Question

A `300*lb` mass of a chemical is accidentally spilled into a dam whose volume is `1.362xx10^4*m^3`... What is the `"ppm"` concentration?

Answer 1

Whoops.....well first we have to have kosher units.......We ASSUME the chemical is homogeneously mixed in the dam, and we finally get a volume of over 10 million litres.........

Explanation:

`"1 ppm"=1*mg*L^-1=10^-3*g*L^-1`. At `"ppm"` levels of concentration we don't really have to worry about solution density.

We gots `300*lb` of stuff, i.e.

`300*lbxx454*g*lb^-1xx10^3*mg*g^-1=1.362xx10^8*mg`

And now we can write out the quotient..........

`"mass"/"volume"="concentration"=10*mg*L^-1`.........

So `"volume"="mass"/"concentration"=(1.362xx10^8*mg)/(10*mg*L^-1)` and we gets an answer in `L`, which we then convert to `m^3`

`=1.362xx10^7*L=1.362xx10^4*m^3`, not an insignificant volume......

All I have done is to use the unit conversions, and know that `"milli"=10^-3`.......I agree that it is not wholly straightforward, but practice is the key.