Osmotic Pressure in Solutions: Principles and Calculations

Osmotic Pressure in Solutions

Introduction to Osmosis and Osmotic Pressure

Osmosis is the movement of water across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. Osmotic pressure is the pressure required to prevent this flow of water, and it is a key concept in understanding solution behavior in chemistry and biology.

• Osmotic pressure is influenced by the concentration of solute particles and the temperature of the solution.

• It is important in physiological processes, such as the regulation of fluids in blood and cells.

Factors Affecting Osmotic Pressure

The osmotic pressure of a solution depends on several variables:

• Concentration: Higher solute concentration increases osmotic pressure.

• Temperature: Higher temperature increases osmotic pressure.

• Van't Hoff Factor (i): Represents the number of particles into which a solute dissociates in solution.

Osmotic Pressure Formula

The osmotic pressure (π) of a solution can be calculated using the following formula:

$\pi = iMRT$

• π: Osmotic pressure (in atm)

• i: Van't Hoff factor (number of particles per formula unit)

• M: Molarity (mol/L)

• R: Gas constant ($0.08206$ L·atm/mol·K)

• T: Temperature in kelvin (K)

Example Calculation

Example: Calculate the osmotic pressure of a solution containing 18.30 mg of ZnO in 15.1 mL of solution at 26°C.

• Convert mass to moles: $\frac{18.30\,\text{mg}}{81.389\,\text{g/mol}} = 0.000225\,\text{mol}$

• Convert volume to liters: $15.1\,\text{mL} = 0.0151\,\text{L}$

• Calculate molarity: $M = \frac{0.000225}{0.0151} = 0.0149\,\text{mol/L}$

• Convert temperature to kelvin: $T = 26 + 273.15 = 299.15\,\text{K}$

• Assume $i = 1$ for ZnO (does not dissociate significantly in water).

• Plug into formula: $\pi = (1)(0.0149)(0.08206)(299.15) = 0.364\,\text{atm}$

Additional info: The example in the image uses slightly different values and units, but the calculation process is as shown above.

Practice Problems

• Practice 1: The osmotic pressure of blood is 5950.8 mmHg at 41°C. What mass of glucose (C6H12O6) is needed to prepare 5.51 L of solution? The osmotic pressure of the glucose solution is equal to the osmotic pressure of blood.

• Practice 2: The osmotic pressure of a solution containing 7.0 g of insulin per liter is 23.07 atm at 25°C. What is the molar mass of insulin? (1 atm = 760 torr)

Unit Conversions and Constants

• Gas constant (R): $0.08206$ L·atm/mol·K

• Temperature: Always convert Celsius to Kelvin by adding 273.15.

• Pressure: 1 atm = 760 mmHg = 760 torr

Summary Table: Osmotic Pressure Variables

Variable	Symbol	Unit	Description
Osmotic Pressure	π	atm	Pressure required to prevent osmosis
Van't Hoff Factor	i	unitless	Number of particles per formula unit
Molarity	M	mol/L	Concentration of solute
Gas Constant	R	L·atm/mol·K	Universal gas constant
Temperature	T	K	Temperature in kelvin