Entropy change in mixing a gas at constant temperature and pressure
The reference you gave involves mixing two different chemical species together at constant temperature and pressure.  The problem you seem to be solving is mixing the same chemical species with itself at constant temperature and pressure.  For that process, the change in entropy is zero.  If you really intended to determine the entropy of mixing two different chemical species, then the path you identified is not a reversible path for transitioning between the initial and final states of the system.