Can you please help me in solving this question of Ionic Equilibria?

Question

The question is on my blog
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please help me solving this.

Answer 1

I like this kind of chellenge problem.
Well, "When 100ml of CaCl2 solution (1.780g/L) is mixed with 100ml Na2CO3 solution (1.700g/L) ....". It really makes this problem difficult.

24. Following is a theoretical deduction (simplify [CO3(2-)] to [A-] and [HCO3-] to [HA]):
H2O == H+ + OH-, Kw
HA == H+ + A-, Ka
A- + H2O == HA + OH-, Kw/Ka
Kw/Ka = [OH-]*[HA]/[A-] = [OH-]^2/[A-]
[OH-] =sqrt( [A-]*Kw /Ka )
pOH = 0.5 (pKw - pKa) - 0.5*log[A-]
pH = 7 + 0.5pKa + 0.5*log([A-]) = 12 + 0.5*log([A-]).
Thus, unless [CO3(2-)] would be less than 0.01M, pH is greater than 11. Since the given Na2CO3 solution density 1.700g/L is far from water density of 1.00g/ml, the correct answer must be (B) between 11-12.

25. I think the problem is wrong: if there is an "initial" concentration of CO3(2-) in the mixture, there must be a "Final" concentration of CO3(2-) in the mixture. That somehow implies the [CO3(2-)] asked for is before precipitation. But we know that Na2CO3 is fully dissociated in solution, and 100ml got diluted to 200ml (by mixing) would only half the CO3(2-) concentration. Adjusting pH to 10.0 would only half the CO3(2-) concentration again (see below). The original CO3(2-) concentration BEFORE mixing must not be too lower than 1M, since the density of th solution is significantly different from th density of water (1g/ml). There is however no choice around 0.01M - 1M. Therefore, the problem very possibly asks for the FINAL CO3(2-) concentration after precipitation.
Now, we know:
HCO3- <==> H+ + CO3(2-), pKa2 = 10.00
Ka2 = [H+]*[CO3(2-)]/[HCO3-]
Since pH = 10. = pKa2, we have: [CO3(2-)] = [HCO3-]
?? I do not know how to get the answer close to any choice given.

26. Must be (B).
Since Ksp for Ca(OH)2 is given 6.46x10^-6, and [OH-] is given 1x10^-4, [Ca++] could be as high as 646M before precipitation. On the other hand, both [Ca++] and [CO3(2-)] are not too far from 1M. Ksp for CaCO3 is only 3.5x10^-9 thus precipitation of CaCO3 must be there.