Question

Consider the reaction that converts pyruvic acid (CH3COCOOH) into gaseous acetaldehyde (CH3CHO) and gaseous CO2, which is catalyzed in aqueous solution by the enzyme pyruvate decarboxylase. Assume ideal gas behavior for CO2.

(a) Calculate delta-G (298 K) for this reaction at 160 bar.

(b) Calculate delta-G (298K) for this reaction at 100 bar. State any important assumption needed in addition to ideal gas behavior.

Answer 1

Ultimately the pyruvic acid created during respiration is metabolized into acetaldehyde and then to ethanol. This process is anaerobic and begins when the dissolved oxygen in solution is exhausted.

dH(reaction) = sum of dH(formation) values for products - sum of dH(formation) values for reactants.
dH(reaction) = [-235.1] - [-241.82 + 52.26] = -45.5 kJ

dS(reaction) = sum of So values for products - sum of So values for reactants.
dS(reaction) = [282.7 - (188.83 + 219.56) = -125.7 J/K

dG = dH - T dS = -45.5 kJ - [298K x (- 0.1257 kJ/K)] =
- 8.0 kJ = - 8000 J

dGo = -RT ln(Kp)
ln(Kp) = dGo / -RT
ln(Kp) = -8,000 J / (- 8.315 J/K mol x 298 K) = 3.23
Kp = e^(3.23) = 25.2

Assume dSo and dHo don't change with temperature.
(Use kelvin temperature in calculations: 250 C = 523 K)

dGo = dHo - T dSo = -45.5 kJ - [523 K (-0.1257 kJ/K)] =
+20.2 kJ/mol

dGo = dHo - T dSo
When dGo = 0, then T = dHo / dSo = -45.5 kJ / -0.1257 kJ/K = 362 K = 89 C

I think I got everything. Good luck in your study of chemistry.