Während der Ruhezeit gasen die Kaffeebohnen aus.

Because während is a preposition here, and it normally takes the genitive case in standard German.

• die Ruhezeit = the resting period
• während der Ruhezeit = during the resting period

For a feminine noun like die Ruhezeit, the genitive article is der, so:

• nominative: die Ruhezeit
• genitive: der Ruhezeit

A useful extra note: in everyday spoken German, some people use the dative after während, but in careful written German, the genitive is preferred.

This is because German main clauses follow the verb-second rule.

The first position in the sentence is taken by the time phrase:

• Während der Ruhezeit

So the finite verb must come next:

• g a s e n

And only after that comes the subject:

• die Kaffeebohnen

So the structure is:

• Während der Ruhezeit | gasen | die Kaffeebohnen | aus

If you started with the subject instead, you would get:

• Die Kaffeebohnen gasen während der Ruhezeit aus.

That is also correct.

Yes, ausgasen is a separable verb.

Its full infinitive is:

• ausgasen = to give off gas, to outgas, to release gas

In a normal main clause, separable verbs split apart:

• Die Kaffeebohnen gasen aus.

In the sentence you were given, the time phrase comes first, so you get:

• Während der Ruhezeit gasen die Kaffeebohnen aus.

But in places where the infinitive or participle is used, it stays together:

• Die Bohnen beginnen auszugasen.
• Die Bohnen haben ausgegast.

Because the subject is plural:

• die Kaffeebohnen = the coffee beans

The verb must agree with the subject:

• ich gase aus
• du gast aus
• er/sie/es gast aus
• wir गैsen aus
• ihr gast aus
• sie/Sie gasen aus

Since Kaffeebohnen is plural, the correct form is gasen.

Here, ausgasen means to release gas or to give off gas.

With coffee, this usually refers to gases such as carbon dioxide being released after roasting. In English, people often say the beans off-gas.

So this is not about the beans actively doing something on purpose; it is a process happening naturally.

Yes, German often uses articles where English may or may not use them.

• die Kaffeebohnen = the coffee beans

Here, the article makes the phrase sound like we are talking about coffee beans in general as the relevant set in this context, or about specific beans being discussed.

You could sometimes see Kaffeebohnen without an article in other contexts, especially in more general or headline-like language, but die Kaffeebohnen is very normal and natural in a full sentence.

It is in the nominative case, because it is the subject of the sentence.

You can identify the subject by asking: Who is releasing gas?

Answer: die Kaffeebohnen

Even though the subject comes after the verb here, it is still the subject and therefore nominative.

Ruhezeit is a compound noun:

• Ruhe = rest, calm
• Zeit = time, period

So Ruhezeit literally means something like resting period or rest period.

German very often forms nouns by combining words into one larger word. This is completely normal:

• Kaffee
  • Bohnen = Kaffeebohnen
• Ruhe
  • Zeit = Ruhezeit

Also, all nouns are capitalized in German, so both Ruhezeit and Kaffeebohnen begin with capital letters.

Yes. Während can be used in two different ways:

1. As a preposition

   • noun
   • während der Ruhezeit

2. As a subordinating conjunction

   • clause
   • während die Kaffeebohnen ruhen

That means:

• Während der Ruhezeit gasen die Kaffeebohnen aus.
• Während die Kaffeebohnen ruhen, gasen sie aus.

Both are possible, but the structure changes. When während introduces a clause, the verb in that clause goes to the end.

Yes. German word order is flexible as long as the grammar rules are respected.

For example:

• Die Kaffeebohnen gasen während der Ruhezeit aus.
• Während der Ruhezeit gasen die Kaffeebohnen aus.

Both are correct.

What does not change is:

• the finite verb stays in second position in a main clause
• the separable prefix aus goes to the end

So if you move another element to the front, the verb still has to stay second.

Yes, it is in the present tense:

• gasen ... aus

But in German, just like in English, the present tense can describe:

• something happening right now
• a general fact
• a regular process

Here it most naturally describes a general process:

• During the resting period, coffee beans release gas.

So it does not have to mean that the speaker is watching the beans at this exact moment.