Learn Hardcore German: Der Geruch in der Mülltonne ist furchtbar.

There is no fully reliable rule that tells you the gender just from the ending -uch, but many words with this ending are masculine (for example der Besuch, der Fluch, der Bruch, der Versuch).

In practice, you need to learn the noun together with its article:

der Geruch (m.)
die Mülltonne (f.)

Why is it in der Mülltonne and not in die Mülltonne?

The preposition in can take either dative or accusative, depending on the meaning:

Dative = position (where something is)
→ in der Mülltonne = in the trash can (already there, location)
Accusative = movement (where something is going to)
→ in die Mülltonne = into the trash can (movement into it)

In this sentence, the smell is already in the trash can; you are talking about a location, not movement. Therefore you use the dative:

in
- die Mülltonne (feminine, accusative) → in die Mülltonne (movement into)
in
- der Mülltonne (feminine, dative) → in der Mülltonne (location in)

Because the meaning is “the smell in the trash can is terrible,” the correct form is in der Mülltonne.

What case is der in in der Mülltonne, and how do I recognize it?

In in der Mülltonne, der is dative feminine singular.

Here is how you can tell:

Preposition
The preposition in can trigger dative (location) or accusative (movement). Here it clearly describes a location, so you know you need dative.
Noun gender
Mülltonne is feminine: die Mülltonne (nominative singular).
Feminine definite article in dative
Feminine die (nominative) becomes der in dative:
- Nominative: die Mülltonne
- Dative: der Mülltonne

So the full analysis:

in → location → dative
feminine noun → die
dative feminine singular → der

Result: in der Mülltonne.

Why is it furchtbar and not furchtbare or furchtbarer?

In this sentence, furchtbar is a predicate adjective: it comes after the verb sein (ist) and describes the subject Der Geruch.

In German, predicate adjectives (after sein, werden, bleiben, and some similar verbs) do not take any endings:

Der Geruch ist furchtbar.
Die Suppe ist kalt.
Das Auto ist neu.

Adjective endings (like -e, -er, -en, etc.) are used when the adjective comes before a noun and is part of the noun phrase:

der furchtbare Geruch = the terrible smell
ein furchtbarer Geruch = a terrible smell
dieser furchtbare Geruch = this terrible smell

But after ist, you keep the base form:

Der Geruch ist furchtbar. ✅
Der Geruch ist furchtbare. ❌

Could I also say Der Geruch in der Mülltonne riecht furchtbar? Is there any difference?

Yes, Der Geruch in der Mülltonne riecht furchtbar is correct and natural, and it is very close in meaning.

Der Geruch in der Mülltonne ist furchtbar.
→ focuses on the quality of the smell: “The smell is terrible.”
Der Geruch in der Mülltonne riecht furchtbar.
→ uses the verb riechen (to smell) and literally says: “The smell in the trash can smells terrible.”

Both are commonly used. The version with ist is a bit more neutral and descriptive; the version with riecht emphasizes the sensory experience (the act of smelling).

Why is Mülltonne one word? What does it literally mean, and what is its gender and plural?

German likes to form compound nouns by joining words together. Mülltonne is such a compound:

Müll = trash, garbage
Tonne = bin, large container (literally “barrel” or “ton” in other contexts)
Mülltonne = trash can / garbage bin

In compounds, the last part decides the gender and plural:

Head noun: Tonne (feminine)
- die Tonne → die Tonnen

So for Mülltonne:

Gender: feminine → die Mülltonne
Plural: die Mülltonnen

Examples:

Die Mülltonne ist voll. = The trash can is full.
Die Mülltonnen sind voll. = The trash cans are full.

Why are Geruch and Mülltonne capitalized?

In German, all nouns are capitalized, regardless of their position in the sentence.

In this sentence:

Geruch is a noun → capitalized
Mülltonne is a noun → capitalized

Adjectives and verbs are not capitalized unless they start the sentence or are turned into nouns:

furchtbar (adjective) → lowercase here
ist (verb) → lowercase here

So the capitalization pattern here is completely regular: every noun gets a capital letter.

What is the difference between Geruch, Gestank, and Duft? Could I use them here?

All three words are related to “smell,” but they have different connotations:

der Geruch
Neutral: “smell,” “odour.” Can be good, bad, or neutral, depending on context.
- Der Geruch des Kaffees = the smell of the coffee (pleasant)
- Der Geruch im Keller = the smell in the basement (could be neutral or bad)
der Gestank
Strongly negative: “stink,” “stinking smell.”
- Der Gestank in der Mülltonne ist furchtbar.
  → emphasizes that it really stinks.
der Duft
Positive: “fragrance,” “pleasant smell.”
- Der Duft der Blumen = the fragrance of the flowers

In your original sentence with furchtbar, both Geruch and Gestank are possible, but Gestank makes the negativity stronger:

Der Geruch in der Mülltonne ist furchtbar.
→ quite natural; context plus furchtbar tells you it’s bad.
Der Gestank in der Mülltonne ist furchtbar.
→ very clearly “The stench in the trash can is terrible.”

You would not use Duft here, because Duft implies a pleasant smell.

How would I say “The smells in the trash can are terrible” in German?

You need the plural of Geruch (Gerüche) and a plural verb:

Die Gerüche in der Mülltonne sind furchtbar.

Breakdown:

Die Gerüche = the smells (plural of der Geruch)
in der Mülltonne = in the trash can (still dative feminine singular)
sind = are (plural of ist)
furchtbar = terrible

You could also make Mülltonne plural if you mean several bins:

Die Gerüche in den Mülltonnen sind furchtbar.
(in the trash cans)

Here den Mülltonnen is dative plural (article den, noun ending -n).