J.R. S. answered • 02/27/21

Ph.D. University Professor with 10+ years Tutoring Experience

We are asked to find the molar mass of hemoglobin (Hgb) so we need the mass and the moles. We are given the mass (1.37 g) so we essentially need to find moles of Hgb. We can do this by finding moles of O_{2} and dividing that by 4 since four moles of O_{2} bind to 1 mole of Hgb.

To find moles of O2, we use the Ideal gas law, PV = nRT and solve for n (moles):

n = PV/RT

P = pressure = 724 torr x 1 atm/760 torr = 0.953 atm

V = volume in L = 2.13 ml x 1 L/1000 ml = 0.00213 L

R = gas constant = 0.0821 Latm/Kmol

T = temp in K = 37º + 273 = 310K

n = (0.953)(0.00213) / (0.0821)(310)

n = 7.98x10^{-5} moles of O_{2} molecules

moles Hgb molecules = 7.98x10^{-5} moles O_{2} x 1 mol Hgb/4 mol O_{2} = 1.99x10^{-5} moles Hgb molecules

molar mass Hgb = g / moles

molar mass Hgb = 1.37 g /1.99x10^{-5} moles = 68,844 g/mol (be sure to check the math)