Living cells actively \"pump\" positive sodium ions (Na+) from inside the cell t

Question

Living cells actively "pump" positive sodium ions (Na+) from inside the cell to outside the cell. This process is referred to as pumping because work must be done on the ions to move them from the negatively charged inner surface of the membrane to the positively charged outer surface. Given that the electric potential is 6.5×102 V higher outside the cell than inside the cell, and that the cell membrane is 0.10 µm thick, calculate the work that must be done (in joules) to move one sodium ion from inside the cell to outside. SHOW YOUR WORK AND THE EQUATIONS USED

Explanation / Answer

The work done on the ion is q*V, where q = charge on the ion and V the voltage change. Na+ has a positive charge equal in magnitude to the electron charge of 1.6*10^-19 C; The work done is then

0.065*1.6*10^-19 = 1.04*10^-20 J

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