You are collecting plasma from a patient with a pheresis machine that takes whol

Question

You are collecting plasma from a patient with a pheresis machine that takes wholeblood from the body, extracts 80% by mass of the plasma and returns the remainderof the blood to the body. For this operation the blood composition can be modeledas 55% by mass plasma and 45% by mass cells. A simplified diagram of theoperation is below. If a patient donates 1.0 liter of plasma (density=1025 kg/m3), calculate the following:

a. The amount (mass) of blood extracted from the donor. (ANS: 2329 g)

b. The concentration (mass fraction) of cells and plasma in the concentrated blood.(ANS: xc=0.804 g cells/g)

c. The mass of concentrated blood returned to the donor. (ANS: 1304 g)

Explanation / Answer

Mass of 1 litre of plasma = volume*density = 0.001*1025 = 1.025 kg

Now, Let the amount of blood extracted be 'x' kg

Thus, 55% of x = 0.55*x = plasma

And 80% of plasma is donated

Hence, 0.8*(0.55*x) = 1.025

or, x = 2.329 kg = 2329 g...............(1)

Now, mass of plasma in blood (2329 g) = 0.55*2329 = 1280.95 g

Mass of cells = 0.45*2329 = 1048.05 g

Thus, concentration (mass fraction) of cells and plasma = 1048.05/1280.95 = 0.818.............(2)

Now, Mass extracted (or donated) of blood = 1025 g

Thus, mass returned to donor = 2329 - 1025 = 1304 g............(3)

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