To....., for ..... and so that...... (purpose)

• We use to ... to say why somebody does something (= the purpose of an action)"Why are you going out? "  "To post a letter".
• We use to .... to say why something exists (its purpose):
• The president has a team of bodyguards to protect him.
• We use to ...... to say what can be done or must be done with something.It's difficult to find a place to park in the centre.(= a place where you can park)Have you got much work to do? (= work that you must do)
• Also money/time/chance/opportunity/energy/courage etc. to (do something)   I need a few days to think about your proposal.

For...... and to....
For + noun                                      to + verb
Let's go to the pool for a swim.      I'm going to Spain to learn Spanish.

You can use for -ing or to.... to talk about the general purpose of something, or what it is generally used for:
Do you use this brush for washing the dishes?  (or ... to wash the dishes?)

So that
We use so that (not to....) especially
When the purpose is negative  (so that.... won't/wouldn't)
I hurried so that I wouldn't be late. (=because I didn't want to be late)
Leave early so that you won't (or don't) miss the train.

With can and could (so that ... can/could):
She's learning English so that she can study in Canada.
We moved to London so that we could see our friends more often.

Explanation taken from English Grammar in Use  ed.Cambridge
 You can do some exercises on This site