Problems
18.1 The lipid bilayer is permeable to what type of small molecules?
18.2 Consider a cell membrane at 298 K which has glucose at the concentration of 200 mM
inside the cell and 2 mM outside the cell, with the voltage being 150 mV lower in the
interior. Calculate the molar free energy difference for transporting the molecule from
the interior to the exterior.
18.3 Consider a cell membrane at 295 K which has glucose at the concentration of 100 mM
inside and 20 mM outside, with the voltage being 100 mV lower in the interior. Calculate
the molar free energy difference for transporting the molecule from the exterior to the
interior.
18.4 Consider a cell membrane at 298 K which has Na+at the concentration of 200 mM inside
the cell and 20 mM outside the cell with the voltage being 100 mV higher in the interior.
Calculate the molar free energy difference for transporting the molecule from the interior
to the exterior.
18.5 A cell membrane at 298 K has a interior concentration of 1 mM Na+and an exterior con-
centration of 20 mM Na+. Assume that equilibrium has been reached and the free energy
difference is zero. Calculate the voltage of the interior relative to the exterior.
18.6 A cell membrane at 298 K has a interior concentration of 3 mM Na+and an exterior con-
centration of 60 mM Na+. Assume that equilibrium has been reached and the free energy
difference is zero. Calculate the voltage of the interior relative to the exterior.
18.7 Suppose that for every Na+transported from the interior to the exterior one K+is transported
from the exterior to the interior. The voltage is 60 mV higher in the exterior. The interior
concentrations are 100 mM for K+and 150 mM for Na+and the exterior concentrations
are 2 mM for K+and 1 mM for Na+. Calculate the molar free energy difference for each
process and the net transport process.
18.8 For all of the following questions consider the Na+/K+-ATPase to be present in a mem-
brane with the following conditions: Na+concentration inside, 20 mM; Na+concentration
outside, 150 mM; K+ concentration inside, 50 mM; K+ concentration outside, 10 mM;
V (inside)–V (outside), −50 mV; temperature, 310 K.
3Na+(in) +2K+(out) +ATP +H 2 O ↔3Na+(out) +2K+(in) +ADP +Pi(a) Calculate the free-energy difference for moving Na+from the inside to the outside.
(b) Calculate the free-energy difference for moving K+from outside to the inside.
(c) Calculate the free-energy difference for moving both Na+ and K+in the observed
stoichiometry.
(d) How should the free-energy difference for the hydrolysis of ATP compare to the value
calculated in part (c) for the reaction to occur?
18.9 Suppose that for every Na+ transported from the interior to the exterior one K+ is
transported from the exterior to the interior. The voltage is 65 mV higher in the
exterior. The interior concentrations are 200 mM for K+and 200 mM for Na+and the
exterior concentrations are 4 mM for K+ and 2 mM for Na+. Calculate the molar free
energy difference for each process and the net transport process at a temperature of
298 K.