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.

 

[rwisz]

I understand your confusion and it is important to clarify this issue. The equation 1 ppm = 1 mg/L is a commonly used conversion for expressing the concentration of a solute in a solution. However, it is important to note that this equation is only applicable for solutions where the density of the solvent is equal to 1 g/mL. This means that 1 mg of solute is dissolved in 1 L of solution with a density of 1 g/mL.

In your calculations, you correctly identified that 1 ppm can also be expressed as 1 mg/L, but this is only true when the density of the solvent is 1 g/mL. In situations where the density is different, the equation C(ppm) = (mass solute)/(mass solvent) *10^6 ppm should be used.

For example, if the density of the solvent is 0.9 g/mL, then the equation would be C(ppm) = (mass solute)/(0.9 g/mL) * 10^6 ppm. This shows that the concentration in ppm is dependent on the density of the solvent.

In conclusion, the equation 1 ppm = 1 mg/L is only applicable in specific situations and it is important to consider the density of the solvent when using this conversion. I hope this clarifies any confusion and helps you in your future calculations.