To find the molar mass of human serum albumin, we can use the ideal gas law in the form of the van 't Hoff equation:
Π = (n/V)RT
Where: Π = osmotic pressure (in atm or mmHg) n = number of moles of solute V = volume of solution (in liters) R = ideal gas constant (0.0821 L·atm/(mol·K)) T = temperature in Kelvin (K)
First, let's convert the osmotic pressure from mmHg to atm:
Π = 5.85 mmHg * (1 atm / 760 mmHg) = 0.0077 atm
Next, let's convert the volume of the solution from mL to liters:
V = 50.00 mL * (1 L / 1000 mL) = 0.0500 L
Now, let's rearrange the van 't Hoff equation to solve for the number of moles of solute:
n = (Π * V) / (R * T)
n = (0.0077 atm * 0.0500 L) / (0.0821 L·atm/(mol·K) * 298 K) n = 0.00188 mol
Next, we can calculate the molar mass (M) of human serum albumin using the formula:
M = mass / moles
M = 1.08 g / 0.00188 mol M ≈ 574.47 g/mol
Therefore, the molar mass of human serum albumin is approximately 574.47 g/mol.