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

Step-by-step explanation:

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

dS =
`(Q)/(T)`

`\int dS = \int (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) (dT)/(T)`

`\Delta S = C_(p) \int_{T_(1)}^{T_(2)} (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)} (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.