Question

Is the following reaction spontaneous at 25 °C in the forward or the reverse direction? What is the highest temperature at which the reaction is spontaneous in the direction as written? N2(g) + 3H2(g) Í 2NH3(g)

Answer 1

N2 + 3H2 --> 2NH3

dH rxn = 2dH NH3 - dH N2 - 3dH H2

               = 2(-45.9) 0- 3(0) = -91.8 KJ

dS rxn = 2 dS NH3 - dS N2 - 3dS H2

              = 2(192.5) - 191.6 - 3(130.5) = -198.1 J/mol K = -0.198 KJ/mol

dG rxn = dH rxn - TdS rxn   where T= 25C = 298 K

dG rxn = -91.8 - ( 298) (-0.198)

       = - 32.76

hence given reaction is spontaneous

Let T be highest temp for sponatenous , then dG rxn = 0

we get

   0 = -91.8 - T( -0.1981)

T = 463.4 K = 463.4-273 = 190.4 C

hence highest temp for sponatenou is 190 C