Answer :
Entropy of system = -80.8 J/K
Entropy of surrounding = 253.7 J/K
Entropy of universe = 172.9 J/K
The reaction is spontaneous.
The process is a spontaneous process.
Explanation :
The given chemical reaction is:
[tex]C(graphite)+2H_2(g)\rightarrow CH_4(g)[/tex]
Entropy of reaction = [tex]\Delta S^o[/tex] = Entropy of system = -80.8 J/K
Now we have to calculate the entropy of surrounding.
Entropy of surrounding = [tex]\frac{-\Delta H^o}{T}[/tex]
Entropy of surrounding = [tex]-\frac{-75.6kJ}{298K}[/tex]
Entropy of surrounding = [tex]\frac{75.6\times 1000J}{298K}[/tex]
Entropy of surrounding = 253.7 J/K
As, we know that:
Entropy of universe = Entropy of system + Entropy of surrounding
Entropy of universe = -80.8 J/K + (253.7 J/K)
Entropy of universe = 172.9 J/K
Now we have to calculate the Gibbs free energy.
As we know that,
[tex]\Delta G^o=\Delta H^o-T\Delta S^o[/tex]
where,
[tex]\Delta G^o[/tex] = standard Gibbs free energy = ?
[tex]\Delta H^o[/tex] = standard enthalpy = -74600 J
[tex]\Delta S^o[/tex] = standard entropy = -80.8 J/K
T = temperature of reaction = 298 K
Now put all the given values in the above formula, we get:
[tex]\Delta G^o=(-74600J)-(298K\times -80.8J/K)[/tex]
[tex]\Delta G^o=-50521.6J=-50.5kJ[/tex]
For the reaction to be spontaneous, the Gibbs free energy of the reaction [tex]\Delta G[/tex] is negative or we can say that the value of
As the value of [tex]\Delta G[/tex] is less than zero that means the reaction is spontaneous.