Question

Calculate the change in Gibbs free energy for transport required to move 1 mol of Na+ions from the outside of the cell (where [Na⁺]=3.9mM ) to the inside (where [Na⁺]=83mM ) when the membrane potential is −17mV and the temperature is 37∘C.

A. 6240 J⋅moln⁻¹
B. −6240 kJ mol⁻¹
C. −1520 J.mol⁻¹
D.​ 9520 J⋅mol⁻¹

Answer 1

The change in Gibbs free energy for transport required to move 1 mol of Na+ ions from the outside of the cell to the inside can be calculated using the Nernst equation. The correct answer is option A.

Step-by-step explanation:

The change in Gibbs free energy for transport required to move 1 mol of Na+ ions from the outside of the cell to the inside can be calculated using the Nernst equation:

ΔG = -nF(Ecell)

Where ΔG is the change in Gibbs free energy, n is the number of moles of electrons transferred (1 mol for Na+), F is the Faraday constant (96485 C/mol), and Ecell is the cell potential.

First, convert the concentration of Na+ ions from mM to M:

[Na+] outside = 3.9 mM = 3.9 × 10⁻³ M

[Na+] inside = 83 mM = 83 × 10⁻³ M

Next, convert the temperature from degrees Celsius to Kelvin:

T = 37°C = 310 K

Now, calculate the cell potential:

Ecell = -17 mV = -17 × 10⁻³ V

Substituting the values into the equation:

ΔG = -1 × 96485 C/mol × (310 K) × (-17 × 10⁻³ V)

ΔG = 6240 J·mol⁻¹

Therefore, the change in Gibbs free energy for transport required to move 1 mol of Na+ ions is 6240 J·mol⁻¹. Therefore, the correct answer is option A.