To exchange something is to give it to someone for something that they give you. The verb exchange is used with both for and with. There is a difference, though.We exchange something for something. We exchange something with someone.
I exchanged my old fridge for a new one. (= I gave my old fridge and got a new one.)
She exchanged her old clothes for new utensils.
She is eager to exchange her job in the private sector for a post in government.
We have to exchange dollars for rupees.
I would like to exchange my old desktop computer for a brand new laptop.
Gift coupons can be exchanged for goods.
The students exchanged pleasantries with each other. (NOT The students exchanged pleasantries for each other.)
I always exchange clothes with my sister.
They exchanged a few words with one another and left in haste.