Post below is an updated and expanded version of CO2 is heavier than coal.
Chemistry: Carbon is an atom with atomic weight of 12. During combustion it combines with two oxygen atoms with atomic weight each of 16. The outcome is a CO2 molecule with atomic weight of 44. The molecule that results from the reaction is 3.7 times as heavy as the carbon atom alone.
Coal is a sedimentary rock that varies by location and type. It is mostly carbon, but not pure. The proportion of carbon varies from 60% in Lignite to 90% in Anthacite. A typical value for discussion purposes is 80%. [Ref Wikipedia] Burning one ton of this typical coal will produce about three tons of CO2.
Calculation: 1 ton x 3.7 x 80% = 3 tons
Many have proposed that a tax or fee be imposed on the CO2 that is emitted from the burning of coal and other fossil fuels. They often suggest that the fee start low, say at $10 per ton of CO2, and rise by this amount each year. The fee on CO2 in Year 10 would be $100 per ton.
With this fee schedule for CO2, the fee on typical coal would be $30 per ton in Year 1 and $300 per ton in Year 10.
The average price of coal in the US in 2013 was about $37 per ton. [Source: US EIA] With this fee schedule, the fee for the CO2 would quickly dominate over the price of the coal before the fee.
Units of Measurement: Proposals for fees on CO2 emissions generally use dollars per metric ton of CO2. One metric ton equals 1000 kilograms, which equals 2205 pounds. One US ton equals 2000 pounds. $10 per metric ton of CO2 work outs to a fee of $9.07 per US ton.
Calculation: $10 x (2000 / 2205) = $9.07
In a model constructed in 2010 I used a fee of $11.50 per metric ton of CO2 that had been proposed by James Hansen. This works out to $10.43 per US ton of CO2. Using the ratio of 3:1 above, this becomes $31.29 per US ton of coal.
Calculation: $11.50 x (2000/2205) x 3 = $31.29
Because the 3:1 ratio is itself only a rough estimate, we may round the last result and stipulate that a fee of $11.50 per metric ton of CO2 works out to a fee of $30 per US ton of typical coal.
Bill Allen 03-21-15