Osmotic pressure and molar mass are inversely proportional; as the molar mass of a solute increases, the osmotic pressure of the solution decreases, assuming all other variables are constant.
Here's a breakdown of the relationship:
Osmotic pressure (π) is a colligative property, meaning it depends on the concentration of solute particles in a solution, not the solute's identity. The van't Hoff equation describes this relationship:
π = iMRT
Where:
- π = Osmotic pressure
- i = van't Hoff factor (number of particles the solute dissociates into)
- M = Molarity of the solution (moles of solute per liter of solution)
- R = Ideal gas constant
- T = Absolute temperature
Since molarity (M) is defined as moles of solute (n) per liter of solution (V), we can rewrite the equation as:
π = i(n/V)RT
The number of moles (n) can be expressed as the mass of the solute (m) divided by its molar mass (Mm):
n = m / Mm
Substituting this into the osmotic pressure equation, we get:
π = i(m / (MmV))RT
Rearranging the equation to highlight the relationship between osmotic pressure (π) and molar mass (Mm):
π = (i m R T) / (Mm V)
From this equation, it's clear that osmotic pressure (π) is inversely proportional to the molar mass (Mm) when i, m, R, T, and V are kept constant. In other words, for a given mass of solute in a given volume and at a constant temperature, a solute with a higher molar mass will exert a lower osmotic pressure than a solute with a lower molar mass.
Example:
Consider two solutions, each containing 1 gram of solute in 1 liter of water at the same temperature.
- Solution A contains a solute with a molar mass of 100 g/mol.
- Solution B contains a solute with a molar mass of 200 g/mol.
Assuming both solutes do not dissociate (i=1), Solution A will have a higher osmotic pressure because it contains more moles of solute per liter than Solution B.
In conclusion, the relationship between molar mass and osmotic pressure is inversely proportional, which is evident from the ideal osmotic pressure equation. Understanding this relationship allows for the determination of the molar mass of an unknown substance by measuring the osmotic pressure of its solution.
