Question

The specific capacitance of most cell membranes is 1 µF / cm2 . A) How many K+ ions must cross the membrane of a spherical cell, 40 µm in diameter, to change the membrane potential by 10 millivolts. B) How many millimoles does this represent. C) What change in cytoplasmic K+ concentration will occur?

Answer 1

Given,

Specific Capacitance = 1 µF / cm2

Diameter of membrane = 40 µm = 0.004 cm

Membrane potential, V = 10mV = 10x10-3 V

= 4*3.14*(0.004)2

= 2.0106 x 10-4

Total capacitance, C = Specific Capacitance x Surface area of the membrane

= 1 x 2.0106 x 10-4

  = 2.0106 x 10-4 µF = 2.0106 x 10-10 F

Charge, Q= C x V

= 2.0106 x 10-10 x 10x10-3

= 2.0106 x 10-12 Coloumb

a) 1 Coloumb charge contains 6.25 x 1018 ions ( positive or negative)

Hence 2.0106 x 10-12 Coloumb charge contains 12566250 K+ ions

b) 1 mole = 96500 Coloumbs

therefore, 2.0106 x 10-12 Coloumb = 0.0208 x 10-12 moles = 0.0208 x 10-9 millimoles

c) During action potential, the K+ ions that leave the cell is less compared to the K+ions within the cell. hence in most cases the cytoplasmic concentration doesnt change.