Respuesta :
Answer: The value of [tex]\Delta G^o[/tex] of the reaction is 28.38 kJ/mol
Explanation:
For the given chemical reaction:
[tex]SO_2(g)+Cl_2(g)\rightarrow SO_2Cl_2(g)[/tex]
- The equation used to calculate enthalpy change is of a reaction is:
[tex]\Delta H^o_{rxn}=\sum [n\times \Delta H^o_f_{(product)}]-\sum [n\times \Delta H^o_f_{(reactant)}][/tex]
The equation for the enthalpy change of the above reaction is:
[tex]\Delta H^o_{rxn}=[(1\times \Delta H^o_f_{(SO_2Cl_2(g))})]-[(1\times \Delta H^o_f_{(SO_2(g))})+(1\times \Delta H^o_f_{(Cl_2(g))})][/tex]
We are given:
[tex]\Delta H^o_f_{(SO_2Cl_2(g))}=-364kJ/mol\\\Delta H^o_f_{(SO_2(g))}=-296.8kJ/mol\\\Delta H^o_f_{(Cl_2(g))}=0kJ/mol[/tex]
Putting values in above equation, we get:
[tex]\Delta H^o_{rxn}=[(1\times (-364))]-[(1\times (-296.8))+(1\times 0)]=-67.2kJ/mol=-67200J/mol[/tex]
- The equation used to calculate entropy change is of a reaction is:
[tex]\Delta S^o_{rxn}=\sum [n\times \Delta S^o_f_{(product)}]-\sum [n\times \Delta S^o_f_{(reactant)}][/tex]
The equation for the entropy change of the above reaction is:
[tex]\Delta S^o_{rxn}=[(1\times \Delta S^o_{(SO_2Cl_2(g))})]-[(1\times \Delta S^o_{(SO_2(g))})+(1\times \Delta S^o_{(Cl_2(g))})][/tex]
We are given:
[tex]\Delta S^o_{(SO_2Cl_2(g))}=311.9J/Kmol\\\Delta S^o_{(SO_2(g))}=248.2J/Kmol\\\Delta S^o_{(Cl_2(g))}=223.0J/Kmol[/tex]
Putting values in above equation, we get:
[tex]\Delta S^o_{rxn}=[(1\times 311.9)]-[(1\times 248.2)+(1\times 223.0)]=-159.3J/Kmol[/tex]
To calculate the standard Gibbs's free energy of the reaction, we use the equation:
[tex]\Delta G^o_{rxn}=\Delta H^o_{rxn}-T\Delta S^o_{rxn}[/tex]
where,
[tex]\Delta H^o_{rxn}[/tex] = standard enthalpy change of the reaction =-67200 J/mol
[tex]\Delta S^o_{rxn}[/tex] = standard entropy change of the reaction =-159.3 J/Kmol
Temperature of the reaction = 600 K
Putting values in above equation, we get:
[tex]\Delta G^o_{rxn}=-67200-(600\times (-159.3))\\\\\Delta G^o_{rxn}=28380J/mol=28.38kJ/mol[/tex]
Hence, the value of [tex]\Delta G^o[/tex] of the reaction is 28.38 kJ/mol
