Question

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∘f (kJ/mol)
C2H2(g)	209.2
H2(g)	0
C2H6(g)	−32.89

Express your answer using two significant figures.

Answer 1

Step 1:

Given:

Gof(C2H2(g)) = 209.2 KJ/mol

Gof(H2(g)) = 0.0 KJ/mol

Gof(C2H6(g)) = -32.89 KJ/mol

Balanced chemical equation is:

C2H2(g) + 2 H2(g) ---> C2H6(g)

ΔGo rxn = 1*Gof(C2H6(g)) - 1*Gof( C2H2(g)) - 2*Gof(H2(g))

ΔGo rxn = 1*(-32.89) - 1*(209.2) - 2*(0.0)

ΔGo rxn = -242.09 KJ

Step 2:

T = 298 K

ΔGo = -242.09 KJ/mol

ΔGo = -242090 J/mol

use:

ΔGo = -R*T*ln Kc

-242090 = - 8.314*298.0* ln(Kc)

ln Kc = 97.7126

Kc = 2.729*10^42

Step 3:

T = 298 K

Δ n = number of gaseous molecule in product - number of gaseous molecule in reactant

Δ n = -2

use:

Kp= Kc (RT)^Δ n

Kp = 2.729*10^42*(0.08206*298.0)^(-2)

Kp = 4.56*10^39

Answer: 4.6*10^39