Question

Our task is to measure the volume of blood in a live hippopotamus. One way to do this would be to drain its blood into a suitable container and measure its volume. Aside from the obviously disastrous effect this method would have on the hippo, it would not be very accurate since some blood would still remain behind in the tissues. Instead, we will inject the hippo with 2.00 mL of a 2.00 M dye solution which the hippo will not appreciably metabolize or excrete in one hour, and then measure the dye concentration in the bloodstream after 30 minutes (which should

be sufficient time for the dye to thoroughly
mix in the bloodstream). After 30 minutes, the concentration of the dye in a 78.0 mL blood sample was found to be 0.0000125 M. What is the volume of blood in the hippo?

Answer 1

Diluting a solution changes molarity, i.e. number of moles os solutes per liter of solution. However, the total number of moles of solute in respective quantities of the undiluted (2.0 mL of 2.0 M dye) and dilutes sample (in hippo’s blood) remains the same. Because, adding water (dilution in blood) does not alters the number of moles of dyes present in solution.

Also, Number of moles of a solute = Molarity of solution x Volume of solution in L

[ Or, n = (n / L) / L = n                , so, n = M x L ]

When both volumes are expresses in mL, they cancel each other. So, it’s not mandatory to use L as unit of volume in calculations used below.

Using, M1V1 = M2V2     --- equation 1

Where, M1= molarity of initial solution 1, V1= volume of initial solution 1 (original dye solution)

            M2= molarity of final solution 2, V2= volume of final solution 2 (hippo’s blood)

Now,

            2.0 M x 2.0 mL = 0.0000125 M x V2

            Or, V 2 = (2.0 M x 2.0 mL) / 0.0000125 M = 320000 mL

Hence, volume of blood in hippo = 320000 mL = 320 L                   [1 L = 1000 mL]