K equil-v:
Only potassium may cross a membrane separating two compartments.
At a temperature of 30∘C, the concentrations of potassium ions are:
intracellular: 280
extracellular: 110
What is the equilibrium potential?
Give a numeric answer within 1%, in mV.
To calculate the equilibrium potential (E), you can use the Nernst equation. The equation is as follows:
E = (RT / zF) * ln([K+]out / [K+]in)
Where:
E is the equilibrium potential (in mV)
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature in Kelvin (30°C = 273 + 30 = 303 K)
z is the valence of the ion (potassium has a valence of 1+)
F is the Faraday constant (96,485 C/mol)
[K+]out is the concentration of potassium ions in the extracellular compartment (110 mM)
[K+]in is the concentration of potassium ions in the intracellular compartment (280 mM)
Using these values, we can now calculate the equilibrium potential for potassium:
E = (8.314 J/(mol·K) * 303 K / (1 * 96,485 C/mol)) * ln(110 mM / 280 mM)
Calculating this equation will give us the equilibrium potential. Let's do the math:
E = (0.025696 * ln(0.392857))
Now we can calculate the natural logarithm:
E = (0.025696 * -0.938604)
Multiplying these values:
E ≈ -0.0246301
Therefore, the equilibrium potential for potassium in this scenario is approximately -24.63 mV. Remember to round the answer within 1%, so the final numeric answer will be -24.6 mV.