[parinaz22]

My friends

Which of the following carbonate species would be present in significant concentrations in a solution of carbonic acid at pH=10
pKa1=6.46
pKa2=10.16

A)H2CO3 only
B)HCO3^- only
C)CO3 ^2- only
D)H2CO3 and HCO^-
E)HCO3- AND CO3^2-

The correct answer is E, but I do not know how to solve the problem.

Thanks

[Borek]

See the formula (2) derived here:

http://www.titrations.info/acid-base-titration-indicators

While the formula is listed in the context of indicators, it holds for every weak acid (just replace pK_Ind with pK_a). Do you see it now?

[parinaz22]

Thanks
but I study for GRE chemistry. we could not use calculator. How I could solve it without calculator?

Thanks

[dan2000]

simple way to think is that pKa indicates the pH in which 2 species are equal in conc.

for example, at pH 6.46, there would be equal conc. of H2CO3 and HCO3-.

at pH 10, which is close to pKa2 (10.17), we can say that most of them will be HCO3- and CO3-2

[mjc123]

A good rule of thumb is to say that when the pH is more than about 2 units below pKa, the protonated form is predominant; and when pH is more than about 2 units above pKa, the deprotonated form is predominant; within this range, there are significant concentrations of each. So in tis case, at a pH of 4 you would have predominantly H₂CO₃, at pH 13 you would have predominantly CO₃^2-; at pH 8.3 you would have mainly HCO₃^-, with a little of the other two. Of course there will be times when you need to determine, say, the small amount of conjugate base present in acid conditions (pH - pKa < -2), but for a qualitative question like this one, the rule of thumb is sufficient.

[Borek]

To chime in again - all the things dan and mjc mentioned are simple conclusions that you can get using the formula derived on the page I linked to. It doesn't require a calculator - it is all about finding the difference between pH and pKa (simple subtraction) and then estimating 10 to the power of the calculated number. You don't need exact value, just an estimate, and chemist that doesn't know what 10³ or 10^-5 is should be fired immediately

At pH 10 pH-pKa1 is 10-6.46, approximately 3.5, so the ratio of concentrations [HCO₃^-]/[H₂CO₃] is 10^3.5 - somewhere between 1000 and 10,000. Guess which one is present in negligible quantities. Now apply the same formula and the same approach to the second dissociation step.