Very low concentrations of detergent make membranes leaky to small molecules and ions without damaging proteins. In isolated mitochondria exposed to detergent, the molecules of the electron transport chain and of ATP synthase remain intact. Do you expect ATP synthesis to continue in the presence of low concentrations of detergent?
A. Yes, because all enzymes and electron carriers are functional
B. No, because with a leaky membrane, the proton gradient cannot be maintained
C. No, because leaky membranes inhibit glycolysis
D. No, because leaky membranes do not allow NADH and FADH2 to donate their electrons to the electron transport chain

B. No, because with a leaky membrane, the proton gradient cannot be maintained

Explanation:

.

The electrochemical  gradients between the   intramembrane and matrix of the mitochondria is maintained by the Proton Motive Force, (PMF)which pumps protons across from the matrix into the intramembrane layer. The force makes  protons concentration  to continuously build up , and this set up an electrochemical /proton gradients  between the intramembrane layer and the matrix.

It  is the diffusion of protons down their concentration gradient  from the intramembrane to the matrix  that generates the needed energy for synthesis of ATPs by ATPase synthase in chemiosmosis.

Therefore, if detergents increases porosity of the membranes, hydrogen ions; protons will leak out,  disrupting the Proton  gradients  because PMF which which set up proton gradient  can not be maintained, and more importantly,  needed energy for ATPase synthesis from influx of protons  can not be generated. Thus B is the answer.