Final answer:
To find the molar mass of the protein, use the osmotic pressure equation Π = iMRT to calculate the molarity (M), and then calculate the number of moles of protein. Finally, divide the mass of the protein by the number of moles to find the molar mass.
Step-by-step explanation:
To calculate the molar mass of the protein, we first need to use the osmotic pressure equation Π = iMRT, where Π is the osmotic pressure, i is the van't Hoff factor (which is 1 for a non-electrolyte such as a protein), M is the molarity of the solution, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin. Given the osmotic pressure (Π) of 0.56 torr (which we convert to atm by dividing by 760 torr/atm), and the temperature (T) of 25°C (which we convert to Kelvin by adding 273.15), we can solve for M (molarity).
Next, we find the number of moles of protein by using the volume of the solution. Since the solution volume is 25.0 mL, which is equivalent to 0.025 L, the number of moles (n) of protein can be calculated by multiplying M (molarity, which is moles per liter) by the volume in liters.
The final step is to determine the molar mass of the protein by dividing the mass of the protein (0.02 g) by the number of moles (n) we just calculated. After calculating the respective values, we'll obtain the molar mass, which is the mass in grams of one mole of the protein substance.