Solubility and Vapor Pressure in Solutions: Effects of Pressure and Temperature

Solubility and Solution Equilibria

Solubility of Solutes in Solvents

Solubility refers to the maximum amount of a solute that can dissolve in a solvent at a given temperature and pressure, forming a saturated solution. When a non-volatile solute is dissolved in a solvent, the system can reach equilibrium, where the rate of dissolution equals the rate of precipitation.

• Saturated Solution: Contains the maximum concentration of solute that can dissolve at a specific temperature.

• Unsaturated Solution: Contains less solute than the maximum amount that can dissolve.

• Supersaturated Solution: Contains more solute than is stable at a given temperature; excess solute may precipitate out.

• Effect of Temperature: Heating a solution can increase solubility for most solids, but may decrease solubility for gases.

Example: In a series of beakers at different temperatures, the concentration of solute in solution may change as temperature changes, but returns to equilibrium when cooled. Additional info: At equilibrium, the concentration of dissolved solute is constant for a given temperature and pressure.

Factors Affecting Solubility

Pressure Effects: Henry's Law

Pressure has a significant effect on the solubility of gases in liquids. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the solution.

• Henry's Law Equation: $S_g = k P_g$ where:

  • $S_g$ = solubility of the gas (mol/L)

  • $k$ = Henry's law constant (mol/(L·atm))

  • $P_g$ = partial pressure of the gas (atm)

• Henry's Law Constant: Varies for each gas-solvent pair and depends on temperature.

• Pressure Effect on Liquids and Solids: Pressure has little effect on the solubility of liquids and solids because their molecules are not easily compressed.

Example Calculation: Given: Solubility of $N_2$ in water at 25°C and 0.78 atm is $5.3 imes 10^{-4}$ M. Find $k$: $k = rac{S}{P} = rac{5.3 imes 10^{-4} ext{ M}}{0.78 ext{ atm}} = 6.8 imes 10^{-4} ext{ mol/(L·atm)}$ Comparison: If Henry's law constant for $O_2$ at 25°C is $1.3 imes 10^{-2}$ mol/(L·atm), $O_2$ is more soluble than $N_2$ under identical conditions.

Table: Henry's Law Constants for Selected Gases in Water at 25°C

Gas	Henry's Law Constant (mol/(L·atm))
N2	6.8 × 10-4
O2	1.3 × 10-2
CO2	1.05 × 10-3
He	Additional info: Value inferred from graph, lower than N2

Temperature Effects on Solubility

Temperature affects the solubility of both gases and solids in liquids, but in opposite ways.

• Gases: Solubility decreases as temperature increases. This is because higher temperatures provide more energy for gas molecules to escape from the solution.

• Solids: Solubility generally increases as temperature increases, allowing more solid to dissolve.

Example: Soda is more bubbly (contains more dissolved CO2) when cold, because gas solubility is higher at lower temperatures.

Table: Effect of Temperature on Gas Solubility in Water

Gas	Trend with Increasing Temperature
CH4	Decreases
O2	Decreases
CO	Decreases
He	Decreases (least change)

Expressing Solution Concentration

Quantitative Measures of Concentration

Concentration describes the amount of solute present in a given quantity of solvent or solution. Several units are commonly used:

• Molarity (M): $M = rac{ ext{moles of solute}}{ ext{liters of solution}}$

• Molality (m): $m = rac{ ext{moles of solute}}{ ext{kilograms of solvent}}$ Useful because mass does not change with temperature.

• Mass Percent (%): $ext{Mass \, ext{percent}} = rac{ ext{mass of component}}{ ext{total mass of solution}} imes 100 ext{ ext{%}}$

• Parts per million (ppm): $ext{ppm} = rac{ ext{mass of component}}{ ext{total mass of solution}} imes 10^6$

• Mole Fraction (X): $X_i = rac{ ext{moles of component } i}{ ext{total moles of all components}}$

Example: Calculating molarity and molality for ethylene glycol in antifreeze, or converting ppm to molarity for lead in toys.

Vapor Pressure and Solutions

Vapor Pressure of Pure Liquids and Solutions

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase in a closed container. When a non-volatile solute is added to a solvent, the vapor pressure of the solution is lower than that of the pure solvent.

• Raoult's Law: The vapor pressure of a solution is proportional to the mole fraction of the solvent. $P_{ ext{solution}} = X_{ ext{solvent}} P^0_{ ext{solvent}}$ where:

  • $P_{ ext{solution}}$ = vapor pressure of the solution

  • $X_{ ext{solvent}}$ = mole fraction of the solvent

  • $P^0_{ ext{solvent}}$ = vapor pressure of pure solvent

• Vapor Pressure Lowering: Non-volatile solutes reduce the ability of solvent molecules to escape, lowering the vapor pressure.

Example: If the vapor pressure of water at 20°C is 17.4 torr, and glucose is added so that $X_{ ext{glucose}} = 0.1$, then $X_{ ext{water}} = 0.9$, and $P_{ ext{solution}} = 0.9 imes 17.4 = 15.66$ torr.

Vapor Pressure of Solutions with Volatile Components: Dalton's Law

For solutions with more than one volatile component, the total vapor pressure is the sum of the partial pressures of each component.

• Dalton's Law: $P_{ ext{total}} = X_A P^0_A + X_B P^0_B$

Example: For a solution of 25.0 g heptane (100 g/mol, $P^0 = 79$ torr) and 35.0 g octane (114 g/mol, $P^0 = 35.2$ torr), calculate mole fractions and total vapor pressure.

Summary Table: Key Equations

Concept	Equation (LaTeX)
Henry's Law	$S_g = k P_g$
Molarity	$M = \frac{\text{moles of solute}}{\text{liters of solution}}$
Molality	$m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}$
Mass Percent	$\text{Mass \%} = \frac{\text{mass of component}}{\text{total mass of solution}} \times 100\%$
ppm	$\text{ppm} = \frac{\text{mass of component}}{\text{total mass of solution}} \times 10^6$
Mole Fraction	$X_i = \frac{\text{moles of component } i}{\text{total moles of all components}}$
Raoult's Law	$P_{\text{solution}} = X_{\text{solvent}} P^0_{\text{solvent}}$
Dalton's Law	$P_{\text{total}} = X_A P^0_A + X_B P^0_B$

Additional info: These concepts are foundational for understanding colligative properties, solution chemistry, and phase equilibria in General Chemistry.