Question

Consider the reaction 2CO2(g) + 5H2(g)C2H2(g) + 4H2O(g) Using the standard thermodynamic data in the tables linked above, calculate G for this reaction at 298.15K if the pressure of each gas is 17.64 mm Hg.

ANSWER:_____ kJ/mol

Answer 1

You need to apply the equation

∆G^o

ΔG_f^o [C₂H₂ (g)] = + 210 kJ/mol

ΔG_f^o [H2O(g)] = -228.61 kJ/mol

ΔG_f^o [CO₂(g)] = -394.4 kJ/mol

ΔG_f^o [H2(g)] = 0 kJ/mol

ΔG_f^o = 210 + 4*(-228.61) - (2*-394.4 + 0 ) = 84.36 KJ / mol

now we have to apply the equilibrium equation for compounds in a gas phase

2CO2(g) + 5H2(g)=======C2H2(g) + 4H2O(g)

Kp = Pp_C2H2 * Pp_H2O⁴ / ( Pp_CO2² * Pp_H2⁵)

let´s change the mm Hg to atmospheres, 1 atm = 760 mm Hg

17.64 / 760 = 0.0232 atm

Kp = 0.0232 * 0.0232⁴ / (0.0232² * 0.0232⁵), simplyfying

Kp = 1 / 0.0232²

Kp = 1857.9

LnKp = ln(1857.9) = 7.527

RT*7.527; R is gas constant 8.314 J / K mol, T is temperature in Kelvin

8.314 J / K mol * 298.15 * 7.527 = 18658.071 J / mol or 18.658 KJ / mol

ΔG = 84.36 + 18.658 = 103.018 KJ / mol