Hi Amy, for this question we just need to know the right formula for parts per million, ppm, and then it's just a matter of plugging the numbers into it, changing to the correct units if necessary.
The parts per million of Cu in the drinking water is defined by the grams of Cu divided by the total grams of the solution, times one million, or
ppm = grams of Cu X 1,000,000
grams of Cu + grams of water
The density of such a dilute solution will be almost exactly the same as that of pure water, 1.00 grams per mL, so we can use the density of water to calculate the total grams of the solution:
1.00 L X 1000 mL X 1.00 g = 1000 g of solution total
1 L mL
We are already given the grams of Cu, so all we have to do is plug the numbers into the formula:
ppm of Cu = 3.0 X 10-5 g X 106 = 0.030 ppm
1000 g
Many people remember "milligrams per liter" as a practical way to calculate ppm. Here, we have 3.0 X 10-2 mg of Cu, or 0.030 mg, divided by 1.00 L, which gives the same answer, 0.030 ppm.
One more note, if you had a much higher amount of Cu in the solution, it may be more appropriate to calculate the concentration in another unit, such as percent:
Percent Cu = grams of Cu X 100
(by weight) grams of Cu + grams of water
It is exactly the same formula we used to calculate ppm, but we just multiply by 100 instead of 1,000,000. But in this case we may not be correct in assuming the density of the solution is 1.00 g/mL, so we would need to be given the grams of Cu and the grams of water it is dissolved in separately. Then we would add them together to get the total grams of solution in the denominator.
Hope this helps!
Steve
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