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⁺] = 2.3 mM) to the inside (where [Na+] = 79 mM) when the membrane potential is -19 mV and the temperature is 37°C.

a) -1820 kJ·mol⁻¹

b) 7280 J·mol⁻¹

c) -10950 J·mol⁻¹

d) 10950 J·mol⁻¹

Answer 1

The change in Gibbs free energy for transport required to move 1 mol of Na⁺ ions from the outside to the inside of the cell is -1820 kJ·mol⁻¹.

Step-by-step explanation:

To calculate the change in Gibbs free energy for transport required to move 1 mol of Na⁺ ions from the outside to the inside of the cell, we need to use the Nernst equation and the formula for Gibbs free energy.

The Nernst equation is given by ΔG = -nFΔE,

where n is the number of moles of electrons transferred,

F is Faraday's constant (96485 C/mol),

ΔE is the change in potential,

Plugging in the values, we get ΔG = -1 mol × 96485 C/mol × (-19 mV)

= 1835.215 J/mol.

Converting this to kJ/mol, we get -1.835215 kJ/mol. Therefore, the correct answer is option a) -1820 kJ·mol⁻¹.