GATE 2023 BM – Question 61
For a membrane at 27°C, use the Goldman–Hodgkin–Katz equation to find the magnitude of membrane potential in mV to one decimal. Ion concentrations (outside,inside) and relative permeabilities are: Na⁺ (140,10),0.02; K⁺ (3,140),1; Cl⁻ (90,3),0.38. Use R=8.31 J mol⁻¹ K⁻¹ and F=96500 C/mol.
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Correct answer: 82.6 to 86.0
Explanation
For intracellular voltage relative to outside, V=(RT/F)ln[(PₖKout+PₙₐNaout+PclClin)/(PₖKin+PₙₐNain+PclClout)]. Chloride concentrations reverse sides because it is an anion. Numerator=3+.02×140+.38×3=6.94; denominator=140+.02×10+.38×90=174.4. With T≈300 K, V≈−.0833 V, whose magnitude is about 83.3 mV.