Note as well that the mass dependence in that equation for the entropy is just an additive term. The absolute value of the entropy may be different but the change in entropy is the same when you heat a 1l container of helium or neon or a mixture of them from 300K to 301K. That's 0.0406 moles of gas. The heat flow is 0.506 joules. The change in entropy is approximately 0.0017 J/K.
> And a gas mix is not an ideal monatomic gas; its entropy increases at the same temperature and volume compared to an equal volume divided between the two gases.
A mix of ideal gases is an ideal gas and its heat capacity is the weighted average of the heat capacities (trivially equal to the heat capacity of the components when it's the same). The change of entropy when you heat one, or the other, or the mix, will be the same (because you're calculating exactly the same integral of the same heat flow).
The difference in absolute value is irrelevant when we are discussing changes in entropy and measurements of the amount of heat needed to increase the temperature and whether you "will get a value that will be different for a gas made up of only argon versus one that contains both neon and argon".