A 250ml aqueous solution contains 45.1 ug of a pesticide. What is the pesticide’s concentration in weight percent parts per million and parts per billion?

Start with the definitions of ppm and ppb.

(Grams solute / grams solution) x 10^6 = ppm

(Grams solute / grams solution) x 10^9 = ppb.

Now since a ug is 10^-6 g, and the solute is given in ug, we can use

ppm = ug solute / g solution and not need a multiplier.

And

pob = ug solute / kg solution and no multiplier is needed.

A solute this dilute will have a negligible effect on the density and the density of water is 1g / mL

So 250 mL solution is near enough to 250 g that we can use it that way.

So, from those definitions,

ppm = 45.1 ug solute / 250 g solution = the ppm answer.

And,

ppb= 45.1 ug solute / 0.250 kg solution = the ppb answer.

For concentration problems you will always need to start with the definition of the unit they want.

I’m no chemist by any means, but this should be simple enough that just about anyone can solve it!

Given that the solution is aqueous, and that water weighs about 1 gram per milliliter at 25° Centigrade, we can safely say that 250 ml. of water weighs 250 grams. A microgram (1 μg) is by definition one-millionth of a gram, or 0.000001 gram. So the pesticide concentration in terms of a weight percentage is

0.0000451 g. / 250 g. * 100% ≈ 0.00001804 percent by weight

In parts per million, this quantity would be

0.0000451 g. / 250 g. * 1,000,000 ≈ 0.1804 of 1 part per million

Lastly, parts per billion:

0.0000451 g. / 250 g. * 1,000,000,000 ≈ 180.4 parts per billion

P.S. I’m not a chemist, and I’m not studying chemistry, as I presume you are. Yet by doing a tiny bit of self-research, and using my noggin for things other than begging for answers on Quora, I was able to solve the problem. You can do it as well. Just learn the necessary definitions, do your own research, and find these solutions on your own!