Question

Imagine a cell with a semi-permeable membrane that is selective to K+ ions only. The internal solution contains 100 mM KCl and the external solution contains 1 mM KCl. What equation would you use to determine the potential (EK) developed across the membrane?

Answer 1

To find the potential across a membrane selectively permeable to K+ ions, the Nernst equation is used, which calculates the equilibrium potential based on ion concentration inside and outside the cell.

Step-by-step explanation:

The equation used to determine the potential difference (EK) across a membrane that is selectively permeable to K+ ions is the Nernst equation. The Nernst equation, which is used to calculate the equilibrium potential for a particular ion, is given by:

\( EK = \frac{RT}{zF} \ln\left(\frac{[K+]_{outside}}{[K+]_{inside}}\right) \)

Where:

• 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 (for K+, z=+1)
• F is the Faraday constant (96485 C/mol)
• [K+]_{outside} and [K+]_{inside} are the external and internal concentrations of K+ ions, respectively

At room temperature (25&Celsius;, or 298K), the Nernst equation for K+ can be simplified to:

\( EK = -61.54 \log\left(\frac{[K+]_{outside}}{[K+]_{inside}}\right) \)

For the given concentrations of 1 mM KCl outside and 100 mM KCl inside the cell, the potential can be calculated directly:

\( EK = -61.54 \log\left(\frac{1 mM}{100 mM}\right) \)

Thus, the membrane potential is determined by the distribution of K+ ions across the semipermeable membrane due to differential diffusion and the resulting electrochemical gradient.

Answer 2

Ek = (RT/zF)*ln ( [k+]o/[K+]i )

Step-by-step explanation:

R = gas constant (8.31 J/Kmol)

T = Temperature (k)

F = Faraday constant (9.65 * 10exp4 coulomb/mole)

z = valence of the ion (1)

[k+]o = Extracellular K concentration in mM

[K+]i = Intracellular K concentration in mM

ln = logarithm with base e