We live in the state of Missouri and The landlord has put the townhouse up for sale and we have found another place to rent and would like to lease it before it is too late. If we break the lease before it is up will we be responsible for the remainder of the lease? Or has our landlord already done that by putting it on the market. Also what is a sufficient amount of time for the realtors to notify us of a prospective buyer to see the unit?

Putting the house up for sale does not break your lease. If the house is sold, your lease if still in effect. You have no excuse for moving. However, the seller might prefer to have the house vacant. So approach the landlord and see if he will let you out or maybe you can buy your way out.

No, you can not break your lease because he put it up for sale.
The new owner is legally obligated to honor your lease. If the as noted by Scott, the current owner will allow you to break the lease, you can.

But if you leave now, yes you will owe and be obligated for the remainder of the lease.

The real estate agents should have to give 24 hour notice to show the unit. They will often prefer you not to be home when it is shown.