Methanol can be prepared synthetically by heating carbon monoxide and hydrogen gases under pressure in the presence of 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 data:
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

To determine the enthalpy change for the reaction

\[ \text{CO(g) + 2H}_2\text{(g)} \rightarrow \text{CH}_3\text{OH(l)} \]

we will use Hess's law and the given reactions. The reactions and their enthalpy changes are:

1. \( \text{C(graphite) + } \frac{1}{2}\text{O}_2(g) \rightarrow \text{CO(g)}, \Delta H^\circ = -110.5 \text{ kJ/mol} \) (A)
2. \( \text{C(graphite) + O}_2(g) \rightarrow \text{CO}_2(g), \Delta H^\circ = -393.5 \text{ kJ/mol} \) (B)
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