They received a final demand for payment.
The goverment is unlikely to agree to the rebel’s demands for independence.
These sentences are from cambridge dictionary. In the second sentence, there is the definite article but could I use the zero article? I cant see any difference between these two sentences, but one is using the definite article and one not. Why?
StoneyB is right about the the in your second example — it refers to the rebel. But you could take out "rebel's" and have the example you are trying to ask about: "The government is unlikely to agree to the demands for independence."
In one sense, the distinction between a and the here is just the normal one — if you said the government was unlikely to agree to a demand for independence, it would mean that no such demand had been given. But saying the demand(s) means that demands have been given. A is indefinite, and the is definite.
But in the first example, there's a bit more nuance. If you change it to "They received the final demand for payment," it would indicate that the demand was expected, even before it was given. Wording it this way indicates that the demand might have been a surprise, or at least that they weren't counting on receiving it.
