The closing date should be agreed between the parties. It will be nominated by the Vendors and their preferred date inserted in the Contract. Your solicitor will discuss this with you and ask you what your preference is.
If you are not happy with the nominated closing date, you can ask for an alternative and try and reach agreement. In the end, if you cannot reach agreement ( and, frankly, if Vendors want to sell their houses, they need to get real on moving out!), it is a very bad omen and maybe time to move on elsewhere.
Your solicitor will advise.
mf