Question

A commercial process for the production of 1,3-butadiene consists of the dehydrogenation of 1-butene in the presence of steam at high temperatures. It is desired to find the maximum conversion of 1-butene to 1,3- butadiene possible at 900 K and 1 bar in a reactor in which the feed consists of 15 moles of steam per mole of 1-butene.

(a) Compute ΔG˚ and K for the dehydrogenation of 1-butene to 1,3-butadiene

(b) Calculate the fraction of 1-butene converted to 1,3-butadiene at equilibrium.

Additional information. Curve fits of the heat capacities: Cp = α+βT+γT² +δT³ (cal/mol K)

Component	α	β⋅102	γ⋅105	δ⋅109
Hydrogen	6.424	0.1039	-0.0078	-
1,3-Butadiene	-1.29	8.35	-5.582	14.24
1-Butene	-0.24	8.65	-5.110	12.04

Other data:

1-butene at 25 ˚C: ΔG˚_f = 17.09kcal/mol and ΔH˚_f = -0.03kcal/mol

1,3-butadiene at 25 ˚C: ΔG˚_f = 36.01kcal/mol and ΔH˚_f = 26.33kcal/mol

Use R = 1.987 cal/(mol K).

Answer 1

b)

From the part a) K= equilibrium constant = 1.88

K = (product)/(reactant)

Fraction of 1-butene converted to 1,3-butadiene will be 1/ K

= 1/1.88

= 0.53. -------> ans