Final answer:
To calculate the molar mass of a polymer from osmotic pressure data, convert the height of the solvent column to pressure, then use the osmotic pressure formula with the ideal gas law to find the molar mass for each data set. Average these values to estimate the polymer's molar mass.
Step-by-step explanation:
Calculating Molar Mass from Osmotic Pressure Data
To calculate the molar mass of polystyrene using osmotic pressure data, we need to know the van't Hoff factor (i), the temperature (T), the osmotic pressure (Π), the concentration of the solution (C), and the density of the solvent (ρ). The van't Hoff factor for polystyrene in toluene is assumed to be 1, as polystyrene is a non-ionic polymer. At 25°C, the temperature in Kelvin is T = 25 + 273 = 298 K. Remember that the osmotic pressure is given by the formula:
Π = iCRT
where R is the gas constant (0.0821 L·atm/K·mol). However, the osmotic pressure is expressed as a height of solvent column (h), which can be converted to pressure (Π) using the formula:
Π = hρg
where g is the acceleration due to gravity, approximately 9.8 m/s². Using the density of the solvent, ρ = 1.004 g/cm³, and the data provided, we can calculate the osmotic pressure for each concentration. Subsequently, we can rearrange the osmotic pressure formula to solve for the molar mass (M):
M = Π / (iCRT)
By applying this process to each set of data (Π and C) and averaging the resulting molar masses, we get an estimate of the polymer's molar mass. The calculation assumes ideal behavior, which may not hold in all situations, so the calculated value is an approximation.
The detailed solution in the student question can serve as an example for calculation technique and understanding osmotic pressure relationships.