When can our prayers change God's mind/will? Is it wrong to pray against the will of God?

Firstly I believe that prayer can change God's mind. Like when Moses asked God to not smite the Israelites. But **when** can our prayers change the will/mind of god? I believe we have to pray that God's will be done, regardless of whether His will lines up with what we pray for. But like in Moses' case, he prayed *against* the will of God. Is this because God made His will known to Moses, that he could pray for God to change his mind? Can we only pray for God to change his will when he shows us what it is, and the rest of the time we have to pray for it to happen? (Obviously we will sometimes unintentionally pray against God's will, if we do not know what it is, but that's not what I'm talking about).