Different concentrations of ions on either side of a cell membrane constitute a concentration cell, which is described by the Nernst equation given below. What is the electrochemical potential across a membrane when the sodium ion concentration is 0.10 M on one side of the membrane and 0.010 M on the other side, and the temperature is 37 $\circ$ C (body temperature)? (Given: , = -2.71 V; F =96,485 C; 1 J = 1 C V; R = 8.315 J / (mol K))
E = E $\circ$ - InQ
A)61.5 mV
B)26.7 mV
C)2.65 V
D)2.68 V
E)2.98 V

Question

Different concentrations of ions on either side of a cell membrane constitute a concentration cell, which is described by the Nernst equation given below. What is the electrochemical potential across a membrane when the sodium ion concentration is 0.10 M on one side of the membrane and 0.010 M on the other side, and the temperature is 37 $\circ$ C (body temperature)? (Given:  ,  = -2.71 V; F =96,485 C; 1 J = 1 C V; R = 8.315 J / (mol K))
E = E $\circ$ -  InQ
A)61.5 mV 
B)26.7 mV 
C)2.65 V 
D)2.68 V 
E)2.98 V

Quizplus · Accepted Answer

Firstly, let's calculate the Nernst potential using the Nernst equation:

E = EF° - (RT/zF) ln(Q)

where 
EF° = 2.71 V (given)
R = 8.315 J/(mol K) (gas constant)
T = 310 K (body temperature)
z = +1 (charge of sodium ion)
F = 96485 C/mol (Faraday constant)
Q = [Na+]outside / [Na+]inside = 0.010/0.10 = 0.1

So, E = 2.71 - (8.315*310/1*96485) ln(0.1) = 0.0615 V = 61.5 mV

The electrochemical potential across the membrane is the same as the Nernst potential for the sodium ion under these conditions. Therefore, the correct answer is A) 61.5 mV.

Different Concentrations of Ions on Either Side of a Cell ∘\circ∘

Different Concentrations of Ions on Either Side of a Cell $\circ$