Determining molecular weight by osmotic pressure involves measuring the pressure required to prevent the flow of solvent across a semi-permeable membrane separating a solution from its pure solvent and relating this pressure to the concentration of the solute.
Here's a breakdown of the process:
Understanding Osmotic Pressure
Osmotic pressure (π) is a colligative property, meaning it depends on the number of solute particles in a solution rather than the identity of the solute. The relationship between osmotic pressure, concentration, and temperature is described by the van't Hoff equation:
π = iMRT
Where:
- π = Osmotic pressure
- i = van't Hoff factor (accounts for the dissociation of solutes; i=1 for non-electrolytes)
- M = Molarity of the solution (mol/L)
- R = Ideal gas constant (0.0821 L atm / (mol K))
- T = Absolute temperature (K)
Determining Molecular Weight
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Rearranging the van't Hoff equation: We can express molarity (M) as the mass of the solute (g) divided by the molecular weight (MW) and the volume of the solution (V) in liters:
M = g / (MW * V)
Substituting this into the van't Hoff equation:
π = (g / (MW V)) RT (assuming i = 1)
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Solving for Molecular Weight (MW): Rearranging the equation to solve for MW:
MW = (gRT) / (πV)
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Experimental Measurement: In practice, osmotic pressure is measured experimentally using an osmometer. A solution of known concentration (g/V) is separated from the pure solvent by a semi-permeable membrane. The pressure required to stop the solvent flow (osmosis) is the osmotic pressure.
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Improving Accuracy: Plotting π/c vs. c: The van't Hoff equation is most accurate at low concentrations. To get a more accurate molecular weight, especially for larger molecules or non-ideal solutions, perform measurements at several different concentrations (c = g/V). Then, plot (π/c) versus concentration (c). Extrapolate the data back to c = 0. The y-intercept of this plot gives a more accurate value for RT/MW. Therefore:
lim (c->0) π/c = RT/MW
MW = RT / (lim (c->0) π/c)
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Accounting for Non-Ideal Behavior: Deviations from the ideal van't Hoff equation can occur at higher concentrations due to solute-solute interactions. By extrapolating to zero concentration, we minimize these non-ideal effects.
Example
Suppose you dissolve 1.0 g of an unknown protein in 100 mL of water at 25°C. You measure the osmotic pressure to be 2.45 mmHg. To find the molecular weight:
- Convert osmotic pressure to atm: 2.45 mmHg * (1 atm / 760 mmHg) = 0.00322 atm
- Convert volume to liters: 100 mL = 0.1 L
- Convert temperature to Kelvin: 25°C + 273.15 = 298.15 K
- Apply the formula (assuming ideality): MW = (1.0 g 0.0821 L atm / (mol K) 298.15 K) / (0.00322 atm * 0.1 L) = 75,650 g/mol
To improve accuracy, you would repeat this measurement at different concentrations and plot π/c vs. c, then extrapolate to c=0 to find a more accurate result.
Key Considerations:
- The semi-permeable membrane must be truly permeable to the solvent but impermeable to the solute.
- Temperature control is crucial because osmotic pressure is temperature-dependent.
- The accuracy of the molecular weight determination is highly dependent on the accuracy of the osmotic pressure measurement, especially at low concentrations.
- This method is most suitable for determining the molecular weights of large molecules, like polymers and proteins, where other colligative properties (like boiling point elevation or freezing point depression) show very small changes that are difficult to measure accurately.
