Greenhouse gas `CO_(2)` can be converted to `CO(g)` by the following reaction
`CO_(2)(g)+H_(2)(g) rarr CO_(2)+H_(2)O(g)` , termed as water gas reaction.
Calculate `DeltaH` at 1400 K using the given data for 1000K , assuming the `C_(p)^(@)` values remain constant in the given temoerature range.
`DeltaH=35040 J"mol"^(-1), C_(p)^(@)(CO_(2))=(42.31 + 10.09 xx 1^(-3)T) J "mol"^(-1)K_(1)`
`C_(P)^(@)(H_(2))=(27.40 + 3.20 xx 10^(-3)T) J"mol"^(-1)K_(1)`
`C_(P)^(@)(CO)=(28.34+ 4.14 xx 10^(-3)T)J"mol"^(-1)K^(-1)`
`C_(P)^(@)(H_(2)O)=(30.09 + 10.67 xx 10^(-3)T)J"mol^(-1)K^(-1)`

Answer

`int_(H_(1))^(H_(2))dH=int_(T_(1))^(T_(2)) Cp.dT`
`DeltaH_(2)-DeltaH_(1) = int_(T_(1))^(T_(2)) (28.35 + 4.14 xx 10^(-3)T + 30.09 + 10.67 xx 10^(-3)T)-(42.31 + 10.09 xx 10^(-3)T + 27.4 + 3.2xx 10^(-3)T)dT`
`=int_(T_(1))^(T_(2)) (-11.28 + 1.52 xx 10^(-3)T)dT`
`=-11.28 xx 400 + 1.52 xx ((1400^(2) - 1000^(2)))/(2) xx 10^(-3)`
`DeltaH_(2) - 35040 =- 3782.4 " " therefore DeltaH_(2) = 31258 "Joule"`