Eu vou aproveitar a tarde para estudar português na biblioteca.

Vou + infinitive is a very common way to talk about the near future in Brazilian Portuguese.

• Eu vou aproveitar... = I’m going to make the most of / use...
• A one-word future like aproveitarei is also correct, but it sounds more formal or literary in many situations.

So in everyday Brazilian Portuguese, vou aproveitar is usually the more natural choice.

Examples:

• Vou estudar mais amanhã.
• Estudarei mais amanhã.
  Both are correct, but the first is more common in speech.

Not always. Portuguese often allows the subject pronoun to be omitted because the verb form already shows who is doing the action.

So both are possible:

• Eu vou aproveitar a tarde...
• Vou aproveitar a tarde...

Including eu can add:

• clarity
• emphasis
• contrast

For example:

• Eu vou aproveitar a tarde, mas ele vai descansar.

In your sentence, eu is perfectly natural, but it is not required.

Here, aproveitar means something like:

• to make good use of
• to make the most of
• to take advantage of in a positive sense

So aproveitar a tarde means using the afternoon well, not wasting it.

This verb can have different meanings depending on context:

• Aproveitar o tempo = make good use of time
• Aproveitar a promoção = take advantage of a sale
• Aproveitar a viagem = enjoy / make the most of the trip

So it is a flexible and very common verb.

This is a very important distinction.

• a tarde = the afternoon as a direct object
• à tarde = in the afternoon as a time expression

In your sentence:

• aproveitar a tarde = make the most of the afternoon

Here, a tarde is the thing being used well, so there is no crasis (à).

Compare:

• Eu vou aproveitar a tarde para estudar.
  = I’m going to make good use of the afternoon to study.

• Eu estudo português à tarde.
  = I study Portuguese in the afternoon.

So the accent in à changes the function completely.

Para + infinitive is used to show purpose.

So:

• para estudar português = in order to study Portuguese

It answers the question why?

• Why will I make the most of the afternoon?
• To study Portuguese.

This structure is extremely common in Portuguese:

• Vou ao mercado para comprar frutas.
• Saí cedo para evitar trânsito.

In informal Brazilian Portuguese, you will also often hear:

• pra estudar português

That is just a spoken/written informal version of para.

After verbs like estudar, falar, aprender, and ensinar, languages are often used without an article.

So the normal form is:

• estudar português
• falar inglês
• aprender espanhol

Using an article is possible in some contexts, but it usually sounds more specific or marked:

• estudar o português do Brasil
• o português que eles falam em Portugal

In your sentence, estudar português is the most natural general form.

In Portuguese, names of languages are normally not capitalized.

So:

• português
• inglês
• espanhol

This is different from English, where you write Portuguese, English, Spanish with capital letters.

The accent in português is required in standard spelling:

• português

It shows the stressed syllable and is part of the correct written form. Without the accent, the spelling is wrong.

The stress falls on the last syllable:

• por-tu-guês

Na is a contraction:

• em + a = na

So:

• na biblioteca = in the library

This happens because biblioteca is feminine singular, and Portuguese commonly uses the definite article with many places.

Related forms:

• no = em + o
• na = em + a
• nos = em + os
• nas = em + as

Examples:

• no mercado
• na escola
• nos Estados Unidos
• nas férias

If you wanted to say in a library instead of in the library, you could say:

• numa biblioteca = em + uma

Yes, to some extent. Portuguese word order is flexible, though some versions sound more natural than others.

Your sentence is very natural:

• Eu vou aproveitar a tarde para estudar português na biblioteca.

You could also say:

• Vou aproveitar a tarde para estudar português na biblioteca.
• Na biblioteca, eu vou aproveitar a tarde para estudar português.

That last version puts extra emphasis on the location.

But not every change sounds equally good. Portuguese usually keeps a fairly clear order:

1. subject
2. verb
3. object
4. purpose
5. location

So your original sentence is a strong, natural model to follow.

Yes, the sentence is natural and correct.

In more casual speech, a Brazilian might make small changes such as:

• dropping eu
• using pra instead of para

For example:

• Vou aproveitar a tarde pra estudar português na biblioteca.

This is very common in conversation.

So:

• Eu vou aproveitar a tarde para estudar português na biblioteca. = correct, neutral, slightly more careful
• Vou aproveitar a tarde pra estudar português na biblioteca. = very natural, everyday spoken Brazilian Portuguese