Temperature dependence of solubility: Calculations and examples

📚 Quick Study Guide

• 🌡️ Solubility generally increases with temperature for solids in liquids.
• 🧊 Solubility of gases in liquids usually decreases with increasing temperature.
• ⚗️ The relationship between solubility and temperature can be represented graphically using solubility curves.
• 📈 The van't Hoff equation describes the quantitative relationship between solubility ($S$) and temperature ($T$): $\frac{d(\ln S)}{dT} = \frac{\Delta H_{sol}}{RT^2}$, where $\Delta H_{sol}$ is the enthalpy of solution and $R$ is the gas constant.
• 🧮 For practical calculations, a simplified form can be used if $\Delta H_{sol}$ is approximately constant over the temperature range: $\ln(\frac{S_2}{S_1}) = -\frac{\Delta H_{sol}}{R}(\frac{1}{T_2} - \frac{1}{T_1})$

Practice Quiz

1. Which of the following statements is generally true regarding the solubility of solids in liquids as temperature increases?

   1. A. Solubility decreases.
   2. B. Solubility remains constant.
   3. C. Solubility increases.
   4. D. Solubility fluctuates unpredictably.

2. What happens to the solubility of gases in liquids as temperature increases?

   1. A. Solubility increases.
   2. B. Solubility decreases.
   3. C. Solubility remains constant.
   4. D. Solubility fluctuates unpredictably.

3. The van't Hoff equation relates solubility to temperature. Which parameter represents the enthalpy of solution in the van't Hoff equation?

   1. A. $R$
   2. B. $T$
   3. C. $\Delta H_{sol}$
   4. D. $S$

4. If a salt's solubility is endothermic, what happens to its solubility as temperature increases?

   1. A. Solubility decreases.
   2. B. Solubility increases.
   3. C. Solubility remains constant.
   4. D. The effect cannot be determined.

5. Using the simplified van't Hoff equation, $\ln(\frac{S_2}{S_1}) = -\frac{\Delta H_{sol}}{R}(\frac{1}{T_2} - \frac{1}{T_1})$, what does $S_1$ represent?

   1. A. Solubility at temperature $T_2$.
   2. B. Solubility at temperature $T_1$.
   3. C. Change in solubility.
   4. D. Enthalpy of solution.

6. A gas has a solubility of 5 g/L at 20°C. If the temperature is increased to 40°C, what will likely happen to its solubility?

   1. A. Increase significantly.
   2. B. Decrease significantly.
   3. C. Remain approximately the same.
   4. D. Double.

7. Which type of plot is typically used to visualize the temperature dependence of solubility for different substances?

   1. A. Pie chart.
   2. B. Bar graph.
   3. C. Solubility curve.
   4. D. Histogram.