To maintain a membrane potential, living cells move sodium ions, Na+, from the inside of the cell to the outside. The electric potential on the membrane is -70 mV. (An interesting fact: this is known as a sodium pump, and it takes about 20% of the human body energy to operate.)
a) How much work is done to move one sodium ion from the inside of the cell to the outside?
b) If the energy is used at a rate of 20W to move sodium ions, how many sodium ions are moved ("pumped") per second?
a) To calculate the work done to move one sodium ion from the inside of the cell to the outside, we can use the formula:
Work = charge x potential difference
Since the charge of one sodium ion is +e (1.6 x 10^-19 C) and the potential difference is 70 mV (or 0.07 V), we can plug in these values:
Work = (+1.6 x 10^-19 C) x (0.07 V)
Work = 1.12 x 10^-20 J
Therefore, the work done to move one sodium ion from the inside of the cell to the outside is 1.12 x 10^-20 Joules.
b) If the energy is used at a rate of 20W to move sodium ions, we can calculate the number of sodium ions moved per second using the work done in part a:
Number of sodium ions moved per second = Energy used per second / Work done to move one sodium ion
Number of sodium ions moved per second = 20 J/s / 1.12 x 10^-20 J
Number of sodium ions moved per second ≈ 1.79 x 10^21 ions/s
Therefore, approximately 1.79 x 10^21 sodium ions are moved per second.