The pH of blood and extracellular fluid is about 7.4. Animal cells have a membrane potential of about -60 mV (negative inside). If the H+ concentration is in equilibrium with the membrane potential, what would the intracellular pH be?
To calculate the intracellular pH, we need to use the Nernst equation, which relates the membrane potential (in volts) to the concentration gradient of a specific ion. In this case, we're interested in the equilibrium between H+ concentration and the membrane potential.
The Nernst equation is given as follows:
E = (RT/zF) * ln ([C ]out/[C ]in)
where:
E = membrane potential (in volts)
R = gas constant (8.314 J/K*mol)
T = temperature in Kelvin
z = valence of the ion (in this case, +1 for H+)
F = Faraday constant (96,485 C/mol)
[C ]out = concentration of ion outside the cell
[C ]in = concentration of ion inside the cell
Given that the extracellular pH is 7.4, we can convert this to H+ concentration using the fact that pH = -log[H+]. Therefore, [H+ ]out = 10^(-pH). We know that the extracellular pH is 7.4, so [H+ ]out = 10^(-7.4).
Additionally, we know that the membrane potential is -60 mV, so E = -0.06 V.
Plugging these values into the Nernst equation, we can solve for the intracellular pH as follows:
-0.06 = (8.314 * T / (1 * 96,485)) * ln ([H+ ]out / [H+ ]in)
The temperature (T) needs to be provided in Kelvin. Once you have the temperature value, you can rearrange the equation and solve for [H+ ]in. However, since we don't have the temperature value given, we cannot provide a numerical answer for the intracellular pH.