Most community water supplies have 0.5 ppm of chlorine added for purification. ...?

Question

Most community water supplies have 0.5 ppm of chlorine added for purification. What mass of chlorine must be added to 132.0 L of water to achieve this level?

Answer 1

divide the grams by 0.5 million... that's not right 'coz you'll not end up with mass chlorine

If you take the volume of chlorine into account, it's going to be a little hard to solve:
0.5mg solute/ 1 L solution = mg chlorine / (132.0 L + L chlorine)

...so I'll just give you the approximate answer:
0.5 ppm = 0.5 mg / L
0.5 mg/L * 132.0 L = 66 mg chlorine (20+mL)

Answer 2

Assume that the density of the water is 1 g /ml.

You have 132.0 L, so it is easy toconvert this to ml and then grams.

From there, divide the grams by 0.5 million and you have your answer.

Answer 3

Assume that the density of the water is 1 g /ml.

You have 132.0 L, so it is easy toconvert this to ml and then grams.

From there, divide the grams by 0.5 million and you have your answer.

Answer 4

This one is very very tricky -- there are at least two ways to do it and I can think of a third, as well.

Let's assume that the 0.5 parts per million is on a weight basis. Then, since you have 132 L of water, or 132,000 milliliters, and, since the density of water at standard temperature and pressure is about 1 gram per milliliter, the total mass of the water is 132,000 grams.

To get the "0.5 ppm", think of it as 0.5 divided by a million or 0.5/10^6 = 0.5 x 10^-6 or 5 x 10^-7.

And 132,000 x 5 x 10^-7 = 0.066 grams.

Only one trouble -- chlorine is a diatomic gas, and so unless we take a 132 L barrel of water, place it on a scale, and bubble chlorine gas from a tank through it until the scale shows an increase of 66 milligrams, it will be hard to get a precise amount of chlorine into the water.

Most water suppliers add chlorine in the form of a dissolved salt of chloride, such as sodium hypochlorite -- formula NaClO, having a molecular weight of 74.4 (grams per mole). Of that, 35.5 grams per mole is chlorine. To get 66 milligrams of chlorine, we would need 0.066 gram / 35.5 grams per mole = 0.00186 mole of NaClO, or 74.4 grams per mole x 0.00186 = 0.138 grams of hypochlorite added to 132 L of water to get 0.5 ppm Cl.

The second way is on a mole fraction basis --

The molecular weight of water is 18 grams per mole. At a density of 1 gram per milliliter, 132 liters of water is

132 L x 1000 ml per L x 1 gram per ml / 18 grams per mole = 7333.33 moles.

0.5 parts per million of 7333.33 is 7333.33 x 5 x 10^-7 = 0.00367 moles.

The atomic weight of chlorine is 35.5 grams per mole, so the mass of chlorine needed is 35.5 grams per mole x 0.00367 moles = 0.130 grams, which is twice the mass calculated on the weight basis.

So you now have two perfectly good answers, each of which can be justified!