Explanation:
First we will convert the given mass from lb to kg as follows.
157 lb = [tex]157 lb \times \frac{1 kg}{2.2046 lb}[/tex]
= 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.
[tex]180 \frac{mg}{kg} \times 71.215 kg[/tex]
= 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
0.65% (w/w) = [tex]\frac{0.65 g}{100 g}[/tex]
= [tex]\frac{0.65 g}{(\frac{100 g}{1.0 g/ml})}[/tex]
= [tex]\frac{0.65 g}{100 ml}[/tex]
Therefore, calculate the volume which contains the amount of caffeine as follows.
12818.7 mg = 12.8187 g = [tex]\frac{12.8187 g}{\frac{0.65 g}{100 ml}}[/tex]
= 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.
