Explanation:
It is known that relation between entropy, heat energy and temperature is as follows.
dS = [tex]\frac{Q}{T}[/tex]
[tex]\int dS = \int \frac{Q}{T}[/tex]
Also we know that at constant pressure, Q = [tex]\Delta H = C_{p} - dT[/tex]
[tex]\int_{S_{1}}^{S_{2}} dS = \int_{T_{1}}^{T_{2}} C_{p} \frac{dT}{T}[/tex]
[tex]\Delta S = C_{p} \int_{T_{1}}^{T_{2}} \frac{dT}{T}[/tex]
As the given data is as follows.
[tex]T_{1}[/tex] = 298 K, [tex]T_{2}[/tex] = 348 K
[tex]C_{p}[/tex] = 29.355 J/K mol
Now, putting the given values into the above formula as follows.
[tex]\Delta S = C_{p} ln {T_{1}}^{T_{2}} \frac{dT}{T}[/tex]
= [tex]29.355 [ln (348) - ln (298)][/tex]
= [tex]29.355 [5.85 - 5.69][/tex]
= 4.48 J/k mol
Thus, we can conclude that the increase in the molar entropy of given oxygen gas is 4.48 J/k mol.
