Given that `C_((g))+O_(2(g)) to CO_(2(g)) DeltaH^@=-a kJ ,
2 CO_((g)) + O_(2(g)) to 2CO_(2(g))
'DeltaH^@`=-b kJ , Calculate the `DeltaH^@` for the reaction `C_((g)) +1//2O_(2(g)) to CO_((g))`

Options

A. `(b+2a)/2`
B. `2a-b`
C. `(2a-b)/2`
D. `(b-2a)/2`

Answer

D

Explanation

`C+O_2 to CO_2 " " DeltaH^0`=- a kJ …..(1)
`2CO+O_2 to 2CO_2 " " DeltaH^0`=- b kJ …..(2)
`C+1//2 O_2 to CO " " DeltaH^0`= ?
(1) x 2
`2C+2O_2 to 2CO_2 " " DeltaH^0`=-2a kJ …(3)
Reverse of equation (2 ) will be
`2CO_2 to 2CO + O_2 " " DeltaH^0`=+ b kJ .....(4)
(3) + (4)
`2C+O_2 to 2CO " " DeltaH^0` =b-2a kJ ...(5)
(5) +2
`C+O_2 to CO " " DeltaH^0=(b-2a)2` kJ