# What is the correct way to specify the weight fraction from bulk compositional data with a listed total % (e.g. from XRF, ICP)?

TL;DR = With bulk composition results, such as from X-Ray Fluorescence (XRF) testing, is the mass fraction of a given analyte that analyte given as a % or the analyte divided by the given total mass %?

Perhaps a silly and very elementary question, but I want to be certain as I've been wondering for a while now and never 100% sure if I'm right or not. But I'd like to be to minimise any potential compounding errors.

I've recently received some X-Ray Fluorescence (XRF) bulk composition analysis of some coal fly ash material I'm going to analyse. The full table of results is as below where the units are listed as %.

(note that I did try to put everything in Chem SE table format but it was too difficult to do, format and the help page didn't provide too much clarity from my POV):

Note that the total % provided is 100.21%. I presume they're not always 100% due to errors with instrumentation detection limits (etc.). However, when I do the sum (i.e. Each analyte % + LOI %) I get 100.06 % =/= 100.21 %.

I understand that the mass (or weight) fraction of a given analyte is given by the formula below where $$w_i$$ and $$m_i$$ is the mass/weight fraction and mass of the given analyte respectively and $$m_{tot}$$ is the mass of the total mixture:

I have been told by some to just assume that the % given for each analyte is the mass fraction but I feel that may not be right and I'd rather less compounding errors than more.

So with this in mind, my questions are:

1. Is the mass fraction of SiO2 from the above tables 54.19% as listed or, for a given mass of 100.21 g for the parent material, $$\frac{54.19 g}{100.21 g} \times 100\%$$ = 54.08%?

2. Can the moisture and LOI analytics be added as part of the total? I.e. should I assume from this table of results that 0.01% of the total mass is H2O and 0.01% is carbon respectively?

• It is not a silly or an elementary question, but perhaps you can add more details about analytical details. XRF and ICP-OES are apples and oranges, for moreso for a heterogeneous mixture like fly ash.
– ACR
Commented Feb 23, 2023 at 16:39
• The only other details I could think of maybe adding from the report is detection limits. What else could I look for to add? Commented Feb 24, 2023 at 0:23