Given the values of ΔH∘rxn, ΔS∘rxn, and T below, determine ΔSuniv and whether they are spontaneous or nonspontaneous:
A. ΔH∘rxn= 80 kJ , ΔSrxn= 143 J/K , T= 290 K
B. ΔH∘rxn= 80 kJ , ΔSrxn= 143 J/K , T= 764 K
C. ΔH∘rxn= 80 kJ , ΔSrxn=− 143 J/K , T= 290 K
D. ΔH∘rxn=− 80 kJ , ΔSrxn= 143 J/K , T= 396 K
Formulae and statment:
ΔSrxn = ΔSsystem.
ΔSsurrounding = -ΔH∘rxn /T
And,
ΔSuniverse = ΔSsystem + ΔSsurrounding.
For spontaneous reaction,
ΔSuniverse > 0 i.e. +ve
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Based on above formulae:
A) Given, ΔH∘rxn = 80 kJ = 80000 J , ΔSrxn= 143 J/K , T= 290 K
ΔSrxn= ΔSsystem = 143 J/K
ΔSsurrounding = -ΔH∘rxn/T = -80000/290 = -275.9
ΔSuniverse = ΔSsystem + ΔSsurrounding
ΔSuniverse = (143) + (-275.9)
ΔSuniverse = - 132.9 J/K
ΔSuniverse < 0 i.e. –ve
Hence reaction is non-spontaneous.
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B)Given, ΔH∘rxn= 80 kJ = 80000 J , ΔSrxn= 143 J/K , T= 764 K
ΔSrxn= ΔSsystem = 143 J/K
ΔSsurrounding = -ΔH∘rxn/T = -80000/764 = -104.7
ΔSuniverse = ΔSsystem + ΔSsurrounding
ΔSuniverse = (143) + (-104.7)
ΔSuniverse = +38.3 J/K
ΔSuniverse > 0 i.e. +ve
Hence reaction is spontaneous.
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C) Given, ΔH∘rxn= 80 kJ = 80000 J , ΔSrxn=− 143 J/K , T= 290 K
ΔSrxn= ΔSsystem = -143 J/K
ΔSsurrounding = -ΔH∘rxn/T = -80000/290 = -275.9 J/K
ΔSuniverse = ΔSsystem + ΔSsurrounding
ΔSuniverse = (-143) + (-275.9)
ΔSuniverse = -418.9 J/K
ΔSuniverse < 0 i.e. -ve
Hence reaction is non-spontaneous.
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Given, ΔH∘rxn=− 80 kJ = -80000 J, ΔSrxn= 143 J/K , T= 396 K
ΔSrxn= ΔSsystem = 143 J/K
ΔSsurrounding = -ΔH∘rxn/T = -(- 80000)/396 = 80000/396 = 202.2 J/K
ΔSuniverse = ΔSsystem + ΔSsurrounding
ΔSuniverse = (143) + (202.2)
ΔSuniverse = +345.2 J/K
ΔSuniverse > 0 i.e. +ve
Hence reaction is spontaneous.
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