
- ΔH > 0: dissolution is endothermic, so increasing temperature usually increases Ksp.
- ΔH < 0: dissolution is exothermic, so increasing temperature usually decreases Ksp.
This aligns with Le Chatelier’s principle. Heat can be treated like a reactant for an endothermic process and like a product for an exothermic process.
Comparison Table: Typical Ksp Values at 25°C
The table below gives a useful sense of scale. Ksp values span many orders of magnitude, which is why scientific notation is essential.
| Compound | Dissolution Equilibrium | Typical Ksp at 25°C | Solubility Insight |
|---|---|---|---|
| AgCl | AgCl(s) ⇌ Ag+ + Cl– | 1.8 × 10-10 | Very low solubility, common textbook example |
| BaSO4 | BaSO4(s) ⇌ Ba2+ + SO42- | 1.1 × 10-10 | Extremely insoluble, used in radiographic contrast media |
| CaCO3 | CaCO3(s) ⇌ Ca2+ + CO32- | 3.3 × 10-9 | Relevant in scale formation and geochemistry |
| CaF2 | CaF2(s) ⇌ Ca2+ + 2F– | 3.9 × 10-11 | Low Ksp, but stoichiometry affects molar solubility |
| PbI2 | PbI2(s) ⇌ Pb2+ + 2I– | 7.1 × 10-9 | Still sparingly soluble, often used in precipitation examples |
Comparison Table: Predicted Ksp Change for Different ΔH Values
The table below shows how strongly the enthalpy term can affect a calculation when temperature rises from 25°C to 35°C, assuming the same starting Ksp of 1.00 × 10-10. These are van’t Hoff estimates, useful for intuition.
| ΔH of Dissolution | Reference Ksp at 25°C | Predicted Ksp at 35°C | Percent Change |
|---|---|---|---|
| -40 kJ/mol | 1.00 × 10-10 | 5.92 × 10-11 | -40.8% |
| +20 kJ/mol | 1.00 × 10-10 | 1.30 × 10-10 | +30.0% |
| +40 kJ/mol | 1.00 × 10-10 | 1.70 × 10-10 | +70.0% |
| +65 kJ/mol | 1.00 × 10-10 | 2.38 × 10-10 | +138.0% |
Common Errors When Calculating Ksp from Temperature
- Using Celsius directly instead of Kelvin.
- Using the wrong sign for ΔH, which flips the direction of the temperature effect.
- Mixing kJ and J. The gas constant 8.314 requires ΔH in J/mol.
- Confusing Ksp with solubility. Ksp is an equilibrium constant, not directly the molar solubility unless you account for stoichiometry.
- Applying the formula over very large temperature ranges where ΔH may no longer be close to constant.
When This Method Works Best
This temperature based Ksp calculation is best for:
- General chemistry and physical chemistry problem solving
- Moderate temperature changes
- Dilute aqueous systems
- Quick engineering or laboratory estimates
It is less reliable when ionic strength is high, multiple equilibria overlap, hydration changes significantly with temperature, or the dissolution process involves polymorphic transitions. In those cases, measured data or advanced models can outperform a simple van’t Hoff estimate.
Ksp Versus Solubility: A Quick Reminder
Students often ask why Ksp cannot simply be read as solubility. The reason is stoichiometry. For AgCl, if the molar solubility is s, then:
But for CaF2, if molar solubility is s:
Two compounds can have similar Ksp values but different molar solubilities because their ions appear with different coefficients.
Authoritative References for Further Reading
For deeper thermodynamic background, gas constant values, and equilibrium concepts, review these reliable sources:
- NIST CODATA gas constant reference
- NIST Chemistry WebBook
- University of Wisconsin Department of Chemistry
Final Takeaway
To calculate Ksp from temperature, you normally need three inputs: a known Ksp at one temperature, the new temperature, and the enthalpy of dissolution. Then you use the integrated van’t Hoff equation with temperatures in Kelvin and ΔH in J/mol. If ΔH is positive, Ksp tends to increase as temperature rises. If ΔH is negative, Ksp tends to decrease. The calculator on this page handles the unit conversions, computes the result instantly, and plots the expected Ksp trend so you can see how sensitive the equilibrium is to temperature changes.