[Rutherford]

If a mixture of Na₂CO₃ and NaHCO₃ is titrated with HCl, why is the amount of NaHCO₃ in the original solution determined by the formula (V₂-V₁)*n_HCl if V₁ is spent for Na2CO3, shouldn't it be (V₂-2V₁)*n_HCl because there is an amount of HCO₃^- made after V₁ is spent for CO₃^2-?

[Hunter2]

Describe more in detail how do you do the analysis, which indicator do you use, or which pH do you titrate if you use a pH-probe.

Let say you have only Carbonate. Then V₁ = V₂ what means no hydrogen carbonate present.

If you have Hydrogen carbonate present then V₁ < V₂ and the result is

V₂-V₁ = V_{hydrogen carbonate}

[Rutherford]

I am not doing the titration, I was solving a problem: http://portal.acs.org/portal/PublicWebSite/education/students/highschool/olympiad/pastexams/CTP_005471 it's 1st, c).
-If there was only Na₂CO₃ in the solution, then V₁ would be spent for:
CO₃^2-+H⁺ HCO₃^-
-V₂ would be spent to titrate all the HCO₃^- made from the first proccess.

In the problem there is a "mixture" of NaHCO₃ and Na₂CO₃. V₁ is used for Na₂CO₃ and V₂ would be used for HCO₃^- ions that come from NaHCO₃ and the HCO₃^- ions that are made from the first equation, so the volume used to titrate only NaHCO₃ would be V₂-2V₁ and not V₂-V₁. Am I right? If not, where I am wrong?

[Hunter2]

No, you are wrong. Who tells you the amount of the additional HCO₃^- is the same as from the carbonate.

Again its a two step titration.  Sodium carbonate requires 2*V₁ for total neutralization. V₁ for Carbonate and again V₁ for Hydrogen carbonate what is actually already V₂.

So it means in this case V₁ = V₂ and V₂-V₁ = 0 what means no free hydrogen carbonate is present.

In the case of the mixture the  volume for hydrogen carbonate is larger and V₂-V₁ > 0 ==> free hydrogen carbonate

[Rutherford]

No  , V₂ should be 2V₁, see the curve before the last one: http://www.chemguide.co.uk/physical/acidbaseeqia/phcurves.html#top
Is V₂ measured from 0, or from V₁(cm³)? Maybe here is the source of mine confusion.

[Hunter2]

V₁ is measured from 0 , V₂ is measured from V₁ otherwise it doesn't work.

In your thinking if V₂ is also measured from 0, then you are right if no hydrogen carbonate is present V₂ = 2*V₁

but what will you do if you have more hydrogen carbonate, the equation is V₂ = 2* V₁ + V_x. This you cannot calculate then.

[Rutherford]

"V1 is measured from 0 , V2 is measured from V1 otherwise it doesn't work."
I didn't know this, so I got confused thinking that V₂ is measured from 0. Thanks for clearing that up.

[Rutherford]

Another issue here. On this site http://www.titrations.info/acid-base-titration-sodium-hydroxide-and-carbonate volume spent for carbonates is V₂-V₁, but if V₂ is calculated from V₁ then it should be V₁-V₂. What is the truth here?

[Borek]

What is the truth here?

Truth is, V₁ and V₂ are just symbols and they don't have to denote the same thing each time they are used.

[Rutherford]

Well, that is pretty ambiguous. The only solution when i get a problem is, to look whether V₂ is lower or higher than V₁.