Colligative Properties: Osmotic Pressure and Vapor Pressure

Osmotic pressure is one of the four colligative properties.
Osmosis is the process where a liquid may or may not pass through a semipermeable membrane.
Semipermeable membranes are common in biological systems, such as cell membranes, which selectively allow substances to pass through.
Basic Setup:
- Imagine a glass tube with a semipermeable membrane at the bottom.
- One side contains pure water, and the other contains water with impurities (e.g., sodium chloride).
Osmosis and Reverse Osmosis (RO):
- Natural osmosis can be reversed using RO.
- RO is used industrially to purify water, such as in coastal regions of Australia where freshwater is scarce.
- Ocean water is processed through RO plants to remove salt.
- The process is expensive due to the cost and fragility of the membranes, which can break and clog easily.
- Large-scale RO is necessary for supplying water to farms and towns.
- Middle Eastern countries with abundant oil resources also use RO to purify seawater.
- RO is less common in areas where water can be easily sourced from aquifers.

Osmosis across a semipermeable membrane generates pressure.
The equation for osmotic pressure ( $\pi$ ) is: $\pi = iMRT$
- $\pi$ = osmotic pressure
- $i$ = Van't Hoff factor (e.g., for NaCl, $i = 2$ , for CaCl2, $i = 3$ )
- $M$ = molarity (moles per liter) of the dissolved substance
- $R$ = the ideal gas constant, 0.0821 L·atm/(K·mol)
- $T$ = temperature in Kelvin
The value of $R$ (0.0821 L·atm/(K·mol)) is analogous to using different units (e.g., feet vs. yards) for the same distance.
Osmotic pressure is a colligative property because it depends on the concentration of solute particles.

Vapor pressure is another colligative property related to the pressure exerted by the vapor of a liquid.
Consider a sealed flask containing methanol.
Methanol was chosen because it does not readily form gas.
The flask contains liquid methanol at the bottom and methanol vapor in the space above the liquid.
The methanol vapor exerts a pressure.
If the flask initially contains no methanol, the initial pressure is zero.
As the amount of methanol increases, the pressure increases. (This pressure remains small.)
If the flask is unsealed, the methanol will evaporate completely (e.g., 50 mL of methanol will evaporate if left open during lunch).
Salt water, however, would remain mostly unchanged because its vapor pressure is much lower.

Molar mass of water (H2O): (2 * 1) + 16 = 18 grams/mole.
Molar mass of methanol (CH3OH): 12 + 16 + (4 * 1) = 32 grams/mole.
Example: Suppose you have 18 grams of water and 32 grams of methanol. Calculate the number of moles for each.
- Moles of water = mass / molar mass = 18 grams / (18 grams/mole) = 1 mole.
- Moles of methanol = 32 grams / (32 grams/mole) = 1 mole.
The mole fraction of water is calculated as:
- Mole fraction of water = (moles of water) / (total moles) = (moles of water) / (moles of water + moles of methanol).
- Mole fraction of water = 1 mole / (1 mole + 1 mole) = 1 / 2 = 0.5.
Mole fractions range from 0 to 1 and should not be negative.

From the ideal gas law, $PV = nRT$ , where:
- $P$ = pressure
- $V$ = volume
- $n$ = number of moles
- $R$ = ideal gas constant
- $T$ = temperature
When temperature and volume are constant, pressure is proportional to the number of moles.
The pressure of a gas is related to its mole fraction by:
$P = \text{Mole Fraction} \times \text{Total Vapor Pressure of Pure Compound}$
For example, the pressure of water in a mixture is:
$P_{\text{water}} = \text{Mole Fraction of Water} \times \text{Vapor Pressure of Pure Water}$
Vapor pressure of pure water can be looked up in reference tables for a given temperature.

In summary, the four colligative properties have been discussed. A free online textbook is available for further reading.