Living cells \"pump\" singly ionized sodium ions, Na+, from the inside of the ce

Question

Living cells "pump" singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential: ?Vmembrane = Vin - Vout = -67mV It is called pumping because work must be done to move a positive ion from the negative inside of the cell to the positive outside, and it must go on continuously because sodium ions "leak" back through the cell wall by diffusion. a) How much work must be done to move one sodium ion from the inside of the cell to the outside? Express your answer to two significant figures and include the appropriate units. W = ? J b) At rest, the human body uses energy at the rate of approximately 99W to maintain basic metabolic functions. It has been estimated that 17% of this energy is used to operate the sodium pumps of the body. Estimate to one significant figurethe number of sodium ions pumped per second. Express your answer using one significant figure. N = ? ions

Explanation / Answer

a) Work done = charge * potential difference = qV charge of Na+ ion = charge of a single proton = 1.6 * 10^-19 C therefore work done = 1.6 * 10^-19 * 67 * 10^-3 = 110 * 10^-22 J b) energy used = 99W energy used by sodium pumps = 17% of this = 17*99/100 W = 16.83W = 16.83 J/s Therefore in one second, energy used for operating sodium pumps = 16.83J from part a, energy required to pump one sodium ion = 110*10^-22 J But energy used up = 16.83J Therfore, number of sodium ions pumped per second = 16.83 / 110*10^-22 = 0.153 * 10^22 = 0.2 * 10^22 (one significant figure) Even if these answers are wrong, the method is correct. the only scope of the answer being wrong is because of the way i have treated significant values.

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