Wenn die Personalabteilung den Urlaubsantrag genehmigt, nehme ich mir frei.

Because the first part, Wenn die Personalabteilung den Urlaubsantrag genehmigt, is a subordinate clause introduced by wenn.

In German, subordinate clauses send the conjugated verb to the end. So:

• die Personalabteilung genehmigt den Urlaubsantrag = normal main clause word order
• wenn die Personalabteilung den Urlaubsantrag genehmigt = subordinate clause, so genehmigt goes to the end

This is one of the most important German word-order patterns to learn.

Because the sentence begins with the wenn-clause, and that entire clause counts as position 1 in the main sentence.

German main clauses follow the verb-second rule, so the conjugated verb must come next:

• Wenn die Personalabteilung den Urlaubsantrag genehmigt, nehme ich mir frei.

Structure:

1. Wenn ... genehmigt = first element
2. nehme = verb in second position
3. ich = subject after the verb

If you started with the main clause instead, you would say:

• Ich nehme mir frei, wenn die Personalabteilung den Urlaubsantrag genehmigt.

Here, wenn means if.

German uses:

• wenn = if / whenever for conditions
• als = when for a single event in the past
• wann = when in a question or indirect question

Examples:

• Wenn es regnet, bleibe ich zu Hause. = If it rains, I stay home.
• Als ich klein war, ... = When I was little, ...
• Wann kommst du? = When are you coming?

So in your sentence, wenn is correct because it expresses a condition: the speaker will take time off if HR approves the request.

Because Urlaubsantrag is the direct object of genehmigen, so it is in the accusative case.

• der Urlaubsantrag = nominative
• den Urlaubsantrag = accusative

The subject is:

• die Personalabteilung = the department doing the approving

So:

• die Personalabteilung = subject
• den Urlaubsantrag = direct object

That is why den is used.

Because sich frei nehmen is a fixed expression, and it uses a dative reflexive pronoun.

So the pattern is:

• ich nehme mir frei
• du nimmst dir frei
• er/sie nimmt sich frei
• wir nehmen uns frei

This expression literally works something like to take oneself free, but in natural English it means to take time off or to take the day off.

So mir is not random—it belongs to the verb phrase sich frei nehmen.

They are similar, but not always exactly the same.

• sich frei nehmen = to take time off
• Urlaub nehmen = to take vacation/leave

sich frei nehmen can sound a bit broader and may refer to taking a day or some time off from work.
Urlaub nehmen is often more directly about official vacation leave.

In this sentence, sich frei nehmen fits well because it follows approval of a leave request.

Personalabteilung means human resources department or HR department.

It is a compound noun:

• Personal = personnel/staff
• Abteilung = department

German often builds long nouns by combining smaller ones.
The grammatical gender comes from the last part, Abteilung, which is feminine:

• die Personalabteilung

Urlaubsantrag is also a compound noun:

• Urlaub = vacation / leave
• Antrag = application / request

Together:

• Urlaubsantrag = vacation request / leave request

The -s- is a common linking element in German compounds. It does not always have a separate meaning; it just helps join the words naturally.

You will see this a lot in German:

• Arbeitszimmer
• Lebensmittel
• Jahresende

So Urlaubsantrag is very normal compound formation.

It is in the present tense: genehmigt and nehme are both present-tense forms.

German often uses the present tense to talk about:

• general truths
• future plans
• conditions referring to the future

So even though the meaning may be future-oriented, German does not need a separate future form here.

English might say:

• If HR approves the leave request, I’ll take time off.

German naturally says:

• Wenn die Personalabteilung den Urlaubsantrag genehmigt, nehme ich mir frei.

Yes, in many contexts you could say:

• Falls die Personalabteilung den Urlaubsantrag genehmigt, nehme ich mir frei.

But there is a slight nuance:

• wenn = neutral if/when
• falls = in case / if indeed

Falls can sound a bit more uncertain or more explicitly conditional.

So:

• wenn is the most common neutral choice
• falls is possible if you want to stress the condition more

Because in German, a subordinate clause is normally separated from the main clause by a comma.

Since Wenn die Personalabteilung den Urlaubsantrag genehmigt is a subordinate clause, a comma is required before the main clause:

• ..., nehme ich mir frei.

German comma rules are stricter than English ones in this area, so this comma is not optional.

Yes. You can also say:

• Ich nehme mir frei, wenn die Personalabteilung den Urlaubsantrag genehmigt.

The meaning stays basically the same.

The difference is mainly about emphasis:

• starting with wenn ... puts the condition first
• starting with ich nehme ... puts the main action first

Both are correct.

The two verbs are:

1. genehmigen = to approve

   • here: genehmigt
   • subject: die Personalabteilung
   • this is 3rd person singular

2. sich frei nehmen = to take time off

   • here: nehme ich mir frei
   • nehme is 1st person singular
   • mir is the dative reflexive pronoun

So the full structure is:

• Wenn die Personalabteilung den Urlaubsantrag genehmigt
• nehme ich mir frei

Yes, depending on context. Possible translations include:

• leave request
• vacation request
• vacation application
• time-off request

In workplace English, leave request or time-off request often sounds the most natural.

So the German word is straightforward, but the best English translation depends on the workplace context.

In sich frei nehmen, frei is part of the fixed expression and functions predicatively rather than like a normal directly-inflected adjective.

You do not say:

• ich nehme mir freien

You say:

• ich nehme mir frei

So for learners, the best approach is to memorize sich frei nehmen as a whole phrase meaning to take time off.