We can use to + infinitive and for + noun to say what is the purpose of an action, or the reason why we do something.

to + infinitive

• I went to the grocery store to buy some vegetables. 
• I studied hard to pass the exam.

for + noun

• Let’s go to the pub for a drink. 
• We climbed to the top for the views.

Compare to vs for:

• I went to the shop to buy some milk. 
• I went to the shop for some milk. 

for + -ing

Don’t use for + -ing to talk about why we do something

We don’t use for + -ing to say what is the purpose of our actions, why we do something.

• I work hard for improving my English.
• I work hard to improve my English.
• Turn the TV on for watching the news.
• Turn the TV on to watch the news.

Use for + -ing to talk about the purpose or function of an object

We use for + ing to talk about the purpose or function of a thing, what an object is used for.

• This machine is used for cleaning cars.
• This is a special camera for photographing small objects.  

Expressing purpose with ‘to’ and ‘for’