Concentration and number of moles confusion

Yes, if you take a sample of 25cm^3, the concentration stays constand and the no. of mol decreases. It's simple logic.

In simplistic terms, in this 250cm^3 sample, all the molecules spread out evenly. When you take 25cm^3, you will obviously decrease the no. of mol because you are taking a fraction of all the molecules within the 250cm^3 and because they are all evenly spread out, the concentration is the same.

You could think of it as there being an equal no. of molecules per cm^3. If we say that this number is 2molecules/cm^3 (extremely unrealistic, but good as an example), then in 2cm^3, for example, there'd be 4. The no. of molecules is different, but the ratio (i.e. concentration) is the same, since 2/1=4/2=6/3 etc.

And yes, you are correct in the second scenario too. When you're simply adding water, you aren't affecting the no. of mol that is in the solution, but the ratio of mol:volume (which is simply another word for concentration). Let's say you add 1 mol and fill it up to 10 cm^3. The ratio would thus be 1:10. If you add another 90cm^3 of water, the ratio would change to 1:100. However, the actual no. of mol wouldn't change.

It's the same principle as when you're drinking a cup of tea and add some sugar. If you find it to be too sweet, you pour some more tea. That way, you decrease the concentration of sugar in the glass of tea and it tastes less sweet. But of course, the sugar doesn't disappear simply because you added more tea.