[Rutherford]

This is about oxygen replacement. For example:
CH₃COOH+CH₃OH CH₃COOCH₃+H₂O
a) Why is the oxygen atom from the alcohol on the ester? Why didn't the previous one remain in that position?

If the ester gets hydrolised by NaOH:
CH₃COOCH₃+NaOH CH₃COONa+CH₃OH
b)Why does the oxygen atom remain now in the acid (salt)?

[Wastrel]

The first follows logically from the mechanism.  The second... looks broken.

[Rutherford]

Why is it so in the mechanism?
How do you mean broken? I found this in a problem where it was asked will the isotope of oxygen from Na¹⁸OH be in the alcohol or in the acid salt after the hydrolysis.

[easyorganic]

I usually teach acyl substitution by way of a "cheater mechanism".  While this is not the actual mechanism, it does provide an easier way for students to predict products.  You should consult your textbook for the complete actual mechanisms.

[Rutherford]

Okay, I can accept this. What about question b)?

[easyorganic]

It goes by similar mechanism.  Of course you need to consider the acid/base properties of the acidic product in a basic solution.

[fledarmus]

It goes by similar mechanism.  Of course you need to consider the acid/base properties of the acidic product in a basic solution.

Which is what Wastrel meant by "broken". This mechanism would suggest that the oxygen should remain with the methyl group in both reactions, which I believe is in fact the case, but is not what is shown in part b above.