Question

The objective is to determine the volume of blood in an elephant. One method requires draining the blood of the elephant into a suitable calibrated container. This method presents some potentially unpleasant side effects for the elephant and possibly should be avoided. Moreover, since some of the blood will remain in the tissues, the method possesses a significant measure of inaccuracy. Because of these problems, we will utilize a different method, requiring that we inject the elephant with 2.00 mL of a 2.00 molar solution of a harmless dye. The dye is such that the elephant will not appreciably metabolize or excrete any of the dye within one hour of injection. A blood sample is drawn (from a different leg than the site of the injection) 30.0 minutes after the injection which is known to be sufficient time to mix the dye thoroughly in the bloodstream.Analysis showed that the resulting of dye in the bloodstream at this point was 1.25 x 10x-5 molar. What is the volume of the blood in the elephant?

Answer 1

This is essentially a dilution problem, we will use a very simple formula

M₁V₁ = M₂V₂

where M₁ = initial concentration of dye = 2 molar,          V₁ = initial volume = 2.00 mL

         M₂ = final concentration = 1.25 x 10^-5 molar         V₂ = final volume to be determined

M₁V₁ = M₂V₂

==> V₂ = (M₁V₁) / M₂ = (2.0 x 2.0 mL) / (1.25 x 10^-5) = 320000 mL

       V₂ = 320 Liters    (Since 1 liter = 1000 mL)

The volume of the blood in the elephant = 320 Liters or simply 320 L

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