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Your number for natural gas which is 97% methane is backwards the chemical formula for methane is CH4 so it’s 75% hydrogen 25% carbon by mole. The rest is ethane,nitrogen,argon,and CO2 at pipeline grade must be less than 3% of the gasses. Even ethane is C2H8 also a 2/8=1/4 ratio of carbon to hydrogen.

For coal carbon content doesn’t take into account that coal has a significant amount of ash. Most power coal in the USA is Subbituminous coal you need to look at it’s chemical composition not it’s carbon content. Here is a typical power coal from one of the largest us coal mines.

Subbituminous coal (PSOC 1488) from the Dietz seam in Montana, U.S.A. was used. The coal contains 76.56% C, 5.27% H, 0.95% N, and 17.22% O (dmmf).

Coal will always make more CO2 per megawatt hour it’s just chemistry of solid carbon based fuel vs gaseous carbon based fuel. Coal is also loaded with sulfur and that nitrogen will form NOx when you burn it even in a pure oxygen burner aka oxyfired boiler. Both SOx and NOx are real pollution which must be reduced to ppm levels in the flue gas. Coal also contains heavy metals that at coal combustion temps form volatile vapors that also must be reduced to ppm levels or less. There is no safe exposure level for lead zero is always better than even ppb levels. Even the most advanced scrubbers in the world barely get to ppm levels. The only way to burn coal and have it not put out SOx,NOx and mercury vapor is to use gasification plant tech turn the coal to syngas then run it through a analytically clean gas clean up train then burn the deeply scrubbed gas in a gas turbine with low NOx burners so atmospheric N2 doesn’t form NOx. If you are burning gas you might as well just skip the gasification plant and gas clean up because natural gas from the ground will always be cleaner than coal syngas given equal gas clean up trains.

The EPA is technology agnostic they simply say you are allowed to emit X grams per kWh or X ppm per 1000 cubic feet of flue gas of each of the criteria pollutants SOx,NOx,particulate matter,mercury ect. How a plant gets to those limits is up to them. Use scribbers, use gasification or change fuels but hit the limits or shut down. So coal must meet the limits that gas turbines hit with ease.allowing coal to pollute while clear tech and power systems are available is not going to happen anymore society said no we don’t want SOx and NOx making our rain acidic no we would like to eat the fish out of our lake house lakes and not have them be full of mercury. My lake house you cannot eat the fish because the watershed was in the stack gas ashfall plume of a coal plant for 40+ years. The levels of mercury in the fish are so high not even a single portion is safe to eat my an adult male which is ten times the limit for breeding age females.

SMU came in and did the isotopic analysis for where the mercury came from it was directly linked by isotope to the coal plants ashfall into the watershed. This is why coal will never be allowed to be burnt directly to the sky ever again in the USA that era is over and rightly so it’s best left in the dust bin of history. Clean coal tech exists ask Mitsubishi for their gasification tech they are the world leaders in it but even then there is still ppm levels of heavy metal vapors in the syngas th at for a right up the stacks.