The osmotic method is an important method for determining the molecular weight of a substance, particularly for substances that form macromolecules such as polymers, proteins, and other high-molecular-weight compounds. The method is based on the measurement of osmotic pressure produced by a dilute solution of the substance.
Principle of the Osmotic Method
When a solution is separated from its pure solvent by a semipermeable membrane, solvent molecules can pass through the membrane, whereas the solute molecules cannot. The movement of solvent through the membrane is called osmosis.
The pressure that must be applied to the solution to stop the flow of solvent through the semipermeable membrane is called osmotic pressure and is represented by π.
For a dilute solution of a non-electrolyte, the relationship between osmotic pressure and concentration is given by the van't Hoff equation:
where:
- π = osmotic pressure of the solution
- C = molar concentration of the solute
- R = gas constant
- T = absolute temperature in kelvin
Derivation of the Molecular Weight Equation
Suppose w grams of a solute having molecular weight M are dissolved to make V litres of solution. The number of moles of solute is:
Therefore, the molar concentration of the solution is:
Substituting this value of C into the van't Hoff equation:
Rearranging the equation gives:
Thus, the molecular weight of the solute can be calculated by measuring its osmotic pressure, the mass of solute, the volume of solution, and the temperature.
The molecular weight of a solute is given by M = wRT / πV.
Units of the Quantities Used
| Symbol | Quantity | SI Unit | Common Laboratory Unit |
|---|---|---|---|
| w | Mass of solute | kg | g |
| V | Volume of solution | m3 | L |
| π | Osmotic pressure | Pa | atm, bar, mmHg |
| T | Absolute temperature | K | K |
| R | Gas constant | 8.314 J mol−1 K−1 | 0.082057 L atm mol−1 K−1 |
| M | Molecular weight / molar mass | kg mol−1 | g mol−1 |
Worked Numerical Example
Problem: A solution is prepared by dissolving 2.00 g of a substance in enough solvent to make 100 mL of solution. The osmotic pressure of the solution is 0.492 atm at 27°C. Calculate the molecular weight of the substance.
Step 1: Write the given data
- Mass, w = 2.00 g
- Volume, V = 100 mL = 0.100 L
- Osmotic pressure, π = 0.492 atm
- Temperature = 27°C
- R = 0.082057 L atm mol−1 K−1
Step 2: Convert temperature to kelvin
Step 3: Use the molecular weight equation
Substituting the values:
Answer
Experimental Method
In practice, the osmotic pressure of a dilute solution is measured using an osmometer. A semipermeable membrane is used to separate the solution from its pure solvent. The apparatus is arranged so that only solvent molecules can cross the membrane.
- Prepare a dilute solution containing a known mass of the substance in a known volume of solvent.
- Place the solution on one side of a suitable semipermeable membrane and the pure solvent on the other side.
- Allow the system to reach equilibrium at a constant temperature.
- Measure the osmotic pressure of the solution using a suitable osmometer.
- Substitute the measured osmotic pressure and other experimental values in the equation: M = wRT / πV.
Why Osmotic Pressure Is Suitable for Molecular Weight Determination
Osmotic pressure is a colligative property, meaning that it depends primarily on the number of solute particles present rather than their chemical identity. Therefore, measurement of osmotic pressure provides a way to determine the number of solute molecules present in a known mass of the substance and hence its molecular weight.
The osmotic method is especially useful for high-molecular-weight substances. For such substances, the osmotic pressure can be measured at relatively low concentrations, reducing the possibility of complications associated with highly concentrated solutions.
Advantages of the Osmotic Method
- It is particularly useful for determining the molecular weights of polymers and other macromolecules.
- Measurements can be made using dilute solutions.
- The method does not require the substance to be volatile.
- It can be applied to substances having very high molecular weights.
- Osmotic pressure can often be measured at moderate temperatures, which is useful for thermally sensitive substances.
Limitations of the Osmotic Method
- A suitable semipermeable membrane must be available.
- The membrane must prevent the passage of solute particles while allowing solvent molecules to pass.
- Accurate measurement of osmotic pressure can be experimentally difficult, particularly when the osmotic pressure is very small.
- The solution should be sufficiently dilute for the ideal dilute-solution relationship to be applicable.
- Impurities, aggregation, dissociation, or interaction between solute and solvent can affect the measured value.
Application to Polymer Molecular Weight
The osmotic method is widely used in polymer chemistry because polymers generally have very high molecular weights. For a polymer solution, osmotic pressure is measured at several low concentrations and the results are extrapolated toward zero concentration to obtain the number-average molecular weight.
For dilute polymer solutions, the relationship is commonly expressed as:
Here, c is the polymer concentration, Mn is the number-average molecular weight, and A2 is the second virial coefficient. A plot of π/c against c can be extrapolated to zero concentration. The intercept provides the value of RT/Mn.
Conclusion
The measurement of molecular weight by the osmotic method is based on the relationship between osmotic pressure and the concentration of a dilute solution. Using the van't Hoff equation, the molecular weight can be calculated from the measured osmotic pressure. Because the method is particularly suitable for high-molecular-weight substances, it has important applications in the study of polymers, proteins, and other macromolecules.