One way to get the equilibrium constants for a reaction we are interested in is

Question

One way to get the equilibrium constants for a reaction we are interested in is to combine other reactions for which we know the constants. Show how this is done by deriving the equilibrium constant for the ion exchange reaction between calcite and gypsum anhydrite, shown below:

CaCO3 (s) + H+ + SO4=    HCO3 + CaSO4 (s)

(a) Combine, by addition or subtraction, the Keq values for the flowing reactions (at STP) to get the K’eq (at STP) for the above ion exchange reaction

CaCO3 (calcite, s) + H+ Ca2+ + HCO3                   log K’so1 = 1.11

CaSO4 (s) Ca2+ + SO4=                                                 log K’so2 = -4.58

(b) Derive an equation that expresses K’eq in terms of the K’so listed above.

(c) The ratio of the concentrations of bicarbonate to sulfate measured in vent water obtained off the coast of Washington is 0.9, while the pH of these fluids is 8.4. Could these vent waters be in equilibrium with both gypsum and calcite phases simultaneously?

Explanation / Answer

answer 1) to get our desired equation we reversed the 2nd equation so that K=1/k

as log K'so2 = -4.58 so k'sO2 = 2.63 *10-5

KSO2 = 1/2.63 *10-5= 38.022*103

Ca2+ + SO42-    ---->     CASO4        

CaCO3 (calcite, s) + H+ Ca2+ + HCO3                   log K’so1 = 1.11 and kso1 = 12.88

adding the above two equation we get

CaCO3 (s) + H+ + SO4=    HCO3 + CaSO4 (s)       Kc = k'so1 * KSO2 = 12.88 *38.022*103 = 489.72 *103

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