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The commercial production of water gas u...

The commercial production of water gas utilizes the reaction under standard conditions: `C + H_2O(g) rarr H_2 + CO`. The heat required for this endothermic reaction may be supplied by adding a limited amount of air and burning some carbon to `CO_2`. How many grams of carbon must be burnt to `CO_2` to provide enough heat for the water gas conversion of 100g carbon. Neglect all heat losses to environment. `Delta H_(f)^(@) "of" CO, H_2O(g) and CO2_(g)` are `–110.53, –241.81 and –393.51 kJ//mol` respectively.

Text Solution

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`C+ H_(2)O(g) to H_(2)(g) + CO(g), DeltaH_(t)^(@) = ?`
`therefore DeltaH^(@) = DeltaH_(CO)^(@) - DeltaH_(H_(2)O)^(@) = -110.53 -(-241.81) = 131.28` kJ/mol.
`(therefore DeltaH^(@))` for C and `H_(2)` are zero
Thus, `DeltaH^(@)` needed for 100 g carbon `=(131.28 xx 100)/12 kJ`
Now, 393.51 kJ energy is provided by 12 g C
`(131.28 xx 100)/12 kJ` energy is provided by `=(12 xx 131.28 xx 100)/(12 xx 393.51) = 33.36` g
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