Question

Consider a cell with intracellular and extracellular concentrations of the four ions listed below. Which of the ions are in electrochemical equilibrium when the membrane potential is -58 mV at 18° C?

Concentration (mmol/L)
Ion Intracellular Extracellular
Cl⁻ 15 150
Mg²⁺ 15 1.5
K⁺ 150 15
Na⁺ 15 150
A) K⁺ and Na⁺
B) Cl⁻ and K⁺
C) Mg²⁺ and K⁺
D) Cl⁻
E) Cl⁻ and Na⁺

Answer 1

Using the Nernst equation, Cl- and K+ are in electrochemical equilibrium at a membrane potential of -58 mV. Other ions listed do not match the equilibrium potential at this membrane potential.

Step-by-step explanation:

To determine which ions are in electrochemical equilibrium at a membrane potential of -58 mV at 18° C, we must use the Nernst equation. The Nernst equation calculates the membrane potential (Vm) at which a particular ion is in equilibrium based on its concentration gradient across the membrane. This equilibrium potential is given by:

Vm = (RT/zF) × ln([ion]_out/[ion]_in)

where R is the gas constant, T is the temperature in Kelvin, z is the charge number of the ion, F is Faraday's constant, [ion]_out is the extracellular concentration, and [ion]_in is the intracellular concentration. For monovalent ions (such as K+ and Cl-) at 18° C, the Nernst equation simplifies to approximately:

Vm ≈ 58 × log([ion]_out/[ion]_in) (in millivolts)

Checking each ion:

• K+ equilibrium potential E(K) = 58 × log(15/150) = -58 mV.
• Na+ equilibrium potential E(Na) = 58 × log(150/15) = 58 mV.
• Cl- equilibrium potential E(Cl) = -58 × log(150/15) = -58 mV.
• Mg2+ is not typically considered for equilibrium as it is usually impermeable.

Based on these calculations, Cl- has an equilibrium potential of -58 mV, which matches the membrane potential given. Therefore, Cl- is in electrochemical equilibrium at -58 mV. K+ is also at equilibrium given the membrane potential is -58 mV, as per E(K).

The correct answer in this scenario is B) Cl- and K+.