Question

A 2.00-mL solution containing 0.113 microcuries per milliliter of tritium was injected into the bloodstream

of a dog. After allowing time for homogenization, a 1.00-mL sample of the blood was found to have a

counting rate of 14.9 counts per second (cps). Calculate the blood volume of the animal.

Short answer

$\text{The blood volume of animal is}559\mathrm{mL}\text{.}$

Step-by-step solution

Given information

The blood volume of the dog is calculated by using the equation of the isotope dilution method. The bloodstream of the dog contained 2.00 mL solution was injected which has $0.113$microcurie per milliliter of tritium. The calculated volume of blood of the dog is 559 mL

Calculation of blood volume 

Given that-

$$\begin{gathered} m_t=2.00mL \\ {m}_m=1.00mL \\ {R}_m=14.90cps \\ {R}_t=0.113microcuriepermL \end{gathered}$$

As

$1curie=3.7\times {10}^{10}Bq$

OR,

$1curie=3.7\times {10}^{10}cps$

$\text{So, for}2.00\mathrm{mL}\text{, radiotracer tracer in}\mathrm{cps}\text{is calculated as-}$

$R_1=0.113\times {10}^{-6}\times 3.7\times {10}^{10}cps\times 200\mathrm{mL}$$R_t=0.113\times {10}^{-6}\times 3.7\times {10}^{10}\mathrm{cps}\times 2.00\mathrm{mL}$

Therefore,

$R_t=8362cps$

Now put the given values in Equ (1)-

role="math" localid="1645977903348" $$\begin{gathered} m_x=\left(8362/14.9\right)\times \left(1.00mL-2.00mL\right) \\ {m}_x=559mL \end{gathered}$$

The volume of sample blood is $559mL$