English has different verb forms. A full infinitive is to + verb. For example, to eat.
Why we do something
When a full infinitive is used at the end of a sentence to explain why we do something, it is called the infinitive of purpose. This only works with verbs, not nouns.
- I went home to eat.
- He's going to the gym to lose weight.
- I will work hard to make more money.
To explain why we do something using a noun, we use for.
- I went home for food.
- He's going to the gym for exercise.
- I will work hard for money.
We can also use for to talk about doing something to help someone.
- I made this video for you to learn.
- There's a cake on the table for you to eat.
Reference: BBC Learning English