doseogwane ganeun gime pyeonuijeomedo deulleulgeyo.

-는 김에 means something like while I’m at it, since I’m doing that anyway, or taking that opportunity to also do X.

So 도서관에 가는 김에 means:

• since I’m going to the library anyway
• while I’m on the way to go to the library
• while I’m at it, as I go to the library

The important nuance is that the first action creates a convenient chance to do the second action.

Because 김에 is used with a verb in a modifier form.

Here, 가다 becomes 가는 to modify 김:

• 가다 = to go
• 가는 = going / that is going
• 가는 김에 = on the occasion of going / since one is going

This is just how the grammar pattern works. You can think of 김에 as needing a phrase before it that describes the action serving as the opportunity.

Because 가다 uses 에 for the destination.

• 도서관에 가다 = to go to the library

By contrast, 에서 usually marks the place where an action happens:

• 도서관에서 공부하다 = to study at the library

So in this sentence, the speaker is moving toward the library, so 에 is the correct particle.

편의점에도 is made of:

• 편의점 = convenience store
• 에 = to / at
• 도 = also, too

So 편의점에도 means to the convenience store too or at the convenience store too, depending on the verb.

In this sentence, because the verb is 들르다 (to stop by), it means:

• I’ll stop by the convenience store too

The 도 shows that this is an additional place, besides the library.

Not exactly. 들르다 means to stop by, to drop in, or to make a brief visit.

That is different from plain 가다 (to go).

So:

• 도서관에 가다 = to go to the library
• 편의점에 들르다 = to stop by the convenience store

Using 들르다 suggests the convenience store is not the main destination; it is an extra stop.

The dictionary form is 들르다.

When you attach -ㄹ게요, it becomes 들를게요.

So:

• 들르다 = to stop by
• 들를게요 = I’ll stop by

This can feel tricky because verbs ending in 르 often change a little when endings are added. For a learner, the main thing to remember is that the natural form here is 들를게요.

-ㄹ게요 often expresses the speaker’s intention, decision, or promise, usually with some awareness of the listener.

So 들를게요 feels like:

• I’ll stop by
• I’ll go ahead and stop by

It is often more natural in conversation than a plain future form when you are telling someone what you are going to do.

Compare:

• 들를게요 = I’ll stop by.
  → sounds like a decision or promise to the listener
• 들을 거예요 = I’m going to stop by / I will stop by
  → a more neutral future statement

The subject is understood as I.

Korean often leaves out subjects when they are clear from context. In this sentence, -ㄹ게요 strongly suggests the speaker is talking about their own action, so 저는 does not need to be said.

So the full idea is:

• (저는) 도서관에 가는 김에 편의점에도 들를게요.
• (I) will stop by the convenience store too since I’m going to the library anyway.

Not necessarily.

김에 is about taking the opportunity to do something extra because you are already doing something else. It does not always mean the second place is literally on the route.

So this sentence can mean:

• the convenience store is on the way, or
• the speaker is already going out to the library, so they may as well stop by the convenience store too

The emphasis is more on since I’m going anyway than on exact geography.

This is a very common question.

• 가는 길에 = on the way
• 가는 김에 = while I’m at it / since I’m going anyway

So:

• 도서관에 가는 길에 편의점에 들를게요
  = I’ll stop by the convenience store on the way to the library.

• 도서관에 가는 김에 편의점에도 들를게요
  = Since I’m going to the library anyway, I’ll stop by the convenience store too.

길에 focuses more on the route or timing.
김에 focuses more on using one action as an opportunity to do another.

Yes, Korean word order is somewhat flexible, especially as long as the particles stay attached to the right words.

The given sentence is very natural:

• 도서관에 가는 김에 편의점에도 들를게요.

You might also hear slight variations for emphasis, but the original order is clear and standard because it presents:

1. the main circumstance: since I’m going to the library
2. the extra action: I’ll also stop by the convenience store

So for a learner, the original sentence is a good model to copy.