Question

C₂H₂ (g) + 3H₂ (g) --> 2CH₄ (g)

ΔH_f:    227                                  -75      (kJ/mol)

S°:    201            131               186      (J/mol K)

At which Kelvin temperature does the reaction switch from being spontaneous to nonspontaneous? (For this question, do not worry about specifying whether it is spontaneous above or below this temperature.)

Answer 1

C₂H₂ (g) + 3H₂ (g) ---------------> 2CH₄ (g)

ΔHrxn = ΔHproducts - ΔHreactants

            = 2 x -75 - (227 + 0)

            = - 377 kJ/mol

ΔSrxn = ΔSproducts - ΔSreactants

           = 2 x 186 - (201 + 3x131)

           = - 222 J/mol K

ΔG = ΔH - T ΔS

for spontaneous reaction ΔG < 0. so

ΔH < T ΔS

T < ΔH/ΔS

   < - 377 x 10^3 / - 222

   < 1698 K

above 1698 K it is spontenous. below this it is non spontenous.