Answer
$\Delta H = -90.7kJ$
Work Step by Step
Use the Hess's law to find the $\Delta H$
1. Reverse the first equation:
$2 CO(g) --> 2 C (s) + O_2 (g): \Delta H = +221kJ$
$2 C(s) + O_2(g) + 4H_2 (g)--> 2CH_3OH(g): \Delta H -402.4kJ$
2. Now, sum the equations:
$2CO(g) + 2C(s) + O_2(g) + 4H_2(g) --> 2C(s) + O_2(g) + 2CH_3OH(g) : \Delta H = -181.4kJ $
*Remove the ones repeating.
$2CO(g) + 4H_2(g) --> 2CH_3OH(g): \Delta H = -181.4kJ$
3. Divide all the coefficients and the $\Delta H$ by 2:
$CO(g) + 2H_2(g) --> CH_3OH(g): \Delta H = -90.7kJ$
