Question

In the Mond process for the purification of nickel, carbon monoxide is reacted with heated nickel to produce Ni(CO)4, which is a gas and can therefore be separated from solid impurities: Ni(s) + 4CO(g) ⇌ Ni(CO)4(g) Given that the standard free energies of formation of CO(g) and Ni(CO)4(g) are −137.3 and −587.4 kJ/mol, respectively, calculate the equilibrium constant of the reaction at 58.0°C. Assume that ΔG o f is temperature-independent.

Answer 1

Answer: The equilibrium constant for this reaction is
`1.068* 10^(6)`

Step-by-step explanation:

The equation used to calculate standard Gibbs free change is of a reaction is:

`\Delta G^o_(rxn)=\sum [n* \Delta G^o_((product))]-\sum [n* \Delta G^o_((reactant))]`

For the given chemical reaction:

`Ni(s)+4CO(g)\rightleftharpoons Ni(CO)_4(g)`

The equation for the standard Gibbs free change of the above reaction is:

`\Delta G^o_(rxn)=[(1* \Delta G^o_((Ni(CO)_4(g))))]-[(1* \Delta G^o_((Ni(s))))+(4* \Delta G^o_((CO(g))))]`

We are given:

`\Delta G^o_((Ni(CO)_4(g)))=-587.4kJ/mol\\\Delta G^o_((Ni(s)))=0kJ/mol\\\Delta G^o_((CO(g)))=-137.3kJ/mol`

Putting values in above equation, we get:

`\Delta G^o_(rxn)=[(1* (-587.4))]-[(1* (0))+(4* (-137.3))]\\\\\Delta G^o_(rxn)=-38.2kJ/mol`

To calculate the equilibrium constant (at 58°C) for given value of Gibbs free energy, we use the relation:

`\Delta G^o=-RT\ln K_(eq)`

where,

`\Delta G^o` = Standard Gibbs free energy = -38.2 kJ/mol = -38200 J/mol (Conversion factor: 1 kJ = 1000 J )

R = Gas constant = 8.314 J/K mol

T = temperature =
`58^oC=[273+58]K=331K`

`K_(eq)` = equilibrium constant at 58°C = ?

Putting values in above equation, we get:

`-38200J/mol=-(8.314J/Kmol)* 331K* \ln K_(eq)\\\\K_(eq)=e^(13.881)=1.068* 10^(6)`

Hence, the equilibrium constant for this reaction is
`1.068* 10^(6)`