Methanol can be prepared synthetically by heating carbon monoxide and hydrogen gases under pressure in the presenc eof a catalyst. The reaction is
`CO(g) +2H_(2)(g) rarr CH_(3)OH(l)`
Determine the enthalpy of this reaction by an appropriate combinantion of the following date:
a. `C_(("graphite")) +(1)/(2)O_(2)(g) rarr CO(g), DeltaH^(Theta)=- 110.5kJ mol^(-1)`
b. `C_(("graphite")) +O_(2)(g) rarr CO_(2)(g), DeltaH^(Theta) =- 393.5 kJ mol^(-1)`
c. `H_(2)(g) +(1)/(2)O_(2)(g) rarr H_(2)O(l), DeltaH^(Theta) =- 285.9kJ mol^(-1)`
d. `CH_(3)OH(l) +(3)/(2)O_(2)(g)rarr CO_(2)(g) +2H_(2)O(l),DeltaH^(Theta) =- 726.6 kJ mol^(-1)`

Explanation

The required equaiton can be obtained in the following manner:
-Equation `(a) +2` Equation `(c ) +` Equation `(b)-`Equation `(d)`
`= CO_(2)(g) +2H_(2)(g) rarr CH_(3)OH(l)`
So, `DeltaH^(Theta) = 110.5 - 571.8 - 393.5 + 726.6 = - 128.2 kJ mol^(-1)`