Question

Estimate the increase in the molar entropy of O2(g) when the temperature is increased at constant pressure from 298 K to 348 K, given that the molar constant-pressure heat capacity of O2 is 29.355 J K−1 mol−1 at 298 K.

Answer 1

Explanation:

It is known that relation between entropy, heat energy and temperature is as follows.

        dS = $\frac{Q}{T}$

        $\int dS = \int \frac{Q}{T}$

Also we know that at constant pressure, Q = $\Delta H = C_{p} - dT$

     $\int_{S_{1}}^{S_{2}} dS = \int_{T_{1}}^{T_{2}} C_{p} \frac{dT}{T}$

     $\Delta S = C_{p} \int_{T_{1}}^{T_{2}} \frac{dT}{T}$

As the given data is as follows.

        $T_{1}$ = 298 K,          $T_{2}$ = 348 K

         $C_{p}$ = 29.355 J/K mol

Now, putting the given values into the above formula as follows.

          $\Delta S = C_{p} ln {T_{1}}^{T_{2}} \frac{dT}{T}$

                  = $29.355 [ln (348) - ln (298)]$

                  = $29.355 [5.85 - 5.69]$

                  = 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.