Final answer:
The molar mass of a protein can be calculated using the osmotic pressure of a solution, the ideal gas law, and counting by weighing in conjunction with Avogadro's number.
Step-by-step explanation:
To calculate the molar mass of a protein given a solution osmotic pressure, you can apply principles from colligative properties and the ideal gas law equation rearranged for concentration.
The osmotic pressure equation (Π = iMRT, where Π is osmotic pressure, i is the van't Hoff factor, M is molarity, R is the gas constant, and T is temperature in Kelvins) can be used in conjunction with the given mass of protein and volume of the solution to compute the molar mass of the protein.
Assuming that the protein does not dissociate or associate in solution (i.e., i=1), and using the information given (0.02 g of protein, 25.0 mL of solution, and 0.56 torr osmotic pressure at 25 °C), you would first convert the temperature to Kelvins and the osmotic pressure to atmospheres.
Then, using the rearranged form of the ideal gas equation, you can compute the molarity of the protein. With the molarity known, dividing the mass of protein by the number of moles (from the computed molarity and given volume) yields the molar mass of the protein.
Counting by weighing and Avogadro's number is a key concept in determining molecular weights. This method involves relating a known mass of a substance to the number of moles, and thereby indirectly counting the molecules. The molar mass of a compound is crucial in this approach, as it enables conversions from mass to moles to numbers of molecules.
In another example, the molar mass of a compound is computed to be 176.124 g/mol. Knowing the molar mass allows for the calculation of the mass of a given number of moles, if the number of moles is known, or vice versa.