Question

part 1: It is recommended that drinking water contain 1.6 ppm fluoride (F^?) for prevention of tooth decay. Consider a reservoir with a diameter of 4.50???10² m and a depth of 14.3 m. (The volume is ?r²h, where r is the radius and h is the height.) How many grams of F^? should be added to give 1.6 ppm?

part 2: Fluoride is provided by hydrogen hexafluorosilicate, H₂SiF₆. How many grams of H₂SiF₆ contain this much F^??

Answer 1

Answer-

Part 1)

We are given, concentration of fluoride F^- = 1.6 ppm

Diameter , d = 4.50*10² m , depth = 14.3 m

Depth means height

We are given formula for volume = pi *r²*h , so this is for cylinder

First we need to calculate the volume of reservoir

r= radius = d/2 = 4.50*10² m / 2 = 225 m

Volume of reservoir = pi *r²*h

                                     = 3.14 * (225 m)² * 14.3 m

                                     = 2.273*10⁶ m³

Now we need to calculate mass of F^- which have concentration 1.6 ppm,

We know, ppm means part per million and it is equal to mg /L

1.6 ppm means 1.6 mg/L

Means, for 1 L = 1.6 mg of F^-

We calculated volume in m³, so we need to convert m³ to dm³.

1 m³ = 1000 dm³

So, 2.273*10⁶ m³ = ? dm³

= 2.273*10⁹ dm³

We also know, 1 dm³ = 1 L

So , volume in L = 2.273*10⁹ L

1 L = 1.6 mg of F^-

2.273*10⁹ L = ? mg

= 3.637*10⁹ mg of F^-

1 mg = 0.001 g

So, 3.637*10⁹ mg = ? g

= 3.6*10⁶ g of F^-

Part 2 ) We calculated mass of F^- now we need to convert this mass of F^- to moles

Moles of F^- = mass of F^- / molar mass of F^-

                      = 3.637*10⁶ g / 18.998 g/mole

                       = 1.914*10⁵ mole of F^-

In the hexafluorosilicate, H₂SiF₆ there are 6 F means,

6 moles of F^- = 1 moles of H₂SiF₆

1.914*10⁵ mole of F^- = ?

= 1.914*10⁵ mole of F^- X 1 moles of H₂SiF₆ / 6 moles of F^-

= 3.191*10⁴ moles of H₂SiF₆

Now convert this moles of H₂SiF₆ to its mass

Mass of H₂SiF₆ = moles of H₂SiF₆ X molar mass of H₂SiF₆

                          = 3.191*10⁴ moles of H₂SiF₆ X 144.0898 g/mole

                          = 4.6*10⁶ g of H₂SiF₆