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 \(2.00 \mathrm{~mL}\) of a \(2.00 \mathrm{M}\) 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 \(78.0 \mathrm{~mL}\) blood sample was found to be \(0.0000125 \mathrm{M}\). What is the volume of blood in the hippo?

Step by step solution

01

Write down the given values

First, let's identify the given values in the problem: \(M_1 = 2.00 \mathrm{M}\) (initial concentration of dye), \(V_1 = 2.00 \mathrm{~mL}\) (volume of dye injected), \(M_2 = 0.0000125 \mathrm{M}\) (concentration of dye after 30 minutes), \(V_2\) = volume of blood in the hippo (unknown).

02

Use the formula \(M_1V_1 = M_2V_2\)

Now, we will use the formula \(M_1V_1 = M_2V_2\) and substitute the given values into the equation: \(M_1V_1 = M_2V_2\)

03

Substitute the given values and solve for V2

Now, let's substitute the given values into the equation: \((2.00 \mathrm{M})(2.00 \mathrm{~mL}) = (0.0000125 \mathrm{M})(V_2)\) Now, solve for \(V_2\): \(V_2 = \frac{(2.00 \mathrm{M})(2.00 \mathrm{~mL})}{(0.0000125 \mathrm{M})}\) \(V_2 = \frac{4.00 \mathrm{~mL}}{0.0000125 \mathrm{M}}\) \(V_2 = 320000 \mathrm{~mL}\) The volume of blood in the live hippopotamus is approximately 320,000 mL.

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