Nernst Equation and Equilibrium Potential for the MCAT

The equilibrium potential of an ion is the membrane voltage at which the electrical force on that ion exactly balances its concentration gradient, so there is no net movement. The Nernst equation calculates it for one ion at a time: E = (RT/zF) ln([ion]_out/[ion]_in). Yes, the Nernst equation is on the MCAT, usually as a membrane potential or electrochemistry passage, and the shortcut form below is the version you will actually use.

The formula and its shortcut

• Full form: E_ion = (RT/zF) ln([out]/[in])
• Base-10 form at 37 C: E_ion = (61.5 mV / z) log₁₀([out]/[in])
• Rounded for exam math: use about 60 mV, or 58 mV at 25 C.

Here z is the charge of the ion (+1 for Na⁺ and K⁺, +2 for Ca²⁺, -1 for Cl^-). Keep the ratio as outside over inside and let z carry the sign. Many people reverse the ratio for anions; that is unnecessary if z is -1.

Worked example: potassium

Typical neuron: [K⁺]_out = 5 mM, [K⁺]_in = 150 mM.

E_K = 61.5 log₁₀(5/150) = 61.5 x log₁₀(0.0333) = 61.5 x (-1.48) = about -90 mV.

Interpretation: K⁺ is concentrated inside, so it tends to leak out, leaving the inside negative. At -90 mV the inward electrical pull exactly cancels the outward chemical push.

Worked example: sodium

[Na⁺]_out = 145 mM, [Na⁺]_in = 15 mM.

E_Na = 61.5 log₁₀(145/15) = 61.5 x 0.985 = about +60 mV.

Na⁺ is concentrated outside, so it wants to flow in, and the inside would have to be positive to hold it back.

A quick way to estimate without a calculator

Each tenfold concentration ratio is worth about 60 mV for a monovalent ion. A ratio of 30 is a bit over one factor of ten, so roughly 60 to 90 mV. Always decide the sign first (cation concentrated outside means positive, cation concentrated inside means negative), then estimate the size.

Equilibrium potential vs resting membrane potential

The resting potential sits near E_K because the resting membrane is far more permeable to K⁺ than to Na⁺. It is a little less negative than E_K because of the small Na⁺ leak. During the action potential, Na⁺ permeability surges, and the membrane voltage moves toward E_Na.

Driving force

Driving force = V_m - E_ion. It tells you the direction and strength of net ion flow when channels open.

At V_m = -70 mV and E_Na = +60 mV, the driving force on Na⁺ is -130 mV, a large inward push. For K⁺ it is -70 - (-90) = +20 mV, a small outward push. This is why opening Na⁺ channels produces a big, fast current and opening K⁺ channels a smaller one.

Link to electrochemistry

The same logic appears in galvanic cells. The cell version is E = E° - (RT/nF) ln Q, which at equilibrium (E = 0) gives the relationship between E° and K. A membrane is a concentration cell: the same ion on both sides, with the "cell potential" set only by the concentration ratio.

Common traps

• Using Nernst for the resting potential. Nernst is for one ion. Several permeable ions need Goldman.
• Flipping the ratio. Use outside over inside, with the sign of z.
• Ignoring z. Ca²⁺ has half the slope of a monovalent ion.
• Forgetting the pump. The Na⁺/K⁺ ATPase builds the gradients; the Nernst potential is set by them, not by the pump's electrogenic contribution.
• Mixing up direction and sign. A negative equilibrium potential means the inside is negative at equilibrium, not that ions flow out.

One-minute recap

• E = (61.5 mV / z) log([out]/[in]) at 37 C.
• E_K is about -90 mV, E_Na about +60 mV in a typical neuron.
• Resting potential (about -70 mV) is closest to E_K because of K⁺ permeability.
• Driving force = V_m - E_ion.