The free energy generated by ion movement in the cell is used by the cell to do

Question

The free energy generated by ion movement in the cell is used by the cell to do work. Compute the minimum number of millimoles of sodium that would be needed to pump one millimole of calcium ions if the following concentrations were present in the cell. Assume the temperature to be 37 degree C and recall that R=0.008314 kJ/mol-K. Na^+(aq, 36mM) rightarrow Na^+(aq, 5.25 mM) Ca^2+ (aq, 39mM) rightarrow Ca^2+ (aq, 1.50 times 10^2 mM) The equation for the conversion of graphite to carbon dioxide is C(s) + O_2(g) CO_2(g) and the change of Gibbs free energy of the reaction can be found by summing the Gibbs energies of the products less the Gibbs energies of the reactants. Standard Gibbs free energies of formation can be found here. To find the expression for the net reaction, add the two chemical equations together. To find the net change in free energy, add the free energy of each reaction together.

Explanation / Answer

The amount of free energy released or consumed can be calculated from the equation

G = RT ln [Xin ]/ [Xout]

G = (2)(273+37) x ln (39/150)
G = -835.19 cal/mole

G = -0.835 cal/mole

Now so

A mole of sodium ions (Na+) moving down this concentration gradient releases 0.835 kcal of free energy.

G = (2)(310) ln (x /5.25)
0.835 kcal = (2)(310) ln (36 /x)

ln (36/x) = 1.34 x 10^-3

x = 36 mmol

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