Question

Consider the following reaction: CO2(g)+CCl4(g)⇌2COCl2(g) Calculate ΔG for this reaction at25 ∘C under these conditions: PCO2PCCl4PCOCl2===0.140atm0.180atm0.760atm ΔG∘f for CO2(g) is −394.4kJ/mol, ΔG∘f for CCl4(g) is −62.3kJ/mol, and ΔG∘f for COCl2(g) is −204.9kJ/mol. Express the energy change in kilojoules per mole to one decimal place.

Answer 1

Answer: The
`\Delta G` for the reaction is 54.6 kJ/mol

Step-by-step explanation:

For the given balanced chemical equation:

`CO_2(g)+CCl_4(g)\rightleftharpoons 2COCl_2(g)`

We are given:

`\Delta G^o_f_(CO_2)=-394.4kJ/mol\\\Delta G^o_f_(CCl_4)=-62.3kJ/mol\\\Delta G^o_f_(COCl_2)=-204.9kJ/mol`

• To calculate
  `\Delta G^o_(rxn)` for the reaction, we use the equation:

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

For the given equation:

`\Delta G^o_(rxn)=[(2* \Delta G^o_f_((COCl_2)))]-[(1* \Delta G^o_f_((CO_2)))+(1* \Delta G^o_f_((CCl_4)))]`

Putting values in above equation, we get:

`\Delta G^o_(rxn)=[(2* (-204.9))-((1* (-394.4))+(1* (-62.3)))]\\\Delta G^o_(rxn)=46.9kJ=46900J`

Conversion factor used = 1 kJ = 1000 J

• The expression of
  `K_p` for the given reaction:

`K_p=((p_(COCl_2))^2)/(p_(CO_2)* p_(CCl_4))`

We are given:

`p_(COCl_2)=0.760atm\\p_(CO_2)=0.140atm\\p_(CCl_4)=0.180atm`

Putting values in above equation, we get:

`K_p=((0.760)^2)/(0.140* 0.180)\\\\K_p=22.92`

• To calculate the Gibbs free energy of the reaction, we use the equation:

`\Delta G=\Delta G^o+RT\ln K_p`

where,

`\Delta G` = Gibbs' free energy of the reaction = ?

`\Delta G^o` = Standard gibbs' free energy change of the reaction = 46900 J

R = Gas constant =
`8.314J/K mol`

T = Temperature =
`25^oC=[25+273]K=298K`

`K_p` = equilibrium constant in terms of partial pressure = 22.92

Putting values in above equation, we get:

`\Delta G=46900J+(8.314J/K.mol* 298K* \ln(22.92))\\\\\Delta G=54659.78J/mol=54.6kJ/mol`

Hence, the
`\Delta G` for the reaction is 54.6 kJ/mol