Proving 1 ppm = 1 mg/L: Conflicting Equations?

[Jimmy25]

My text claims that 1 ppm = 1 mg/L. I tried to prove this for myself but I seem to be stuck. This is what I have so far:

1 mg(solute)/L(solvent) = 1 mg(solute) / 1*10^6 mg(solvent)

But:

C(ppm) = (mass solute)/(mass solvent) *10^6 ppm

These seem to be in conflict, what am I not seeing?

 

[Borek]

1 ppm = 1 mg/L for water solutions, when you can assume mass of 1L to be close to 1 kg.

 

[Jimmy25]

Yes, but how can it be proved?

 

[Borek]

1 mg/1 kg = 10^-6, I am not sure where the problem is.