Question

During chemical weathering, forsterite is dissolved by the carbonic acid in rainwater. The weathering reaction is:

Mg2SiO4 forsterite + 4H2CO3 (aq) ? 2Mg2+ + 4HCO3- + H4SiO4 (aq) Use the thermodynamic data from Appendix II, source 2, for the following calculations.

4a. Calculate the Keq for this weathering reaction at 25 �C.

4b. If the reaction is at equilibrium, using Le Cha?telier�s principle, predict what would happen if Mg2+ ions were added to the solution

4c. Using Le Cha?telier�s principle, predict what would happen to the equilibrium constant if the reaction occurred at a higher temperature.

4d. Calculate the Keq for this reaction at 40 �C. Does the solubility of forsterite increase or decrease with increasing temperature? How does this result compare with your prediction in part (c).

Appendix II standard state = 298.15 k 10^5 pa

Mg2SiO4 =
Delta G f= 2056.7 kJ mol^-1
Delta H f= 2175.7 kJ mil ^-1
S= 95.2 J mol^-1 k^-1

4H2CO3 =
Delta G f= 623.14 kJ mol^-1
Delta H f= 699.09 kJ mil ^-1
S= 189.31 J mol^-1 k^-1

2mg^2+ =
Delta G f= 455.4 kJ mol^-1
Delta H f= 467.0 kJ mil ^-1
S= 137 J mol^-1 k^-1

4HcO3^- =
Delta G f= 586.8 kJ mol^-1
Delta H f= 689.93 kJ mil ^-1
S= 98.4 J mol^-1 k^-1

H4SiO4 =
Delta G f= 1307.9 kJ mol^-1
Delta H f= 1457.3 kJ mil ^-1
S= 180 J mol^-1 k^-1

Answer 1

Mg2SiO4 forsterite + 4H2CO3 (aq) ? 2Mg2+ + 4HCO3- + H4SiO4 (aq)

4a. Calculate the Keq for this weathering reaction at 25 �C.

For KEq... we need dG

dG = -RT*lnK

K = exp(-dG/(RT))

dG = Gproducts - Greactants = (2*455.4 + 4*586.8+1307.9) - (2056.7+4*623.14) = 16.64 kJ/mol = 16640 J/mol

then

K = exp(16640 /(8.314*298)) = 825.7

4b. If the reaction is at equilibrium, using Le Cha?telier�s principle, predict what would happen if Mg2+ ions were added to the solution

if we add Mg+2 ions, then we favour REACTANTS or a shift toward left, since the Mg+2 will increase the Q to products, so the equilibrium must increase the reactants to maintain the Qvalue

4c. Using Le Cha?telier�s principle, predict what would happen to the equilibrium constant if the reaction occurred at a higher temperature.

Keq --> if T increass; we will need the enthalpy of reaction:

Hrxn = Hproducts- Hreactants = 2*467 + 4*689.93 + 1457.3 - (2175.57 + 4*699.09) = 179.09 kJ/mol = 179090 J/mol

since this is acid + mineral reaction, expect endothermic reaction, meaning it needs energy

so, for an increase of T, expect a shift toward products, that is, the right

4d. Calculate the Keq for this reaction at 40 �C. Does the solubility of forsterite increase or decrease with increasing temperature? How does this result compare with your prediction in part

ln(K2/K1) = H/R(1/T1-1/T2)

ln(k2/825.7) = 179090 /8.314* ( 1/298 - 1/(40+273))

k2 = 825.7*exp(3.4641) =

k2 = 26379.210