Question

T. Svedberg measured the molecular weight of carbonyl hemoglobin by velocity centrifugation. In this experiment, 0.96 g of protein were dissolved in 100. mL of water at 303 K , and the solution was spun at 39,300 rpm. After 30.0 min, the concentration boundary advanced by 0.074 cm from an initial position of 4.525 cm. Calculate the molecular weight of carbonyl hemoglobin.

Answer 1

Answer:

The molecular weight is 77.7 kg/mol

Explanation:

The molecular mass of hemoglobin is equal to:

$M=\frac{RTs}{D(1-Vp)}$

Where

R = molar gas constant = 8.315 J/K mol

p = density = 0.998 g/mL

V = specific volume = 0.755 mL/g

s = sedimentation rate = ?

D = diffusion rate = 7x10⁻¹¹m²/s

T = temperature = 303 K

The sedimentation rate is equal to:

$s=\frac{1}{w^{2}t } ln(\frac{x_{b,t} }{x_{b,0} } )$

Where

w = angular velocity = 39300 rpm = 246929.18 rad/min

xb,30 = boundary midpoint distance at 30 min = 4.525 + 0.074 cm

t = time = 30 min

xb,0 = boundary midpoint distante at 0 min = 4.525 cm

$s=\frac{1}{246929.18^{2}*30 } ln(\frac{4.525+0.074}{4.525} )=8.87x10^{-13} min=5.32x10^{-13} s$

The molecular weight is:

$M=\frac{8.315*303*5.32x10^{-13} }{7x10^{-11}*(1-(0.755*0.998)) } =77.7kg/mol$