Final answer:
The equilibrium potential for Na+ across a plasma membrane with an extracellular Na+ concentration of 150 mM and an intracellular Na+ concentration of 15 mM is approximately +61.54 mV, calculated using the Nernst equation.
Step-by-step explanation:
The question involves determining the equilibrium potential of a plasma membrane that is permeable only to sodium ions (Na+), given the concentrations of sodium inside and outside the cell. The Nernst equation is typically used for calculating equilibrium potentials. Given an extracellular Na concentration of 150 mM (millimoles per liter) and an intracellular Na concentration of 15 mM, we can use the Nernst equation to find the equilibrium potential for Na+ across a cell membrane.
The Nernst equation is given by:
E = (RT/zF) * ln([Na+]outside/[Na+]inside)
Where:
- E is the equilibrium potential
- R is the universal gas constant (8.314 J/(mol K))
- T is the temperature in Kelvin
- z is the charge number of the ion
- F is Faraday's constant (96485 C/mol)
- [Na+]outside is the extracellular sodium concentration
- [Na+]inside is the intracellular sodium concentration
At physiological temperature (37°C or 310K), the equation simplifies to:
E = (61.54 mV/z) * log([Na+]outside/[Na+]inside)
Since Na+ has a charge of +1, z = 1, and we can calculate:
E = 61.54 mV * log(150/15) = 61.54 mV * log(10) = 61.54 mV * 1
This yields an equilibrium potential (E) of approximately +61.54 mV.
The equilibrium potential is the voltage across the plasma membrane at which there is no net flow of a particular ion in or out of the cell. It plays a critical role in neuronal function and muscle cell excitability.