Final answer:
The potential difference for Na+ is likely greater than K+ at equilibrium across a cell membrane due to a stronger electrochemical gradient for Na+ to enter the cell. The resting membrane potential is about -70 mV, and the Na+/K+ pump contributes to this charge distribution.
Step-by-step explanation:
To calculate the potential differences for Na+ and K+ ions across a cell membrane at 310K, we need to consider the electrochemical gradients and how these ions interact with the cell at equilibrium. Given that the cell membrane has different concentrations of these ions on either side and the inside of the cell is negatively charged relative to the outside, we can infer the behavior of these ions.
The sodium-potassium pump actively moves Na+ outside and K+ inside the cell. Potassium ions (K+) can leave the cell through frequently open channels, whereas sodium (Na+) channels are rarely open, keeping Na+ primarily outside the cell. Because of the high concentration gradient and the negative charge inside the cell, Na+ has a strong electrochemical gradient to enter the cell, and K+ has a tendency to leave the cell.
The resting membrane potential is typically around -70 mV, indicating that the inside of the cell is negatively charged compared to the outside. This value implies a separation of electrical charge that can do work, similar to a battery. Considering this and the ion distributions, we can conclude that the potential difference for Na+ is likely to be greater than for K+ because Na+ ions are driven by a stronger combined electrochemical gradient to move into the cell. Therefore, the correct answer is (b) Na+ potential difference > K+ potential difference.