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?

Substaance .. G∘f (kJ/mol)

C2H2(g)               209.2

H2(g) 0

  C2H6(g)                -32.89   

Answer 1

Answer – We are given, reaction –

C₂H₂(g) + 2 H₂(g) <-----> C₂H₆ (g)

Now first we need to calculate the ΔG^o rxn

ΔG^o rxn = sum of the ΔG^o product – sum of the ΔG^o reactant

               = [ΔG^o C₂H₆ (g)] – [ ΔG^o C₂H₂(g) + 2* ΔG^o H₂(g)]

             = (-32.89 ) - (209.2 + 2*0.0)

                = -242.09 kJ/mol

We know the formula ,

ΔG^o = -RT ln Kp

So, ΔG^o in J

1 kJ = 1000 kJ

So, -242.09 kJ = ?

= -2.42*10⁵ J/mol

Now plugging the values in the formula,

-2.42*10⁵ J/mol = - 8.314J.mol^-1.K^-1 * 298 K * ln Kp

ln Kp = -2.42*10⁵ J/mol / - 8.314J.mol^-1.K^-1 * 298 K

ln Kp = 97.71

now taking antiln from both side

Kp = 2.69*10⁴²