You are observing a cell at equilibrium with respect to the

You are observing a cell at equilibrium with respect to the potassium cation (K+). The cell is in a bathing solution of 1 mM potassium, and you measure the membrane potential of the cell to be -118 mV. What is the internal potassium concentration? show steps

100 mM 10 mM 0.01 mM 1 mM 0.1 mM

Solution

The resting membrane potential of a cell is around -70 mV (most neurons). [K+] is an intracellular cation with a normal intracellular concentration of 140 mM and extracellular concentration of 4 mM. Equilibrium of [K+] ion is achieved at around -92.6 mV. That is, due to high intracelluar concentration of [K+] ions, they diffuse out of the cell and the membrane potential further drops due to efflux of positive ions. An equilibrium in [K+] ion concentration across the membrane occurs when the membrane potential is -92.6 mV.

To calculate the concentration of a particular ion at a particular membrane potential, we use the Nerst Equation:

E_in - E_out =(60 mV/z) log (C_out/C_in),

Where,

E_in - E_out : is the equilibrium membrane potential

C_out : is the [K+] concentration in the bathing solution

and C_in : is the [K+] concentration in the cell

Therefore,

-118 = 60 X Log (1/C_in)

Log (1/C_in) = - 1.966

1/C_in = 0.010

Therefore, C_in = 100 mM