ICP-OES data treatment: correct for dilution and inweight, the units

Let's say the ICP-OES software gives me a concentration of 186,49 ppm (mg/L) of Mn. I diluted the acid digested sample to 14.2 mL. I weighed in 10.17 mg of the powder I analyzed. I need to calculate the actual concentration.

It is quite logical in my head what I need to do: multiply by diluted volume and divide by inweight. However, I don't understand my units.

When I multiply 186.49 mg/L with 0.0142 L, I get 22,648 mg. When I then divide this by 10.17 mg, I end up with 0.260. But this is unitless. How do I know what unit I have? I thought I converted the w/V concentration to w/w by this procedure, but the units does not follow.

Is it so, that I end up with a ratio (not sure what kind of ratio)? Then I think I understand. 0.26 would then represent 26 %, meaning my sample contains 26 % Mn. But how do I know that this is in w/w, and not w/V as I started with. I just don't get the units to add up.

I think you have a typo in your calculation (also, using both dots and commas as the decimal point is rather confusing), but you're on the right track. The unfortunate thing about elemental analysis is that %, ppm, ppb, ppt, etc. get misused in a confusing way. These units are supposed to be used for only dimensionless ratios, the units you start with, ppm is actually mg/L which represents mass concentration, not mass ratio. Your calculations are correct:

$$\left(186.49 \frac{\mathrm{mg}}{\mathrm{L}}\right)\left(0.0142\mathrm{\ L}\right) = 2.648 \mathrm{\ mg}$$ gives the mass of the Mn in your sample, so when you divide by the sample mass:

$$\frac{2.648 \mathrm{\ mg}}{10.17\mathrm{\ mg}}=0.260$$ you get the mass fraction of Mn in your sample, and you know it's a mass fraction because you have mass units in both the numerator and the denominator, leaving you dimensionless. You can express it just like that, or you can convert it to 26.0% (and this is a dimensionless ratio, so it actually makes sense to use % here), or else express it as the mass of Mn in an arbitrary sample mass: 26.0 g/100 g.

• Thanks a lot! So, if I so wanted, I could write 260 promille, or 260000 ppm Mn? I will second the confusing use of ppm. The instrument gives me ppm, but it is the actual units I am interested in. ppm, ppb, etc are fine for reporting LOD's and LOQ's. Thanks again, Mr. Dryden. – Yoda Nov 9 '14 at 19:27
• Yeah, you can use ppm if you want, though it's ambiguous and discouraged because it doesn't say whether you're using mass fraction, volume fraction, or mole fraction. mg/kg or the like is more explicit. – Michael DM Dryden Nov 9 '14 at 19:39