El wifi en la biblioteca es muy lento.

In Spanish, common nouns almost always take an article (el, la, los, las) when you talk about them in a general, specific way.

• El wifi = the wifi (the connection in that place)
• Just wifi with no article is less common in a full sentence like this.

Compare:

• El wifi en la biblioteca es muy lento. – The wifi in the library is very slow.
• Hay wifi en la biblioteca. – There is wifi in the library.
  (Here we don’t use the article because wifi is part of an existential structure with hay.)

So in this sentence, el is normal and sounds natural.

In most of Latin America, wifi is treated as a masculine noun, so it uses el:

• el wifi rápido / el wifi lento

In some parts of Spain, people may say la wifi, treating it as feminine, but that’s much less common in Latin America.

For Latin American Spanish, using el wifi is the safest choice.

In Latin America, the most common pronunciations are:

• [WEE-fee] (like “wee-fee”) – spelled in IPA: /ˈwi.fi/
• You may also hear something close to the English sound, but /ˈwi.fi/ is very common and widely understood.

So the sentence would sound like:
el WEE-fee en la bee-blio-TEH-ca es MOY LEN-to.

Because en is the usual preposition to talk about location (in / at).

• en la biblioteca = in the library / at the library

a usually means to (direction):

• Voy a la biblioteca. – I’m going to the library.

de usually means of / from (possession/origin):

• el wifi de la biblioteca – the library’s wifi / the wifi of the library.

In your sentence you’re saying where the wifi is slow, so en is the correct preposition.

Biblioteca is a feminine noun in Spanish, so it uses the feminine article la:

• la biblioteca – the library
• las bibliotecas – the libraries

Most nouns ending in -a are feminine, and biblioteca follows this pattern.

Example:

• La biblioteca está cerrada. – The library is closed.

This is a classic “false friend”:

• biblioteca = library (you borrow books; public/college library)
• librería = bookstore (you buy books)

So:

• El wifi en la biblioteca es muy lento. – The wifi in the library is very slow.
• El wifi en la librería es muy lento. – The wifi in the bookstore is very slow.

Be careful not to confuse them.

Both are possible, but they sound a bit different:

• es muy lento (with ser) suggests you see the wifi as characteristically / generally slow there.
  → It’s just (always) slow in that place.

• está muy lento (with estar) suggests more of a current state or condition, possibly temporary.
  → It’s being very slow right now / lately.

In everyday speech, people do say both; es muy lento feels more like a general complaint about that wifi.

In Spanish:

• muy is used with adjectives and adverbs:

  • muy lento – very slow
  • muy rápido – very fast
  • muy bien – very well

• mucho is used with nouns or verbs:

  • mucho wifi – a lot of wifi (rare phrasing, but grammatically this is the pattern)
  • trabaja mucho – he/she works a lot

So with an adjective (lento), you must use muy, not mucho:

• ✅ muy lento
• ❌ mucho lento

In Spanish:

• lento is an adjective = slow

  • El wifi es lento. – The wifi is slow.

• despacio is an adverb = slowly

  • La página carga despacio. – The page loads slowly.

In your sentence you need an adjective to describe wifi (a noun), so:

• El wifi … es lento. – The wifi … is slow.

If you talk about how something happens (the action), you use despacio:

• El wifi carga las páginas muy despacio. – The wifi loads pages very slowly.

Yes, that’s very natural too, especially in Latin America:

• El wifi en la biblioteca es muy lento. – Emphasizes the wifi connection.
• El internet en la biblioteca es muy lento. – Emphasizes the internet in general there.

In Latin America el internet is common. Some places use la internet, but el internet is widely understood and safe to use.

Yes, that’s also correct:

• El wifi en la biblioteca es muy lento.
• El wifi es muy lento en la biblioteca.

Both are grammatical. The original order slightly groups wifi + en la biblioteca together, emphasizing that you’re talking specifically about the wifi in the library. The meaning is basically the same, and both versions are natural.

If you mean several distinct wifi networks, you’d usually make red (network) plural, not wifi:

• Las redes wifi en la biblioteca son muy lentas.
  – The wifi networks in the library are very slow.

In real life, many speakers keep wifi invariable (no plural ending), and change only the article and adjectives as needed.