i byeongeun jaehwaryongi dwaeyo.

Yes, here 병 means bottle. Korean has many homonyms, and 병 is one of them. It can mean:

• bottle
• illness/disease

The context makes the meaning clear. Since the sentence is about recycling, bottle is the natural interpretation.

은 is the topic particle. It marks 이 병 as the thing the sentence is talking about.

So 이 병은 has the feeling of:

• as for this bottle
• this bottle, ...

This is very common in Korean. It does not always need to sound contrastive in English, but it can sometimes suggest a slight contrast, like this bottle, at least, can be recycled.

They look the same, but they do different jobs:

• 이 병은: here 이 means this
• 재활용이 돼요: here 이 is a particle

So the first 이 is a demonstrative adjective, while the second 이 is grammatical marking attached to 재활용.

재활용 is a noun meaning recycling.
되다 often means to become, to work, or to be possible.

So 재활용이 되다 literally has a sense like:

• recycling becomes possible
• it works for recycling
• it qualifies for recycling

In natural English, this is usually translated as:

• can be recycled
• is recyclable

Because this sentence is not phrased as an action that someone performs on the bottle.

Compare these:

• 이 병은 재활용이 돼요
  = This bottle can be recycled / is recyclable

• 이 병을 재활용해요
  = Someone recycles this bottle

In the second sentence, 병을 is the object of the action 재활용해요.
In your sentence, the bottle is being described, not acted on directly.

The dictionary form is 되다.

The polite present form is originally 되어요, and that contracts to 돼요.

So:

• 되다 → dictionary form
• 되어요 → full polite form
• 돼요 → contracted polite form, and the one most people normally use

Not exactly in the same way English uses a passive like is recycled.

Korean often uses 되다 to express ideas such as:

• something becomes possible
• something works
• something gets done
• something ends up in a certain state

So 재활용이 돼요 feels passive-like in English, but grammatically it is the very common Korean pattern noun + 이/가 + 되다.

Yes, absolutely. That is correct and natural.

The difference is mainly in style and nuance:

• 이 병은 재활용이 돼요
  = very natural in everyday speech, signs, notices, product labels

• 이 병은 재활용할 수 있어요
  = more explicit about ability/possibility

Both are good. The sentence you gave is especially common in practical contexts like sorting trash or talking about packaging.

Usually it means it can be recycled or it is recyclable.

In real-life contexts such as:

• recycling instructions
• packaging labels
• sorting rules

the sentence normally describes the bottle’s recyclability, not a guaranteed future action.

So the most natural understanding is:

• This bottle is recyclable

Because the correct form comes from 되어요, which contracts to 돼요.

So:

• 되어요 → 돼요 ✅
• 되요 ❌ standard spelling

Many learners confuse these because the pronunciation can sound similar, but standard Korean spelling is 돼요.

It is usually pronounced roughly like dwae-yo.

In actual speech, depending on speaker and speed, it may sound a bit closer to dwe-yo, but the standard spelling remains 돼요.

For a learner, dwae-yo is a good approximation.

Yes, you may also see 재활용돼요.

There are two related ways to think about it:

• 재활용이 돼요: noun + particle + 되다
• 재활용돼요: a combined verb form from 재활용되다

Both are understandable and natural. The version in your sentence, 재활용이 돼요, is very common in everyday Korean.