Question

Acetylene, C2H2, can be converted to ethane, C2H6, by a process known as hydrogenation. The reaction is

C2H2(g)+2H2(g)⇌C2H6(g)

At 25 ∘C the reaction from ^ has a composition as shown in the table below.

Substance	Pressure (atm)
C2H2(g)	5.35
H2(g)	5.75
C2H6(g)	5.25×10−2

What is the free energy change, ΔG, in kilojoules for the reaction under these conditions?

Express your answer numerically in kilojoules.

Answer 1

Write the reation as follows: C,H,(8) + 2H, () → C,H(8) Calculate the standard Gibbs free energy as follows: AG° = AG;(CH)-4G,(CH2)-24G; (H) AG" =-32.89 kJ/mol – 2092 kJ/mol -20) AG" =- 242.09 kJ/mol - - - - - - - - - - - - - - - Equilibrium constant is defined as the ratio of product of parti al pressures of products raised to the powers of their stoichiometric coefficients to the product of parti al pressures of reactants raised to the powers of their stoichiometric coefficients. K, = — Catted .... (1) Given, Pcm, = 5.25x10 - atm PeyHx = 5.35 atm P, = 5.75 atm Substitute the corresponding valuesin equation (1) and calculate Ky K- 5.25x10- atm Ky = 5.35 atm (5.75 atm ) K, = 2.97x10+ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - The relation between AGº and K is as folows: AG = AGⓇ +RT In K,..... (2) Gibbs energy at standard temperature, AG° = -242.09 kJ/mol here, Ris gas constant = 8.314 J/molK Tis temperature= 25°C= (25+273) K= 298 K Substitute the corresopnding value in equation (2) and calculate the value of AG AG = AGⓇ +RT In K 40° = - 242.09 kJ/mol + ( 8.314J/molK)(298 K)x1n (2.97x10*) 1kJ AGⓇ = - 242.09 kJ/mol – 20120J/mol x- 103 J AG° = - 242.09 kJ/mol - 20.12 kJ/mol AGⓇ = - 262.21kJ/mol Therefore, the required solution is f-262.21kJ)