Compute the total Gibbs energy change in a system in which 13 mu mol of atmosphe

Question

Compute the total Gibbs energy change in a system in which 13 mu mol of atmospheric CO_2 combines with water to form 30 mu mol of H^+ and 15 mol of CO_3^2, which are present at concentrations of 10^-8 and 10^-7 M, respectively, in a system at 25 degree C. The reaction and the standard Gibbs energies of formation of the constituents are given below. The partial pressure of CO_2(g) in the atmosphere is 3 times 10^-4 bar. Assume that the volume of solution is large enough that dissolution of this amount of CO_2 does not change the concentrations of dissolved H^+ and CO_3^2- significantly, and that all activity coefficients are approximately 1.00. Is the reaction thermodynamically favorable? You must show all your works that support the answer. G_1 degree (kJ/mol) CO_2(g) -394.37 + H_2O_(1) -237.18 rightarrow 2H^+ 0.00 + CO_3^2 -527.9 In the system, CO_2(g) 3 times 10^-4 bar + H_2O_(1) nearly pure rightarrow 2H^+ 10^-8 mol/L + CO_3^2- 10^-7 mol/L

Explanation / Answer

We know that

G = G0 - RT ln Q

R = gas constant = 8.314 J / mol K

T= 298 K

G0 = Sum of G0 products - sum of G0 reactants

G0 = (-527.9) - ( -394.37 + (-237.18) = 103.65 KJ / mole

Q = [H+]^2 [CO3-2] / [pCO2]

Q = 10^-16 X 10^-7 / 3 X 10^-4

Q = 3.33 X 10^-20

lnQ = 2.303 X log Q = -44.86

G = 103.65 X 10^3 - 8.314 X 298 X (-44.86)

G = -7493.87 Joules / mole = -7.493 KJ / mole

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