Membrane Potential Homework: Calculating [Na+] Inside Cell

[higherme]

Homework Statement

a biological cell is immersed in a 50mM solution of NaCl at 37C. the cell's membrane is permeable only to Na+ ions. When the system reaches equilibrium, a potential diff of 54.9mV is measured between the inside and the outside of the cell where the inside has the higher( more positive potential.

Calculate [Na+] inside the cell, assuming the amount of Na+ ions transferred is negligible compared to the total amoiunt of Na+ ions in the solution.

Can anyone tell me where to start?

 

[Gokul43201]

Do you know what a concentration cell is?

 

[Blueshift5]

To calculate the [Na+] inside the cell, you will need to use the Nernst equation, which relates the membrane potential (V) to the concentration of ions inside and outside the cell. The equation is as follows:

V = (RT/zF) * ln([ion]outside/[ion]inside)

Where:
R = gas constant (8.314 J/mol*K)
T = temperature in Kelvin (37C = 310K)
z = valence of the ion (in this case, Na+ has a valence of 1)
F = Faraday's constant (96,485 C/mol)
[ion]outside = concentration of ions outside the cell (50mM)
[ion]inside = concentration of ions inside the cell (what we are trying to calculate)

To solve for [ion]inside, we can rearrange the equation as follows:

[ion]inside = [ion]outside * e^(zFV/RT)

Plugging in the values given in the problem, we get:

[ion]inside = 50mM * e^(1*96,485 C/mol * 54.9mV / (8.314 J/mol*K * 310K))

Solving for [ion]inside, we get a concentration of approximately 104mM. This means that the concentration of Na+ inside the cell is approximately twice the concentration outside the cell. This makes sense, as there is a net movement of Na+ into the cell, causing the inside to have a higher concentration.

It is important to note that this calculation assumes that the amount of Na+ ions transferred is negligible compared to the total amount of Na+ ions in the solution. If this is not the case, the calculation may be slightly different. Additionally, the Nernst equation is a simplified model and may not accurately reflect the true membrane potential in a biological system.