If intracellular is 15 mM and the extracellular is 150mM, what is the equilibrium potential for
## **Core Concept**
The equilibrium potential for an ion is the membrane potential at which the electrical and chemical gradients for that ion are equal, resulting in no net movement of the ion across the membrane. This concept is based on the Nernst equation, which calculates the equilibrium potential for a specific ion. The Nernst equation takes into account the concentration of the ion inside and outside the cell.
## **Why the Correct Answer is Right**
To calculate the equilibrium potential for (sodium), we use the Nernst equation at body temperature (37°C), which simplifies to:
[ E_{ion} = frac{RT}{zF} lnleft(frac{[ion]_{outside}}{[ion]_{inside}}right) ]
For at 37°C, and are approximately 61.5 mV. Given mM and mM:
[ E_{Na} = 61.5 logleft(frac{150}{15}right) ]
[ E_{Na} = 61.5 log(10) ]
[ E_{Na} = 61.5 times 1 ]
[ E_{Na} = +60 , mV ]
This matches option , confirming that the equilibrium potential for under these conditions is approximately +60 mV.
## **Why Each Wrong Option is Incorrect**
- **Option A:** is incorrect because it does not match the calculated value for the equilibrium potential of .
- **Option B:** is incorrect as it suggests a negative value, which does not align with the positive equilibrium potential expected for .
- **Option D:** is incorrect because it provides a value that does not correspond to the calculated equilibrium potential for .
## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the resting membrane potential of most neurons is approximately -70 mV, which is close to the **Option C:** value but actually generated mainly by distribution and permeability. The equilibrium potential for is around +60 mV, and for , it's about -90 mV. The resting membrane potential is primarily determined by permeability.
## **Correct Answer:** . +60 mV