A Whole Blood unit contains 475 ml with a hematocrit of 42%. How much plasma needs to be removed to achieve a hematocrit of 75% in RBCs?

To determine how much plasma needs to be removed to achieve a target hematocrit of 75%, it is essential to understand the relationship between total volume, red blood cell (RBC) volume, plasma volume, and hematocrit.

Initially, the whole blood unit has a volume of 475 ml and a hematocrit of 42%. To begin calculations, we can find the initial volume of red blood cells in this unit. The hematocrit percentage indicates what fraction of the blood volume is made up of RBCs. In this case:

RBC volume = Total Blood Volume × Hematocrit

RBC volume = 475 ml × 0.42 = 199.5 ml

The plasma volume can be determined by subtracting the RBC volume from the total blood volume:

Plasma volume = Total Blood Volume - RBC volume

Plasma volume = 475 ml - 199.5 ml = 275.5 ml

To achieve the target hematocrit of 75%, we need to calculate the new total blood volume required to maintain the fixed RBC volume of 199.5 ml:

Let V be the new total volume after plasma removal. The target hematocrit can be expressed as:

Hematoc