Question

To aid in the prevention of tooth decay, it is recommended that drinking water contain 1.10 ppm fluoride (F–). (a) How many grams of F– must be added to a cylindrical water reservoir having a diameter of 4.03 × 102 m and a depth of 55.43 m? (b) How many grams of sodium fluoride, NaF, contain this much fluoride?

Answer 1

ppm means 1mg solute dissolved in 1 liter solution
1ppm = 1mg/l

Let us find out volume of solution .For that we should
calculate volume of cylinder
which is
V = pi*r^2*h
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where r= radius of cylinder
here diameter is given ,So
Radius r= diameter/2 =4.03 × 102 m/2 = 2.015 x10^2 m
h= depth of cylinder =55.43 m

Plug in these numbers to obtain volume of cylinder
=3.14*[ 2.015 x10^2 m]^2* 55.43 m= 706.68 x10^4 m^3= 706.68x10^7 Liters

Require concentration of F- = 1.10 ppm
that means 1.10 mg in 1 liter water

So in 706.68x10^7 Liters water
mass of F- = 706.68x10^7 * 1.10 mg = 777.348x10^7 mg

Mass of F- in grams=777.348 x10^4 g

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let us use mole concept

1 mole F- has mass= 19 g
777.348 x10^4 g F- = 40.91 x10^4 moles
1 mole NaF has 1 mole F-
40.91x10^4 moles F- has 40.91x10^4 mole NaF
So mass of NaF = moles of NaF * molar mass of NaF = s 40.91x10^4 *42 g/mol
= 1718x10^4 g of NaF
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Thank you .Hope it is helpful :)