Determine the molecular mass of a solution if prepared by dissolving 6.00 g of an unknown nonelectrolyte in enough water to make 1.00 L of solution. The osmotic pressure of this solution is 0.750 atm at 25.0 °C.
pi = MRT
0.750 = M*0.0821*(273+25)
Solve for M then M = mols/L.
You know M and L, solve for mols.
Then mols = grams/molar mass. You know mols and grams. solve for molar mass. Post your work if you get stuck.
To determine the molecular mass of a solution using its osmotic pressure, you can use the formula:
Π = iMRT
where:
Π = osmotic pressure (in atm)
i = van't Hoff factor (dimensionless)
M = molar concentration (in mol/L)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
In this case, we have the osmotic pressure (0.750 atm) and the temperature (25.0 °C, which must be converted to Kelvin: T = 25.0 + 273 = 298 K).
Since we are dealing with a nonelectrolyte, the van't Hoff factor (i) is 1. This is because nonelectrolytes do not dissociate into ions in solution.
The molar concentration (M) can be calculated by dividing the mass of the unknown substance (6.00 g) by its molecular mass (Mw) and then dividing by the volume of the solution (1.00 L):
M = (6.00 g / Mw) / 1.00 L
Now we can substitute all the known values into the formula and rearrange to solve for the molecular mass (Mw):
0.750 atm = (1)(M / (0.0821 L·atm/(mol·K))) * 298 K
Simplifying, we have:
0.750 = M / 24.47
M = 18.35 g/mol
Therefore, the molecular mass of the unknown nonelectrolyte is 18.35 g/mol.