a solution of kcl is saturated at 50 c
A solution of kcl is saturated at 50 c when the dissolved amount of KCl has reached its solubility limit at 50 °C, so additional solid KCl remains undissolved at equilibrium.
Solubility statement and quantitative basis
Saturation for an ionic solid such as KCl in water is commonly reported as a mass ratio: grams of KCl that dissolve in 100 g of water at a specified temperature. That format links directly to mass-based concentration measures and to crystallization upon cooling.
Numerical values below use a typical KCl solubility curve for water near 1 atm. Small variations occur with measurement source and experimental conditions; the thermodynamic logic of saturation and precipitation remains the same.
Reference solubility values used
| Temperature (°C) | Solubility (g KCl per 100 g water) |
|---|---|
| 0 | 28.0 |
| 20 | 34.0 |
| 40 | 39.8 |
| 50 | 42.6 |
| 60 | 45.8 |
| 80 | 50.3 |
| 100 | 56.3 |
The values at 50 °C and 20 °C anchor the dissolved mass at saturation and the amount remaining dissolved after cooling.
Interpretation for a 100 g water basis
- Solubility at 50 °C: 42.6 g KCl dissolved per 100 g water at saturation.
- Solubility at 20 °C: 34.0 g KCl dissolved per 100 g water at saturation.
- Cooling behavior: the dissolved amount moves from the 50 °C limit toward the 20 °C limit; excess KCl appears as solid crystals if equilibrium is reached.
Dissolved mass at 50 °C and crystallization on cooling
A 100 g water basis makes the mass accounting direct.
Dissolved KCl at 50 °C saturation: \[ m_{50} \approx 42.6\ \text{g KCl per 100 g water}. \]
Dissolved KCl at 20 °C saturation: \[ m_{20} \approx 34.0\ \text{g KCl per 100 g water}. \]
Expected crystallized mass on cooling from 50 °C to 20 °C (equilibrium reached, no water loss): \[ m_{\text{crystals}} = m_{50} - m_{20} \approx 42.6 - 34.0 = 8.6\ \text{g}. \]
The crystallized solid is KCl(s); the remaining solution at 20 °C is saturated and contains about 34.0 g KCl per 100 g water.
Mass percent concentration connection
The solubility basis converts to mass percent using \[ \%\,(m/m) = \frac{m_{\text{solute}}}{m_{\text{solute}} + m_{\text{solvent}}}\times 100. \]
Mass percent for the saturated solution at 50 °C (100 g water basis): \[ \%\,(m/m)_{50} = \frac{42.6}{42.6 + 100}\times 100 \approx 29.9\%. \]
Mass percent for the saturated solution at 20 °C (100 g water basis): \[ \%\,(m/m)_{20} = \frac{34.0}{34.0 + 100}\times 100 \approx 25.4\%. \]
Common pitfalls
- Water mass changes: evaporation during heating changes the 100 g water basis and shifts the crystallized mass away from the simple difference in solubilities.
- Non-equilibrium cooling: rapid cooling can temporarily produce a supersaturated solution; delayed crystallization changes what is observed at a given moment.
- Basis confusion: “g per 100 g water” differs from “g per 100 g solution”; the two forms convert by including total solution mass in the denominator.
A solution of kcl is saturated at 50 c when it contains the maximum dissolved KCl allowed by the 50 °C solubility; cooling to a lower temperature decreases that limit and the excess KCl appears as solid crystals at equilibrium.