Final answer:
The equilibrium potential for cation X, given the internal concentration of 150mM and external concentration of 75mM, can be calculated using the Nernst equation.
Step-by-step explanation:
The student has asked to calculate the equilibrium potential for a cation X with a given concentration inside and outside of a cell. To calculate this, we use the Nernst equation, which is used to determine the electrical potential across a cell membrane that balances the concentration gradient of ions. The formula for calculating the equilibrium potential (E) for a monovalent cation is as follows:
E = (RT/zF) * ln([X⁺]_out / [X⁺]_in)
Where:
R is the gas constant (8.314 J/(mol K))
T is the absolute temperature in Kelvin
z is the charge number of the ion
F is the Faraday constant (96485 C/mol)
[X⁺]_out is the concentration of the cation outside the cell
[X⁺]_in is the concentration of the cation inside the cell
At standard human body temperature (which is approximately 37°C or 310 K), and for monovalent cations like X⁺, the simplified Nernst equation at physiological temperature becomes:
E = (61.5 mV) * log([X⁺]_out / [X⁺]_in)
Given that the concentration of cation X⁺ inside the cell is 150mM and outside is 75mM, we can plug in the values:
E = (61.5 mV) * log(75 mM / 150 mM)
After calculation, the equilibrium potential, E, will be found which tells us the voltage necessary to balance the concentration gradient of cation X⁺. This contributes to the overall resting membrane potential which is a critical aspect of cellular function.