Determining ppm concentrations from food label information for ICP-OES analysis?

Overview: I am looking to determine what ppm values of trace metals are present in a particular formula while considering digestion, dilution, and detection limits for ICP-OES. For example, one serving is 15 g of powdered formula which is then dissolved in 150 mL of solution, according to the label. The label reads 15 micrograms of Mn.

Goal: Find concentration of a metal from analysis of 1 g of formula digested and then diluted to 100 mL.

Attempt: 15 micrograms of Mn per 15 g of powdered formula. As that microgram/g is equivalent to ppm (15ug/15g = 1.0 ppm), there should be 1 ppm of Mn per 15 g of dry formula.

Taking 1 g of the formula, digesting it, and diluting to 100 mL: 100mL/1g x (X read) = 1 ug/g (ppm)

The AAS or ICP-OES read value should then be 0.01 ppm.

This would be well within the detection limit for ICP-OES. However, I am not sure if my above approach is correct. Is there something obvious that I am missing? Any insight would be appreciated.

You should not have a single sample preparation for all the elements. The sample preparation will depend on element by element. Your calculations have subtle misconceptions. Don't convert to concentrations but work with masses for such problems.

So, you have 15 $$\mu$$g Mn in 15 g sample. This means you have 1 $$\mu$$g Mn in 1 g sample (see, I am avoiding calculating ppm in the solid as yet). So, if you dissolve 1 $$\mu$$g of Mn in 100 mL of water, your final solution Mn concentration is 0.001 mg Mn/ 0.1 L or 0.01 mg/L Mn. So our numerical values match but your statement is slightly problematic.

there should be 1 ppm of Mn per 15 g of dry formula.

No, even if you take one ton of sample, it will still be 1 ppm Mn (w/w), because concentration does not depend on sample mass or volume. Analyte masses do, so if you take a larger sample mass, analyte mass will increase too, but its concentration in the sample will remain the same. This is reason to work with masses and then calculate concentration at the end.

As you already know AAS is less sensitive than ICP-OES in general, but it is less expensive. The critical info is called characteristic concentration in AAS for a each element, which is defined as the concentration that will produce 0.0044 absorbance units under optimized concentrations in air acetylene flame on a standard 10 cm burner head. Clearly, 0.01 ppm Mn is out of question on FAAS, because even under the best conditions, 0.05 ppm will produce an absorbance 0.0044. Such a value is prone to tons of errors. As a result you need a concentration sample, which is 10x fold more concentrated. I will leave it as an exercise.

This is a screenshot of a so-called Cookbook of Perkin Elmer's AAS.

The AAS or ICP-OES read value should then be 0.01 ppm.

Don't trust machine calculated concentrations. Make a calibration curve youself. No instrument can tell you the concentration without a calibration curve.