a. The mess your friends made in your room is yours to clean up.

(Meaning: You have to clean up the mess your friends made in your room.)

b. The dessert is yours to make.

(Meaning: You have to make the dessert.)

Are (a) and (b) grammatically correct with the meanings I have assigned to them?

I think they don't work in British English, but I am not sure whether they work in American English or not.

This construct can be used for rights and privileges, but I don't know whether it can be used for expressing duties.