Question

It is recommended the drinking water contain 1.6 ppm fluoride (F-) to prevent tooth decay. Consider a cylindrical reservoir with a diameter of 5.00 x 102 m and a depth of 20.0 m (the volume of a cylinder = r2h). How many grams of fluoride should be added to give 1.6 ppm? Fluoride is provided by dissolving H2SiF6. How many grams of H2SiF6 contain this amount of fluoride?

Answer 1

radius = d/2 = ( 500 /2) = 250 m , h = 20m

volume of cylinder = p x r^2 x h = ( 3.14 x 250^2 x 20) = 3925000 m^3 = 3925000 x 1000 L

we need 1.6 ppm F-   for 3925000 x 1000 L

1.6 ppm means 1.6 mg of F- per 1Liter     ( 1ppm = 1mg/L)

hence for 3925000 x 1000 Liters F-mass = ( 1.6 x 3925000 x 1000)mg = 628 x 10^7 mg = 628 x 10^4 g

Hence we need 6.28 x 10^ 6 grams

Moles of F- = mass of F- / atomic mass of F- = 6.28x10^6 / 19 = 3.305 x 10^5

each H2SiF6 gives 6 F-

henceH2SiF6 moles = ( 3.305x10^ 5) / 6 = 5.5088 x 10^4

Mass of H2SiF6 = moles of it x molar mass of H2SiF6 = 5.5088 x 10^4 x 144.09 = 7.937 x 10^ g