You need to prepare blood for a transfusion. You have the following three proces

Question

You need to prepare blood for a transfusion. You have the following three processed blood packs available:

Pack A – Enriched in red blood cells (RBCs)

Contents: 2.5 wt% white blood cells (WBCs); 50.0 wt% isotonic fluid; the rest is RBCs.

Pack B – Enriched in serum proteins

Contents: 50.0 wt% serum proteins; 1.0 wt% WBCs; 18.0 wt% isotonic fluid; the rest is RBCs

Pack C – Isotonic fluid

Contents: 100.0 wt% isotonic fluid
All three packs must be mixed in the correct proportions to generate blood for a transfusion pack. The transfusion pack needs to have the following composition: 2.0 wt% WBCs and 12.6 wt% serum proteins. How much of each processed blood pack do you need to mix to get 100 g of reconstituted blood for a transfusion pack?

Explanation / Answer

Weight percent is mass of a given substance expressed in grams in terms of 100.

We need 100g of a transfusion pack with 2.0 wt% WBCs which means 2.0g of WBC should be prsent in 100g pack.

Also, the amount of serum proteins must be 12.6 wt% which means, 12.6g of serum proteins should be present in 100g pack.

In order to get this amount, lets first calculate the amount of solution from part B to be taken because this solution is rich in serum proteins.

1. Pack B contains 50.0 wt% of serum proteins. If the whole solution in part B pack contains 50g of serum proteins, then what amount contain 12.6g?

a) 100 muliplied by 12.6 / 50 = 25.2 g of part be solution.

But this solution also contain WBCs, calculating its amount,

b) if 100g of part B solution contain 1.0wt% WBCs, then 25.2g should contain 0.252g (by cross multiplication)

2. Now, the amount of WBCs needed is 2.0 wt%.

But part 25.2g of part B solution already taken has 0.252g of WBCs. Therefore, we need 1.748g of WBCs from part A solution.

a) part A has 2.5 wt% of WBCs.

To get 1.748g of WBCs, 100 multiplied by 1.748 / 2.5 = 69.92g

3. Therefore, part A + part B = 69.92+25.2=95.12.

The remaining solution must be taken from pack C as it contains isotonic solution.

100 subtracted by 95.12= 4.88g.

Final answer: Part A+part B+part C= 69.92+25.2+4.88=100g reconstituted pack of blood.

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