Learn Hardcore German: Die Hausschuhe sind nass; ich stelle sie zum Trocknen auf den Balkon. - The slippers are wet; I put them on the balcony to dry.

Because auf is a two‑way preposition. Use Accusative for movement toward a place and Dative for location. With stellen you’re placing them somewhere (movement), so it’s Accusative: der Balkon → den Balkon. If you were describing location only, you’d use Dative: auf dem Balkon (e.g., Sie trocknen auf dem Balkon).

Why auf and not in the balcony?

A Balkon is a platform/surface. For platforms, surfaces, and open public places German uses auf: auf den Balkon, auf die Terrasse, auf den Marktplatz. Use in for enclosed spaces: ins Zimmer, in die Küche.

What exactly is "zum Trocknen," and why is "Trocknen" capitalized?

zum = zu dem. Trocknen is the verb infinitive turned into a noun (a nominalized infinitive), so it’s capitalized: das Trocknen. The preposition zu takes Dative, hence zu dem → zum. The phrase expresses purpose: “for drying.”

Can I say "um sie zu trocknen" instead of "zum Trocknen"?

Yes. Both express purpose.

zum Trocknen is compact and very common for everyday purposes.
um sie zu trocknen is a purpose clause; it must share the subject with the main clause (here it does). It can sound a bit more deliberate/explicit. Both are idiomatic.

Why use "stellen" and not "legen" or "setzen"?

German links placement verbs to the resulting position:

stellen → causes something to stehen (stand, upright/on its base).
legen → causes something to liegen (lying on its side/flat).
setzen → causes someone/something to sitzen (mainly for people/animals). Shoes placed on their soles “stehen,” so you stellst them. If you put them on their side, you could say ich lege sie hin.

Is "rausstellen" also possible?

Yes: Ich stelle sie zum Trocknen raus. That’s colloquial but very common. More formal is hinausstellen. You can also be specific: Ich stelle sie auf den Balkon or combine: Ich stelle sie raus auf den Balkon (a bit redundant but not wrong).

Is the order "zum Trocknen auf den Balkon" important?

It’s natural because of the Te‑Ka‑Mo‑Lo tendency (Time–Cause–Manner–Place). zum Trocknen (purpose/cause) before auf den Balkon (place) fits this. You can also say Ich stelle sie auf den Balkon zum Trocknen; both are correct.

Where should the pronoun "sie" go?

Object pronouns typically come early, before heavier adverbial phrases: Ich stelle sie zum Trocknen auf den Balkon. Ich stelle zum Trocknen sie … sounds wrong.

What does "sie" refer to here? Could it be the formal "Sie"?

Here sie is the Accusative plural “them,” referring to die Hausschuhe. It’s lowercase, so it’s not the formal Sie (You). The subject Die Hausschuhe sind nass also signals plurality.

Why is there a semicolon? Could I use a comma or a period instead?

The semicolon separates two closely related main clauses. In German you may also use a comma or a period:

Die Hausschuhe sind nass, ich stelle sie … (comma between main clauses is allowed)
Die Hausschuhe sind nass. Ich stelle sie … (two sentences) Semicolons are stylistic and a bit formal.

Do I need a comma before "zum Trocknen"?

No. zum Trocknen is a prepositional phrase, not a clause. No comma is used unless you insert a parenthetical element.

Why isn’t it “nassen” — why just “nass”?

After sein, adjectives are predicative and take no endings: Die Hausschuhe sind nass. With an attributive adjective, you add an ending: die nassen Hausschuhe.

What’s the singular of "Hausschuhe," and are there any case quirks?

Singular: der Hausschuh. Plural: die Hausschuhe. Dative plural takes -n: mit den Hausschuhen. The article die signals plural here; it’s the same form as feminine singular, but the verb sind makes the plural clear.

Can I say "aufs Balkon"?

No. aufs = auf das and is only used with neuter nouns. Balkon is masculine (der Balkon), so you need auf den Balkon. You can say aufs Sofa (das Sofa), but not aufs Balkon.

Could I use the future tense: "Ich werde sie … stellen"?

You could, but it’s unnecessary. German often uses the present for near‑future plans: Ich stelle sie … comfortably means you’re about to do it.

Is "zur Trocknung" or "zum Austrocknen" possible?

Both exist but have different tones:

zur Trocknung sounds technical/formal.
zum Austrocknen suggests drying out completely and can sound stronger. For everyday speech, zum Trocknen is the most natural.