Answer: Maximum work that can be obtained by given amount of methanol is -343kJ.
Explanation:
For the given chemical reaction:
[tex]2CH_3OH(l)+3O_2(g)\rightarrow 2CO_2(g)+4H_2O(g);\Delta G_{rxn}=-1372kJ/mol[/tex]
By Stoichiometry of the reaction:
2 moles of methanol does a work of 1372 kJ.
So, 0.5 moles of methanol will do a work of = [tex]\frac{1372kJ}{2}\times 0.5=343kJ[/tex]
Hence, maximum work that can be obtained by given amount of methanol is -343kJ.