Answer : The values of
are
respectively.
Explanation :
The given balanced chemical reaction is,
![2Ag_2O(s)\rightarrow 4Ag(s)+O_2(g)](https://tex.z-dn.net/?f=2Ag_2O%28s%29%5Crightarrow%204Ag%28s%29%2BO_2%28g%29)
First we have to calculate the enthalpy of reaction
.
![\Delta H^o=H_f_{product}-H_f_{product}](https://tex.z-dn.net/?f=%5CDelta%20H%5Eo%3DH_f_%7Bproduct%7D-H_f_%7Bproduct%7D)
![\Delta H^o=[n_{Ag}\times \Delta H_f^0_{(Ag)}+n_{O_2}\times \Delta H_f^0_{(O_2)}]-[n_{Ag_2O}\times \Delta H_f^0_{(Ag_2O)}]](https://tex.z-dn.net/?f=%5CDelta%20H%5Eo%3D%5Bn_%7BAg%7D%5Ctimes%20%5CDelta%20H_f%5E0_%7B%28Ag%29%7D%2Bn_%7BO_2%7D%5Ctimes%20%5CDelta%20H_f%5E0_%7B%28O_2%29%7D%5D-%5Bn_%7BAg_2O%7D%5Ctimes%20%5CDelta%20H_f%5E0_%7B%28Ag_2O%29%7D%5D)
where,
= enthalpy of reaction = ?
n = number of moles
= standard enthalpy of formation
Now put all the given values in this expression, we get:
![\Delta H^o=[4mole\times (0kJ/mol)+1mole\times (0kJ/mol)}]-[2mole\times (-31.1kJ/mol)]](https://tex.z-dn.net/?f=%5CDelta%20H%5Eo%3D%5B4mole%5Ctimes%20%280kJ%2Fmol%29%2B1mole%5Ctimes%20%280kJ%2Fmol%29%7D%5D-%5B2mole%5Ctimes%20%28-31.1kJ%2Fmol%29%5D)
![\Delta H^o=62.2kJ=62200J](https://tex.z-dn.net/?f=%5CDelta%20H%5Eo%3D62.2kJ%3D62200J)
conversion used : (1 kJ = 1000 J)
Now we have to calculate the entropy of reaction
.
![\Delta S^o=S_f_{product}-S_f_{product}](https://tex.z-dn.net/?f=%5CDelta%20S%5Eo%3DS_f_%7Bproduct%7D-S_f_%7Bproduct%7D)
![\Delta S^o=[n_{Ag}\times \Delta S_f^0_{(Ag)}+n_{O_2}\times \Delta S_f^0_{(O_2)}]-[n_{Ag_2O}\times \Delta S_f^0_{(Ag_2O)}]](https://tex.z-dn.net/?f=%5CDelta%20S%5Eo%3D%5Bn_%7BAg%7D%5Ctimes%20%5CDelta%20S_f%5E0_%7B%28Ag%29%7D%2Bn_%7BO_2%7D%5Ctimes%20%5CDelta%20S_f%5E0_%7B%28O_2%29%7D%5D-%5Bn_%7BAg_2O%7D%5Ctimes%20%5CDelta%20S_f%5E0_%7B%28Ag_2O%29%7D%5D)
where,
= entropy of reaction = ?
n = number of moles
= standard entropy of formation
Now put all the given values in this expression, we get:
![\Delta S^o=[4mole\times (42.55J/K.mole)+1mole\times (205.07J/K.mole)}]-[2mole\times (121.3J/K.mole)]](https://tex.z-dn.net/?f=%5CDelta%20S%5Eo%3D%5B4mole%5Ctimes%20%2842.55J%2FK.mole%29%2B1mole%5Ctimes%20%28205.07J%2FK.mole%29%7D%5D-%5B2mole%5Ctimes%20%28121.3J%2FK.mole%29%5D)
![\Delta S^o=132.67J/K](https://tex.z-dn.net/?f=%5CDelta%20S%5Eo%3D132.67J%2FK)
Now we have to calculate the Gibbs free energy of reaction
.
As we know that,
![\Delta G^o=\Delta H^o-T\Delta S^o](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D%5CDelta%20H%5Eo-T%5CDelta%20S%5Eo)
At room temperature, the temperature is 298 K.
![\Delta G^o=(62200J)-(298K\times 132.67J/K)](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D%2862200J%29-%28298K%5Ctimes%20132.67J%2FK%29)
![\Delta G^o=22664.34J=22.66kJ](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D22664.34J%3D22.66kJ)
Therefore, the values of
are
respectively.