Use of definite article

Question

I know this keeps coming up, but in the examples we see: “las llaves de la casa”, and “la reserva de hotel”. Both these expressions follow the structure of NOUN + DE + NOUN. Why do we only use “la” for the first one?

Accepted Answer

Hola Marcos
Both examples could be using the article or not, it doesn't have a specific nuance if you use it or drop it.
If you say: 
Vosotros no encontráis las llaves de casa
they would be still referring to their house keys.The use of the article in "de la casa", however, is a bit more open to two interpretations:1. it could be referring to a specific house they have in mind (they identify in their mind), a house they all know and it's not their own house2. it could be referring to their own house because this group of words/ phrase is common when talking about your house
In:
Ellos no encuentran la reserva de hotel.
they would be referring to the same hotel reservation whether they use the article or omit it. But there are two ways to see this phrase:
1. la reserva de hotel (without the article) is a phrase that refers to a hotel reservation used as a "generic concept", the same way we say for example: un vaso de agua, una lámpara de techo, una mesita de noche... - it's using the preposition "de" with another noun in a descriptive way. 
2. la reserva del hotel (with the article "del") would have been the choice if they are thinking more specifically about the reservation of that specific hotel they booked. They identify in their minds the actual hotel they are going to. 
As usual, the use or omission of the definite article is a tricky one, something that we drop or use depending on the perspective of the speaker, often being related to being more generic or more specific. 
Saludos
Inma

Answer

So it all comes back to what the speaker wants to emphasize. Come to think of it, we do the same in English. We could say “Do you have the hotel reservation?” or “Do you have the reservation for the hotel?” Each has a slightly different nuance.