Final answer:
The molecular mass of bovine serum albumin (BSA) is calculated to be approximately 66,410 g/mol using the osmotic pressure data given and the van't Hoff equation.
Step-by-step explanation:
To calculate the molecular mass of bovine serum albumin (BSA) using osmotic pressure, we need to apply the van't Hoff equation which relates osmotic pressure (Π) to molarity (M):
Π = iMRT
Where:
- i is the van't Hoff factor (for non-electrolytes like BSA, i = 1),
- M is the molarity of the solution,
- R is the ideal gas constant (0.0831 L·bar/K·mol),
- T is the temperature in Kelvin (298 K for 25°C).
First, we convert the osmotic pressure from mbar to bar by dividing by 1000 (0.899 mbar = 0.000899 bar). Then, we rearrange the van't Hoff equation to solve for M:
M = Π / (iRT)
Plugging the values we get:
M = 0.000899 bar / (1 · 0.0831 L·bar/K·mol · 298 K)
M ≈ 3.63 × 10⁻µ mol/L
We then find moles of BSA in the entire 0.179 L solution:
moles of BSA = M × volume = 3.63 × 10⁻µ mol/L × 0.179 L
moles of BSA ≈ 6.49 × 10⁻¶ mol
The molecular mass (MM) of BSA is calculated using the mass (in grams) of the sample divided by the moles:
MM = mass / moles
MM = 0.431 g / 6.49 × 10⁻¶ mol
MM ≈ 66,410 g/mol
Therefore, the molecular mass of BSA is approximately 66,410 g/mol.