A high H\(_2\)/CO ratio can overstate the suitability of plastic-derived synthesis gas for methanol production when CO\(_2\) is also present. This study quantifies the hydrogen requirement and carbon-retention limit of ten-batch polyethylene-reforming gas containing 229.3 mmol H\(_2\), 95.1 mmol CO, 37.7 mmol CO\(_2\), and 36.9 mmol CH\(_4\). An analytical stoichiometric bound is verified by reaction-network linear programming and used to compare hydrogen addition, selective CO\(_2\) removal, water–gas shift, and conditional methane reforming. Despite an H\(_2\)/CO ratio of 2.411, the gas has a methanol stoichiometric number of 1.443 and a 74.0 mmol hydrogen deficit. Without additional hydrogen, the methanol ceiling is 108.13 mmol, corresponding to 81.43% of the initial carbon-oxide carbon. Removing 24.67 mmol CO\(_2\) balances the retained gas without increasing this ceiling; adding 74.0 mmol H\(_2\) instead permits retention of all 132.8 mmol carbon oxides. Water–gas shift leaves the deficit unchanged. Complete steam reforming of the measured methane would raise the ceiling to 157.33 mmol but leave a 37.1 mmol hydrogen deficit for the enlarged carbon pool. Independent \(\pm5\%\) composition perturbations give deficits of 47.37–100.63 mmol. Numerical and analytical results agree across 10,201 conditioning points. The results quantify the carbon cost of reducing external hydrogen demand; they are stoichiometric limits, not measured methanol yields or predictions of plant performance.
