Calculate the standard enthalpy of formation of liquid methanol, CH3OH(l), using the following information: C(graphite) + O2 --> CO2(g) LaTeX: \DeltaΔH° = –393.5 kJ/mol H2(g) + (1/2)O2 --> H2O(l) LaTeX: \DeltaΔH° = –285.8 kJ/mol CH3OH(l) + (3/2)O2(g) --> CO2(g) + 2H2O(l) LaTeX: \DeltaΔH° = –726.4 kJ/mol

Standard formation of reaction : It is a chemical reaction that forms one mole of a substance from its constituent elements in their standard states.

According to Hess’s law of constant heat summation, the heat absorbed or evolved in a given chemical equation is the same whether the process occurs in one step or several steps.

According to this law, the chemical equation can be treated as ordinary algebraic expression and can be added or subtracted to yield the required equation. That means the enthalpy change of the overall reaction is the sum of the enthalpy changes of the intermediate reactions.

The formation reaction of [tex]CH_3OH[/tex] will be,

[tex]C(s)+2H_2(g)+\frac{1}{2}O_2\rightarrow CH_3OH(g)[/tex] [tex]\Delta H_{formation}=?[/tex]

The intermediate balanced chemical reaction will be,

(1) [tex]C(graphite)+O_2(g)\rightarrow CO_2(g)[/tex] [tex]\Delta H_2=-393.5kJ/mole[/tex]

(2) [tex]H_2(g)+\frac{1}{2}O_2(g)\rightarrow H_2O(l)[/tex] [tex]\Delta H_3=-285.8kJ/mole[/tex]

(3) [tex]CH_3OH(g)+\frac{3}{2}O_2(g)\rightarrow CO_2(g)+2H_2O(l)[/tex] [tex]\Delta H_1=-726.4kJ/mole[/tex]

Now we will reverse the reaction 3, multiply reaction 2 by 2 then adding all the equations, we get :

(1) [tex]C(graphite)+O_2(g)\rightarrow CO_2(g)[/tex] [tex]\Delta H_1=-393.5kJ/mole[/tex]

(2) [tex]2H_2(g)+2O_2(g)\rightarrow 2H_2O(l)[/tex] [tex]\Delta H_2=2\times (-285.8kJ/mole)=-571.6kJ/mol[/tex]

(3) [tex]CO_2(g)+2H_2O(l)\rightarrow CH_3OH(g)+\frac{3}{2}O_2(g)[/tex] [tex]\Delta H_3=726.4kJ/mole[/tex]

The expression for enthalpy of formation of [tex]C_2H_4[/tex] will be,

[tex]\Delta H_{formation}=\Delta H_1+\Delta H_2+\Delta H_3[/tex]

[tex]\Delta H=(-393.5kJ/mole)+(-571.6kJ/mole)+(726.4kJ/mole)[/tex]

[tex]\Delta H=-238.7kJ/mole[/tex]

Therefore, the standard enthalpy of formation of methanol is, -238.7 kJ/mole