How do I check that the ESI-MS peaks on a COA actually correspond to semaglutide or tirzepatide?

I have two third-party reports in front of me. Both say "identity confirmed by ESI-MS" and both include a spectrum, but the spectra look nothing like the single clean peak I expected.

The semaglutide report has its biggest peak at 1372.2 and smaller ones at 2057.8 and 1029.4. The tirzepatide report has peaks at 1605.5, 1204.4 and 963.7. Neither report shows anything anywhere near 4113 or 4813, which are the molecular weights I keep seeing quoted for these two compounds.

I understand at a hand-waving level that electrospray produces multiply charged ions, so the instrument is not measuring mass, it is measuring mass-to-charge. What I cannot do is the arithmetic in reverse. Given a molecular weight I trust from the literature, how do I predict where the peaks should land, and given a list of observed peaks, how do I work out the neutral mass and satisfy myself that it is the right compound?

Second part: one report gives the parent mass as 4113.6 and the other as 4111.1 for what is supposedly the same peptide. That is a 2.5 Da gap, which is far too big to be instrument error on a modern instrument. Is one of them wrong, or am I comparing two different quantities?

One addition to the accepted answer, because it explains why the tallest peak is where it is rather than at 1+ or 6+.

The charge-state distribution in positive-mode ESI is roughly governed by how many basic sites the peptide has that are accessible in the spray droplet, and by the solvent. For a 30-to-40 residue peptide you typically see a bell of three to five charge states with the apex at 3+ or 4+, because that is about the number of readily protonated sites (N-terminal amine plus arginine, lysine and histidine side chains) that survive the droplet chemistry.

Semaglutide has a His at the N-terminus, two Arg and one Lys, but the Lys epsilon-amine is acylated with the AEEA-AEEA-gamma-Glu-C18 diacid side chain, so it is not available for protonation and the side chain itself contributes two carboxylates that fight against positive charging. That is why semaglutide spectra are 2+/3+/4+ dominant rather than pushing to 5+ and 6+ like an unmodified peptide of the same length would.

Practical consequences you can actually use:

• Acid matters. Running 0.1% TFA gives a lower average charge state and much worse absolute signal than 0.1% formic acid, because trifluoroacetate ion-pairs with the protonated sites and suppresses ionisation. If two labs show you spectra with different charge distributions, mobile phase is the first thing to suspect, not sample difference.
• Charge envelope shape is a folding readout. A denatured peptide exposes more basic sites and shifts the envelope to higher charge. A tight, low-charge envelope on something that should be flexible sometimes indicates aggregation. This is qualitative and I would not put weight on it, but it is a free observation.
• Never quantify off charge states. The intensity split between 2+, 3+ and 4+ is not a property of the peptide, it is a property of the day. Peak height in an ESI spectrum tells you approximately nothing about how much material is in the vial.

Deconvolution software (the maximum-entropy and Fourier-based algorithms in the vendor packages) does exactly the arithmetic the accepted answer does by hand, across every peak simultaneously, and outputs a single neutral-mass spectrum. That deconvolved trace is what you actually want to see on a COA, alongside the raw m/z spectrum. A report that shows only the deconvolved mass has hidden the evidence; a report that shows only raw m/z has made you do the work. Good ones show both.

Worth stating the boring failure mode explicitly, because it is the one I see most often on vendor-supplied reports rather than independent ones.

A surprising number of "MS confirmation" images are simply the wrong compound's spectrum, reused. The way to catch it in thirty seconds is to do the arithmetic in the accepted answer and check every annotated peak, not just the tallest. Retatrutide, tirzepatide and semaglutide have distinct enough masses that the 3+ and 4+ ions are nowhere near each other:

Retatrutide and tirzepatide are only about 82 Da apart, which is 27 Da at the 3+ peak. That is trivially resolvable on any instrument but very easy to gloss over if you are reading a low-resolution PDF screenshot and pattern-matching on peak shape. Check the numbers.

Second thing: if a report gives you a mass and no spectrum at all, it is a claim, not data. Janoshik, Medutest and PeptideMeter all publish the actual trace with the report identifier on it. Any report you cannot trace back to the testing service with an identifier is worth exactly what you paid for it.

Three precision traps in the arithmetic above, in ascending order of how much damage they do. Worth knowing which ones matter, because people fuss over the small one and skip the large one.

Proton mass versus hydrogen atom mass. Protonation adds H+, a proton with no electron: 1.007276 Da. A neutral hydrogen atom is 1.007825 Da. The difference is one electron, 0.000549 Da. On a 4+ ion that accumulates to 0.0022 Da in the deconvolved neutral mass, which on a 4813 Da peptide is 0.46 ppm — roughly a tenth of the error budget on an instrument specified at better than 5 ppm. Small, but free to get right, so use 1.00728.

Mixing average and monoisotopic constants. This is the one that actually ruins calculations. Using average atomic masses (C 12.011, H 1.008) and then comparing against a monoisotopic measurement gives you a 2.5 to 3 Da discrepancy at this molecular size, which is 600 ppm and looks exactly like a real chemical difference. Pick a convention and apply it to every term in the calculation, including the proton.

Charge-state misassignment. The worst, because the error scales with z. Assign a 3+ peak as 4+ and your neutral mass is out by a third. This is where the isotope-spacing check earns its keep: spacing of 1/z within the envelope is an independent confirmation of the charge, and it costs one glance at the raw trace.

Where the millidaltons genuinely matter is impurity assignment rather than identity. To tell a missing Gln (residue mass 128.0586) from a missing Lys (128.0949) you must resolve a 0.0364 Da gap on a roughly 4685 Da fragment, which is 7.8 ppm. To call it confidently you want mass accuracy comfortably better than half that gap, so around 3 to 4 ppm — achievable on an Orbitrap or a well-calibrated TOF, and not achievable on the single-quadrupole instruments behind a fair number of the reports circulating in this market. If a report distinguishes those two deletions, check that it states an instrument capable of it.