На кухне стоит большое мусорное ведро для общих отходов.

Кухне is in the prepositional case (also called locative), used to show location after certain prepositions, including на and в.

• Dictionary form: кухня (nominative, “kitchen”)
• Prepositional singular: кухне → used after на when it means “on / in (a surface/area)”.

So:

• кухня – subject form:
  Кухня маленькая. – The kitchen is small.
• на кухне – “in the kitchen”:
  Мы сидим на кухне. – We are sitting in the kitchen.

You cannot say на кухня for location; the case must change to кухне.

For many places, Russian uses a fixed preposition, and you just have to learn it:

• на кухне = in the kitchen (standard, natural)
• в кухне is almost never used and would sound strange in this sense.

General tendency:

• на is used for:
  • open areas: на улице (in the street), на площади (on the square)
  • many locations seen as functional spaces: на работе (at work), на почте (at the post office), на кухне (in the kitchen)
• в is used for:
  • enclosed spaces: в комнате (in the room), в доме (in the house)

Even though a kitchen is a room, Russian treats it more as a functional space (“the place where you cook”), so the fixed phrase is на кухне.

Стоит is 3rd person singular of стоять – “to stand”. Russian often uses стоять for objects that are upright or just positioned somewhere:

• На столе стоит ваза. – There is a vase on the table (literally “A vase stands on the table.”)
• В углу стоит шкаф. – There is a wardrobe in the corner.

In your sentence, стоит conveys “is located / is placed (upright)”. Alternatives:

• На кухне есть большое мусорное ведро…
  Grammatically correct, but more neutral, just “there is”.
• На кухне находится большое мусорное ведро…
  Also correct, more formal or bookish.

Стоит is the most natural choice here, because a bucket is an upright object that “stands” somewhere.

Yes, стоит agrees with ведро, which is:

• ведро – neuter, singular
• Verb form: он/она/оно стоит – “he/she/it stands”

So:

• На кухне стоит большое мусорное ведро.
  One bucket → стоит (singular)

If you had more than one bucket:

• На кухне стоят большие мусорные ведра.
  Many buckets → стоят (plural)

Russian word order is flexible, but it affects emphasis.

Your original sentence:

• На кухне стоит большое мусорное ведро для общих отходов.
  Emphasis: “In the kitchen, there is a big trash bin for general waste.”

Possible variants:

1. Большое мусорное ведро для общих отходов стоит на кухне.
   Neutral, maybe slightly emphasizing the bin and its purpose.

2. На кухне большое мусорное ведро для общих отходов стоит.
   Grammatically okay, but feels unusual; the стоит is oddly delayed.

Your suggested:

• Большое мусорное ведро стоит на кухне для общих отходов.
  Grammatically possible, but для общих отходов sounds slightly detached, as if “the kitchen is for general waste”. Native speakers usually keep для общих отходов right after ведро, so it clearly belongs to the bucket.

Most natural patterns:

• На кухне стоит большое мусорное ведро для общих отходов.
• Большое мусорное ведро для общих отходов стоит на кухне.

Adjectives in Russian must agree with the noun in:

• gender
• number
• case

Ведро is:

• neuter
• singular
• nominative (it’s the subject with стоит)

Neuter singular nominative adjectives take -ое:

• большое (from большой)
• мусорное (from мусорный)

So we get:

• большое мусорное ведро

Compare:

• большой стол (masc. sg. nom.)
• большая комната (fem. sg. nom.)
• большие ведра (plural)

Both are correct and common:

• мусорное ведро – literally “trash-y bucket”, i.e. trash bin / trash can.
  This is a compound noun phrase (adjective + noun).

• ведро для мусора – “bucket for trash”.
  This uses a prepositional phrase with для.

Nuances:

• мусорное ведро sounds a bit more compact and “default”, like the normal word you’d use in everyday speech.
• ведро для мусора can emphasize the purpose more clearly (“a bucket that is used for trash, not for something else”).

In most neutral contexts, мусорное ведро is the go‑to phrase.

The preposition для (“for”) always requires the genitive case.

• отходы – “waste” (plural nominative)
• Genitive plural: отходов

So, after для:

• для отходов – “for waste”

Общий is an adjective meaning “common, general”. It must agree with отходов:

• masculine / neuter plural genitive adjective ending: -их
• → общих отходов

So:

• для общих отходов = “for general waste”
  (genitive plural after для)

You can say для мусора; it’s very common and completely natural:

• мусорное ведро для мусора – “a trash bin for trash”

Для общих отходов is more specific:

• мусор – general word: trash / garbage
• отходы – “waste”, often used in more formal, technical, or sorting contexts (household waste, industrial waste, etc.).
• общие отходы – “general waste” (not separated into recycling, bio, etc.), as opposed to пищевые отходы (food waste), пластиковые отходы (plastic waste), etc.

So для общих отходов sounds a bit more formal/technical, like a label in a sorting system, while для мусора is simpler everyday speech.

Both can be translated as “waste / trash”, but:

• мусор

  • Everyday word: trash, rubbish, garbage.
  • Used in daily situations: выбросить мусор (take out the trash).

• отходы

  • More formal/technical: “waste, residues, by-products”.
  • Often used with a qualifier:
    • бытовые отходы – household waste
    • пищевые отходы – food waste
    • промышленные отходы – industrial waste

In your sentence, общие отходы suggests “general (unsorted) waste”, not separated into types.

Approximate transcription with stress marked by ´:

• На к´ухне стоит больш´ое м´усорное ведр´о для ´общих отх´одов.

Syllable-by-syllable:

• На – na
• к´ух-не – KOOH-kne (stress on кух-)
• сто-´ит – sta-EET (stress on -ит)
• боль-ш´о-е – bal’-SHO-ye (stress on шо)
• м´у-сор-но-е – MOO-sar-na-ye (stress on му)
• ведр´о – ve-dRO (stress on дро)
• для – dlya (one syllable, [dlʲa])
• ´об-ших – OB-shikh (stress on об)
• от-х´о-дов – at-KHO-daf (stress on хо; final в often sounds like ф)

Natural speech will link words smoothly, without strong pauses inside the phrase.