Q143CP - Chemistry: Molecular Nature Of Matter And Change

Question

Fluoride ion is poisonous in relatively low amounts: 0.2 g of F^- per 70 kg of body weight can cause death. Nevertheless, in order to prevent tooth decay, F^- ions are added to drinking water at a concentration of 1 mg of F^- ion per L of water. How many liters of fluoridated drinking water would a 70-kg person have to consume in one day to reach this toxic level? How many kilograms of sodium fluoride would be needed to treat a 8.50×10⁷ -gal reservoir?

Step-by-Step Solution

Answer

(a) The person need to drink 200 L of water to reach toxic level.

(b) There is a need of $\mathbf{3}\mathbf{.}\mathbf{2172}\mathbf{\times }{\mathbf{10}}^{\mathbf{2}}\mathbf{Kg}$ of fluoride for $\mathbf{8}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathbf{gal}$ of water.

Step 1: Calculating the toxic level

The concentration and toxic amount can be 1 mg/L and 0.2 g respectively.

$$\begin{gathered} \mathbf{V}\mathbf{(}\mathbf{water}\mathbf{,}\mathbf{toxic}\mathbf{)}\mathbf{=}\frac{\mathbf{toxic}\mathbf{ }\mathbf{amount}}{\mathbf{concentration}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{g}}{{\mathbf{10}}^{\mathbf{‐}\mathbf{3}}\mathbf{g}\mathbf{/}\mathbf{L}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{200}\mathbf{L} \end{gathered}$$

Step 2: Calculating the amount of sodium fluoride would be needed to treat a 8.50×10 7 -gal reservoir

It can be calculated as,

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{gallon}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{785}\mathbf{liters} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{V}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathbf{gal} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathbf{gal}\mathbf{\times }\frac{\mathbf{3}\mathbf{.}\mathbf{785}\mathbf{liters}}{\mathbf{1}\mathbf{ }\mathbf{gallon}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{2172}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{L} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{m}\mathbf{=}\mathbf{ }\mathbf{volume}\mathbf{\times }\mathbf{density} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{2172}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{L}\mathbf{\times }\mathbf{1}\mathbf{mg}\mathbf{/}\mathbf{L} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{2172}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}\mathbf{mg} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{m}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{2172}\mathbf{\times }{\mathbf{10}}^{\mathbf{2}}\mathbf{kg} \end{gathered}$$