The extracellular concentrations of Na+ and K+ are 135mM and 6mM, respectively.

The intracellular concentrations of Na+ and K+ are 10mM and 105mM, respectively.
The membrane potential is 75mV. For Na+/K+ ATPase, 3Na+ are exported and 2K+ are imported. Calculate the total free energy in KJ/mole required to transport the ions.

To calculate the total free energy required to transport the ions using the Na+/K+ ATPase, we can use the Nernst equation and the formula for the Gibbs free energy change (ΔG).

1. Calculate the electrical potential energy:
The electrical potential energy is given by the Nernst equation:
ΔG_electrical = (RT / zF) * ln(K_out/K_in)

Where:
R = Universal gas constant (8.314 J/(mol·K))
T = Temperature in Kelvin (usually 298K)
z = Charge of the ion (in this case, +1 for both Na+ and K+)
F = Faraday's constant (96485 C/mol)
K_out/K_in = Ratio of extracellular concentration to intracellular concentration for the respective ion

For Na+:
ΔG_electrical_Na = (8.314 * 298 / (1 * 96485)) * ln(135/10) [molar concentrations are used]

For K+:
ΔG_electrical_K = (8.314 * 298 / (1 * 96485)) * ln(6/105) [molar concentrations are used]

2. Calculate the entropy change (ΔS):
The entropy change can be calculated using the formula:
ΔS = R * ln(K_out/K_in)

For Na+:
ΔS_Na = 8.314 * ln(135/10) [molar concentrations are used]

For K+:
ΔS_K = 8.314 * ln(6/105) [molar concentrations are used]

3. Calculate the total free energy change (ΔG):
The total free energy change is calculated by adding the electrical and entropy changes:
ΔG = ΔG_electrical + TΔS

For Na+:
ΔG_Na = ΔG_electrical_Na + (298 * ΔS_Na)

For K+:
ΔG_K = ΔG_electrical_K + (298 * ΔS_K)

4. Calculate the total free energy required:
The total free energy required is given by the difference between the free energy change for Na+ and K+:
Total ΔG = 3 * ΔG_Na - 2 * ΔG_K

Therefore,
Total ΔG = 3 * (ΔG_electrical_Na + (298 * ΔS_Na)) - 2 * (ΔG_electrical_K + (298 * ΔS_K))

Plug in the appropriate values for each step and calculate using a calculator or programming software to find the total free energy required in KJ/mol.