Not much glycine is lost with usual aspirin doses (30% or less of the aspirin weight).
The amount of sodium eliminated in pairing with salicylate ions should also be low. Approximations:
Aspirin
1 mmol per 180 mg (from 180 g/mol⇈) 5.5 mmol per 1000 mgSodium
5.5 mmol of sodium is 130 mg (from: 5.5 mmol × 23 mg/mmol)Maximum direct sodium loss:
130 mg Na/g aspirinIt may seem negligible, but it depends on the amount consumed of each.
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For a person ingesting an average amount of sodium (4 g), taking high doses of aspirin can induce the depletion of a considerable share of the sodium intake.
As for the alkalinization, it may enhance the activity of acyl-CoA synthetases (ACS), mentioned above as the limiting step, similar to the disinhibition effect on some glycolysis enzymes.