Question

The equilibrium constant of a system, K, can be related to the standard free energy change, ΔG∘

ΔG∘=−RTlnK

where T is a specified temperature in kelvins (usually 298 KK) and R is equal to 8.314 J/(K⋅mol)

Under conditions other than standard state, the following equation applies:

ΔG=ΔG∘+RTlnQ

In this equation, Q is the reaction quotient and is defined the same manner as KK except that the concentrations or pressures used are not necessarily the equilibrium values.

Part A

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

C2H2(g)+2H2(g)⇌C2H6(g)

Given the following data at standard conditions (all pressures equal to 1 atm and the common reference temperature 298 K), what is the value of Kp for this reaction?

Substance	ΔG∘fΔGf∘ (kJ/molkJ/mol)
C2H2(g)C2H2(g)	209.2
H2(g)H2(g)	0
C2H6(g)C2H6(g)	−−32.89

kp= 2.7×1042

Part B

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

Substance	Pressure (atmatm)
C2H2(g)C2H2(g)	3.85
H2(g)H2(g)	4.95
C2H6(g)C2H6(g)	5.25×10−2

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

Answer 1

Part Az C2 Hq + 2H₂ = Ca MG Auf 209.2 o -32.89 shran sus (C2 Ho) -AGE (C 2 Hz) - 2xA cis (Hz) = -32.89 - 209.2 - 2x0 = -242.09 kJ/mol ii -(-242.09 x103 Jimor) - 16 RT 8,314 TK 'moplx 298k 97. 7126 è AGIRT . ..K= e +9707126 Ik = 2.7 X10 42 | Parts a t Peato Puth x Piz 5.25 x 10-2 3.85 *(4-95) = 5.565 x10-4 sh= - shiron + RT in Q 8 - 242.09 kJ/mol + (8.314 x 298 J/mol in 5.565X1024) - - 242.09 kJ/mol of - 18.566 KTimol AG = -260.656 kJ/mol