Question

Making methanol the element hydrogen is not abundant in nature, but it is a useful reagent in, for example, the potential synthesis of the liquid fuel methanol from gaseous carbon monoxide: $$2h2​(g)+co(g) ch3​oh(g) δh°f, kj/mol δs°f, j/mol·k h2(g) 0 130.6 co(g) -110.5 197.7 ch3oh(g) -238.7 126.8 1st attempt see hintsee periodic table this reaction is spontaneous at temperatures lower than:

Answer 1

ΔG⁰ = ΔH⁰ - TΔS
ΔH⁰ = Hf,(CH₃OH) - Hf,(CO) = -238.7 + 110.5 = -128.2 kJ/mol
ΔS = S(CH₃OH) - S(CO) - 2S(H₂) = 126.8 - 197.7 - 2 x 130.6 = -332.1 J/mol.K
So 
ΔG⁰ = - 128200 + 332.1 T
For the reaction to be spontaneous:
ΔG⁰ < 0
So: -128200 + 332.1 T < 0
332.1 T < 128200
T < 386.028 K