Most of the cells in your body pump potassium ion inward to

Most of the cells in your body pump potassium ion inward to maintain an inward K+ concentration that is 35 times the external concentration. a) For a nerve cell with a membrane potential of-60 mv, what is the Delta G (at 37 degree C) for the inward transport of K+ ions? b) For the nerve cell in part a), what is the maximum number of K+ ions that can be pumped inward by the hydrolysis of one ATP molecule if the ATP/ADP ratio in the cell is 5:1 and the inorganic phosphate concentration is 10 mM (assume Delta G degree is -32 kJ/mol for ATP hydrolysis).

Solution

The formula to calculate Gibb\'s free energy is G = RT ln C2/C1 + FV.

We know R = 8.315 J/mol-K,

Converting 37 to absolute temperature

T = 37 + 273 = 310,

V = -0.06 V,

F is Faraday\'s constant = 96.5 kJ/mole-volt,

we know the concentration difference is 35 (C2/C1) [ln 35 = 3.5]

Substituting the given values in the formula

G = (8.315) (310) (3.5) * (96.5) (-0.06)

= 9021.8 - 5.79

= 9016 J/mol

= 9.016 kJ/mol