Q.45 The equilibrium potential of a biological membrane for
Na+ is 55 mV at 37 °C.
Concentration of Na+ inside the cell is 20 mM.
Assuming the membrane is permeable to Na+ only, the Na+
concentration outside the membrane will be ______ mM.
(Faraday constant: 23062 cal·V−1·mol−1,
Gas constant: 1.98 cal·mol−1·K−1)
Introduction
The equilibrium potential biological membrane Na+ of +55 mV represents the membrane voltage
at which there is no net movement of sodium ions across the membrane.
Using the Nernst equation and a given intracellular Na+ concentration of 20 mM,
the extracellular Na+ concentration can be calculated.
Nernst Equation
Equation:
E = RT/zF ln ([Na+]out /[Na+]in)
Given Values
- E = 55 mV = 0.055 V
- T = 37℃ = 310 K
- [Na+]in = 20 mM
- R = 1.98 cal mol-1 K-1
- F = 23062 cal V-1 mol-1
- z = +1
Step-by-Step Calculation
Step 1: Calculate RT/F
RT/F = (1.98 × 310) / 23062 = 613.8 / 23062 ≈ 0.02662 V
Step 2: Solve for ln(r)
ln(r) = E / (RT/F) = 0.055 / 0.02662 ≈ 2.0657
Step 3: Solve for r
r = e2.0657 ≈ 7.89
Step 4: Calculate [Na+]out
[Na+]out = 20 × 7.89 ≈ 157.8 mM
Correct Answer
[Na+]out ≈ 158 mM
(Physiological approximation: ~145 mM)
Base-10 (Log) Form of Nernst Equation
E = 2.303RT/zF log10 ([Na+]out / [Na+]in)
At 37℃: 2.303 × 0.02662 ≈ 0.0613 V (≈ 61 mV per decade)
Common Errors
| Error | Resulting r | [Na+]out (mM) |
|---|---|---|
| Using log10 instead of ln | 14.5 | ≈ 290 |
| Using 25℃ instead of 37℃ | 7.3 | ≈ 146 |
| Forgetting temperature correction | Variable | Incorrect |
Physiological Significance
Since the resting membrane potential (~ −70 mV) is much lower than
ENa (+55 mV), sodium ions strongly favor inward movement.
This electrochemical gradient is essential for action potential generation
and is integrated with potassium dynamics via the Goldman equation.
