Nach dem Essen ist das Aufräumen in der Küche anstrengend.

Because nach takes the dative case when it means after.

So:

• das Essen = the meal / the eating
• dem Essen = dative form of das Essen

That is why you say:

• nach dem Essen = after the meal / after eating

This is a fixed grammar rule: nach + dative.

Because Essen is being used as a noun, not as a verb.

Compare:

• essen = to eat (verb)
• das Essen = the meal / the food / the act of eating (noun)

In German, all nouns are capitalized, so Essen gets a capital E.

In this sentence, dem Essen means something like the meal or eating as a noun.

It means after the meal or after eating.

German often uses a noun where English might prefer a clause or gerund. So instead of saying:

• After we eat...
• After eating...

German can simply say:

• Nach dem Essen...

It is a very natural everyday expression.

German main clauses usually follow the verb-second (V2) rule.

In this sentence, the first element is:

• Nach dem Essen

Then the conjugated verb must come next:

• ist

So the structure is:

• Nach dem Essen | ist | das Aufräumen in der Küche | anstrengend

Even though the subject comes after the verb, the sentence is still correct because German cares about the verb being second, not necessarily the subject being first.

If you started with the subject instead, you could also say:

• Das Aufräumen in der Küche ist nach dem Essen anstrengend.

That is grammatical too, though the original sentence sounds more natural in many contexts.

It is a nominalized verb: a verb that is being used as a noun.

• aufräumen = to tidy up / to clean up
• das Aufräumen = the tidying up / cleaning up

When a verb is turned into a noun in German:

• it is capitalized
• it often takes the article das

So das Aufräumen means the act of tidying up.

Because when an infinitive verb is used as a noun in German, it is normally treated as a neuter noun and takes das.

Examples:

• das Essen = eating / food / meal
• das Lesen = reading
• das Schwimmen = swimming
• das Aufräumen = tidying up

So das Aufräumen is not just a verb sitting in the sentence; it is a noun phrase and needs the article das.

Because in can take either dative or accusative, depending on the meaning.

Here it answers the question where?, not where to?

• in der Küche = in the kitchen (location)
• in die Küche = into the kitchen (movement toward)

This sentence is about where the tidying up happens, so it uses the dative:

• in der Küche

It most naturally goes with das Aufräumen:

• das Aufräumen in der Küche = the tidying up in the kitchen

So the sentence means that the act of tidying up in the kitchen is tiring.

Grammatically, it is part of the subject phrase:

• das Aufräumen in der Küche

Then the predicate is:

• ist anstrengend = is tiring

Because anstrengend is being used as a predicate adjective, after the verb sein.

In German, predicate adjectives do not take adjective endings.

Compare:

• Das Aufräumen ist anstrengend.
  Here anstrengend stays plain.

But before a noun, it would take an ending:

• eine anstrengende Aufgabe = a tiring task

So after ist, the basic form anstrengend is correct.

The subject is:

• das Aufräumen in der Küche

You can tell because that is the thing being described as anstrengend.

So the structure is:

• Nach dem Essen = time expression
• ist = verb
• das Aufräumen in der Küche = subject
• anstrengend = predicate adjective

Even though the subject comes after the verb, it is still the subject.

Because the subject, das Aufräumen in der Küche, is grammatically singular.

A nominalized infinitive like das Aufräumen is treated as a singular neuter noun.

So:

• das Aufräumen ... ist ...

not

• das Aufräumen ... sind ...

Sometimes das Essen can mean food, but in nach dem Essen, it usually means the meal or the act of eating.

So in this sentence, the most natural understanding is:

• after the meal
• after eating

not specifically after the food.

The context makes that clear.

Yes, you may hear or see that, especially in more general statements, but das Aufräumen is very natural and clear here.

Using das makes the activity feel more like a defined thing:

• das Aufräumen in der Küche = the tidying up in the kitchen

Without the article:

• Aufräumen in der Küche ist anstrengend

it sounds a bit more general, like Tidying up in the kitchen is tiring as an activity in general.

Both can work, but the version with das is very normal.

It can be understood either way, depending on context.

Without extra context, it often sounds like a general statement:

• After eating, tidying up in the kitchen is tiring.

But it could also refer to a specific situation if the surrounding conversation makes that clear.

German often leaves that kind of distinction to context.

Yes, that is grammatically correct.

The difference is mainly focus:

• Nach dem Essen ist das Aufräumen in der Küche anstrengend.
  This emphasizes the time: after the meal

• Das Aufräumen in der Küche ist nach dem Essen anstrengend.
  This starts with the activity itself.

German word order is flexible, but the verb in a main clause still stays in second position.

A helpful breakdown is:

• Nach dem Essen = time phrase
• ist = verb
• das Aufräumen in der Küche = subject
• anstrengend = predicate adjective

So the core sentence is:

• Das Aufräumen in der Küche ist anstrengend.

And Nach dem Essen is added at the front to say when this is true.