Question

A solution contains 0.1 m total carbonate (H2CO3 + HCO3- + CO32-).

a. If the pH is 6, find the concentration of each carbonate species present.

b. If the solution contains also 10-4 m Ca2+, is it saturated, unsaturated, or supersaturated with respect to CaCO3?

Answer 1

a) H₂CO₃(acid) <---------------> H⁺ + HCO₃^- (conjugate base)
Dissociation Constants and PK a Values for carbonic acid at 25°C
P_Ka1 = 3.6 at 25 °C
Use henderson hasselbalch equation,
P^H =  P_Ka1 + log₁₀ [ HCO₃^- / H₂CO₃]
6 = 3.6 + log₁₀ [ HCO₃^- / H₂CO₃]
2.4 = log₁₀ [ HCO₃^- / H₂CO₃]
251.1886 =   [ HCO₃^- / H₂CO₃]
[H₂CO₃] = [HCO₃^-] / 251.1886 -------------(1)
HCO₃⁻ <-----------------> CO₃²⁻ + H⁺
P_Ka2 = 10.329 at 25 °C
6 = 10.329 + log₁₀ [ CO₃²⁻ / HCO₃⁻]
[HCO₃⁻] * 4.6881*10^-5 =  [ CO₃²⁻] -----------(2)
H₂CO₃ + HCO₃^- + CO₃^2- = 0.1 --------- (3)
substitute (1) &(2) in equation (3)
[HCO₃^-] / 251.1886 +[HCO₃⁻] * 4.6881*10^-5 + [ HCO₃^-] = 0.1
1.004027 * [HCO₃^-] = 0.1
  [HCO₃^-] = 0.099598 m
substitute the above value inequations (1) and (2) to get [H₂CO₃] & [CO₃^2-]
[H₂CO₃] = 0.099598 / 251.1886 = 3.9651 *10^-4 m
[CO₃²⁻] = 0.099598* 4.6881*10^-5 = 4.6692*10^-6 m

b) calculate ionic strength for Ca+2 ,I = 1/2 (mz2) = 1/2 (10-4 * 22) =2*10-4
   m is molality Z is charge , I is ionic strength
   log γ+ = -0.509 | Z+| (I)1/2 = -0.509* |2|*(2*10-4)0.5 = -0.01439
   γ+ = - log(0.01439) = - (- 1.84173)
     γca2+ = 1.84173(for Ca2+)
for CO32- , I = 1/2 ( 4.6692*10-6 * 22) = 9.3384*10-6
       log γ- = -0.509 |-2| * (9.3384*10-6)0.5 = -3.11088*10-3
  γ- ( for CO32-) = 2.50711
Ion activity product for Ca2+ = aca2+ =  γca2+ * [Ca2+] = 1.84173*10-4
Ion activity product for CO32- = aco32- = 2.50711 * [4.6692*10-6 ] = 1.1706*10-5
Ion activity product =  aca2+ * aco32- = 1.84173*10-4 * 1.1706*10-5 = 2.1559 *10-9
IAP =   2.1559 *10-9
Ksp of CaCO3 at 25o C is 3.36*10-9
Saturation Index,SI = log (IAP / KSP) = log (2.1559 *10-9 / 3.36*10-9 ) = 0.64163
  SI = 0.64163 > 0
If SI > 0 then the solution is supersaturated with respect to CaCO3 .