CHM110 Vapor Pressure and Osmotic Pressure

Molecular Weight of Water

Water's chemical formula is $H_2O$ .
The molecular weight of water is the sum of the atomic weights of its constituent atoms.
Hydrogen (H) has an atomic weight of approximately $1.008$ amu (atomic mass units).
Oxygen (O) has an atomic weight of approximately $15.999$ amu.
Therefore, the molecular weight of water is calculated as $(2 \times 1.008) + 15.999 = 2.016 + 15.999 = 18.015$ amu.
This molecular weight is crucial for understanding its concentration in solutions and its role in chemical reactions.

Vapor Pressure (P and P0)

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.
$P_0$ represents the vapor pressure of a pure solvent, such as pure water.
$P$ represents the vapor pressure of a solution, which contains a solute dissolved in the solvent.
According to Raoult's Law, the vapor pressure of a solvent above a solution ( $P$ ) is equal to the mole fraction of the solvent ( $X<em>{solvent}$ ) multiplied by the vapor pressure of the pure solvent ( $P</em>0$ ): $P = X<em>{solvent} \times P</em>0$ .
The presence of a non-volatile solute always lowers the vapor pressure of the solvent, meaning P < P_0. This is a colligative property.
When discussing vapor pressure, it is essential to identify whether the pressure refers to the pure solvent ( $P_0$ ) or the solution ( $P$ ), as their values and implications differ significantly, especially in the context of osmotic pressure and other colligative properties.
Units for pressure should also be consistently identified (e.g., mmHg, torr, kPa, atm).

Osmotic Pressure

Osmotic pressure ( $\Pi$ ) is the pressure that needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane.
It is a colligative property, meaning it depends on the concentration of solute particles, not on their identity.
Osmosis is the net movement of solvent molecules (e.g., water) from a region of higher solvent concentration (lower solute concentration) to a region of lower solvent concentration (higher solute concentration) through a selectively permeable membrane until equilibrium is reached.
The van 't Hoff equation is commonly used to calculate osmotic pressure: $\Pi = iMRT$
- $i$ = van 't Hoff factor (number of particles a solute dissociates into in solution; for non-electrolytes, $i=1$ ).
- $M$ = Molar concentration (moles of solute per liter of solution).
- $R$ = Ideal gas constant ( $0.08206 \text{ L}\cdot\text{atm/mol}\cdot\text{K}$ or $8.314 \text{ J/mol}\cdot\text{K}$ ).
- $T$ = Absolute temperature in Kelvin ( $K = \text{Celsius} + 273.15$ ).
Osmotic pressure plays a crucial role in biological systems, such as maintaining cell turgor and kidney function, as well as in industrial processes like desalination (reverse osmosis).