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?

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?

Wyatt Adkins · Accepted Answer

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.........

#"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.

Naomi Aronson · Answer

undefined PPM concentration = (mass of chemical / volume of dam) * 1,000,000
PPM concentration = (300 lb / 1.362 x 10^4 m^3) * 1,000,000
PPM concentration ≈ 22,033.90 ppm