<u>Answer:</u> The
for the reaction is 54.425 kJ/mol
<u>Explanation:</u>
For the given balanced chemical equation:
![CO_2(g)+CCl_4(g)\rightleftharpoons 2COCl_2(g)](https://tex.z-dn.net/?f=CO_2%28g%29%2BCCl_4%28g%29%5Crightleftharpoons%202COCl_2%28g%29)
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](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo_f_%7BCO_2%7D%3D-394.4kJ%2Fmol%5C%5C%5CDelta%20G%5Eo_f_%7BCCl_4%7D%3D-62.3kJ%2Fmol%5C%5C%5CDelta%20G%5Eo_f_%7BCOCl_2%7D%3D-204.9kJ%2Fmol)
To calculate
for the reaction, we use the equation:
![\Delta G^o_{rxn}=\sum [n\times \Delta G_f(product)]-\sum [n\times \Delta G_f(reactant)]](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo_%7Brxn%7D%3D%5Csum%20%5Bn%5Ctimes%20%5CDelta%20G_f%28product%29%5D-%5Csum%20%5Bn%5Ctimes%20%5CDelta%20G_f%28reactant%29%5D)
For the given equation:
![\Delta G^o_{rxn}=[(2\times \Delta G^o_f_{(COCl_2)})]-[(1\times \Delta G^o_f_{(CO_2)})+(1\times \Delta G^o_f_{(CCl_4)})]](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo_%7Brxn%7D%3D%5B%282%5Ctimes%20%5CDelta%20G%5Eo_f_%7B%28COCl_2%29%7D%29%5D-%5B%281%5Ctimes%20%5CDelta%20G%5Eo_f_%7B%28CO_2%29%7D%29%2B%281%5Ctimes%20%5CDelta%20G%5Eo_f_%7B%28CCl_4%29%7D%29%5D)
Putting values in above equation, we get:
![\Delta G^o_{rxn}=[(2\times (-204.9))-((1\times (-394.4))+(1\times (-62.3)))]\\\Delta G^o_{rxn}=46.9kJ=46900J](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo_%7Brxn%7D%3D%5B%282%5Ctimes%20%28-204.9%29%29-%28%281%5Ctimes%20%28-394.4%29%29%2B%281%5Ctimes%20%28-62.3%29%29%29%5D%5C%5C%5CDelta%20G%5Eo_%7Brxn%7D%3D46.9kJ%3D46900J)
Conversion factor used = 1 kJ = 1000 J
The expression of
for the given reaction:
![K_p=\frac{(p_{COCl_2})^2}{p_{CO_2}\times p_{CCl_4}}](https://tex.z-dn.net/?f=K_p%3D%5Cfrac%7B%28p_%7BCOCl_2%7D%29%5E2%7D%7Bp_%7BCO_2%7D%5Ctimes%20p_%7BCCl_4%7D%7D)
We are given:
![p_{COCl_2}=0.735atm\\p_{CO_2}=0.140atm\\p_{CCl_4}=0.185atm](https://tex.z-dn.net/?f=p_%7BCOCl_2%7D%3D0.735atm%5C%5Cp_%7BCO_2%7D%3D0.140atm%5C%5Cp_%7BCCl_4%7D%3D0.185atm)
Putting values in above equation, we get:
![K_p=\frac{(0.735)^2}{0.410\times 0.185}\\\\K_p=20.85](https://tex.z-dn.net/?f=K_p%3D%5Cfrac%7B%280.735%29%5E2%7D%7B0.410%5Ctimes%200.185%7D%5C%5C%5C%5CK_p%3D20.85)
To calculate the gibbs free energy of the reaction, we use the equation:
![\Delta G=\Delta G^o+RT\ln K_p](https://tex.z-dn.net/?f=%5CDelta%20G%3D%5CDelta%20G%5Eo%2BRT%5Cln%20K_p)
where,
= Gibbs' free energy of the reaction = ?
= Standard gibbs' free energy change of the reaction = 46900 J
R = Gas constant = ![8.314J/K mol](https://tex.z-dn.net/?f=8.314J%2FK%20mol)
T = Temperature = ![25^oC=[25+273]K=298K](https://tex.z-dn.net/?f=25%5EoC%3D%5B25%2B273%5DK%3D298K)
= equilibrium constant in terms of partial pressure = 20.85
Putting values in above equation, we get:
![\Delta G=46900J+(8.314J/K.mol\times 298K\times \ln(20.85))\\\\\Delta G=54425.26J/mol=54.425kJ/mol](https://tex.z-dn.net/?f=%5CDelta%20G%3D46900J%2B%288.314J%2FK.mol%5Ctimes%20298K%5Ctimes%20%5Cln%2820.85%29%29%5C%5C%5C%5C%5CDelta%20G%3D54425.26J%2Fmol%3D54.425kJ%2Fmol)
Hence, the
for the reaction is 54.425 kJ/mol