Drugs known as uncouplers facilitate diffusion of protons across the membrane. Brown fat can generate heat without ATP by using uncouplers. With an uncoupler, what will happen to ATP synthesis and oxygen consumption if the rates of glycolysis and the citric acid cycle stay the same?

ATP synthesis will diminish or decrease, whereas oxygen consumption will most probably stay the same.

Explanation:

Uncoupler is an agent which which has the ability to disrupt oxidative phosphorylation in mitochondria and prokaryotes and also disrupts photophosphorylation in chloroplasts and cyanobacteria by detaching the reactions of ATP formation from the electron transport chain or ETP.

So, in the presence of uncoupler, ATP synthesis will decrease but it will most probably do not effect oxygen consumption.