A laboratory worker prepared a 1:200 dilution of whole blood. The diluted blood gave a count of 30 RBCs per hemocytometer square (100 µm × 100 µm). How many RBCs are in 1 mL of the diluted blood and in 1 mL of the whole blood?

1 Answer
Aug 22, 2017

Answer:

There are #"3,0" × 10^7# red blood cells in 1 mL of the diluted blood and #"6,0" × 10^9# RBCs in 1 mL of whole blood.

Explanation:

Step 1. Calculate the volume of a hemocytomer square

#V = lwh = 100 color(red)(cancel(color(black)("µm"))) × 100 color(red)(cancel(color(black)("µm"))) × "0,10" "mm" × ((1 "mm")/(1000 color(red)(cancel(color(black)("µm")))))^2#

# = "1,00" × 10^"-3" color(white)(l)"mm"^3#

So, there are 30 RBCs in #"1,00" × 10^"-3"color(white)(l) "mm"^3#.

Step 2. Calculate the number of RBCs in a volume of #"1 cm"^3# (1 mL)

#"RBCs" = 1 color(red)(cancel(color(black)("cm"^3))) × ((10 color(red)(cancel(color(black)("mm"))))/(1 color(red)(cancel(color(black)("cm")))))^3 × "30 RBCs"/("1,00" × 10^"-3" color(red)(cancel(color(black)("mm"^3)))) = "3,0" × 10^7color(white)(l) "RBCs"#

Step 3. Calculate the number of RBCs in 1 mL of whole blood

Your dilution factor is 200.

∴ In 1 mL of whole blood,

#"RBCs" = 200 × "3,0" × 10^7color(white)(l) "RBCs" = "6,0" × 10^9 color(white)(l)"RBCs"#