[guidob]

I want to add some pH curves to my assignments (It's not necessary but I can't stand the lack of them and I'm also interested in a general method for making them). The point is that after trying for hours I can't get a way to obtain the values in the middle of some buffer solution.

In particular, the curve I have problems with is the pH of a solution of Na2CO3 10ml 0.1N adding HCl 0.1N.

I know can get the pH of the solution without HCl or the pH when Na2CO3 is completely replaced by NaHCO3 and so on but not the pH in the middle of that events.

I don't want estimates, I want a method so I can finish a code to obtain the ideal data. Thanks in advance.

[Borek]

Fishing theory:

http://www.chembuddy.com/?left=pH-calculation&right=toc

Fishing rod:

http://www.chembuddy.com/?left=BATE&right=pH-calculator

fish:

[guidob]

That's the curve! Thanks for your reply, the fact is that I don't know much about pH and for some reason fail trying to calculate those points.

Then I used Henderson-Hasselbalch approximation but it fails in the extremes


I'm not supposed to make these curves (or calculate pH of any point) but I want to know how and put them in my report.

So I'm possibly wrong but when I have only Na2CO3 I should treat it like a weak base of CO₃^2- and its kb = 2.1·10^-4. So I solve the quadratic equation:
$$ x^2 + kb\cdot x - kb\cdot concentration = 0 $$
Then to the solution x₁ I obtain pH from:
$$ pH = 14 + log(x_1) $$
And obtain 11.65
I know that if I add some HCl the following reaction takes place:
Na₂CO₃ + HCl  NaHCO₃ + NaCl
And with de NaHCO₃:
CO₃^2- + H⁺  HCO3^-
Then if I add 10 ml of HCl all the Na₂CO₃ will be replaced by NaHCO₃ and I calculate that pH knowing that HCO3^- kb = 4.8·10^-11 and the concentration is:
$$ Concentration = \frac{0.1\cdot \textit{ml added}}{\textit{total ml}} $$
Then solving again the quadratic equation:
$$ x^2 + kb\cdot x - kb\cdot concentration = 0 $$
And again:
$$ pH = 14 + log(x_1) $$
Obtaining 8.35
For the intermediate points my logic was: take the pH of both, apply exponential to get the [H⁺] concentrations, multiply it by their volumen, add the H⁺ divide them by the total volume to gent the [H⁺] of the solution and apply -log() to get the pH. But that doesn't work.

[Borek]

HCO3^- kb = 4.8·10^-11

Is it? That's not what I see in tables.

Then solving again the quadratic equation:
$$ x^2 + kb\cdot x - kb\cdot concentration = 0 $$
And again:
$$ pH = 14 + log(x_1) $$
Obtaining 8.35

And that doesn't look like a correct way of finding pH of the amphiprotic salt. The correct approach is described in the lectures I linked to.

[guidob]

You mean that the kb of HCO₃^- is 2.4·10^-8 ? I'm pretty lost right now. Could you show me the generic approach?, my course didn't analysis pH of solutions (it's a general chemistry class in electromechanical engineering), they just give us the graphics to use in titration.

[Borek]

You mean that the kb of HCO₃^- is 2.4·10^-8

That's much better.

Could you show me the generic approach?

Sorry, it is not something that can be explained in a single post. That's why I linked to the lectures.

Have you seen the amphoteric salt pH page? There is a formula derived there.

[guidob]

Have you seen the amphoteric salt pH page? There is a formula derived there.

I took a look but I couldn't understand much
I've also been reading Chang's "general chemistry"  but I couldn't find the approach with a solution of a salt of a polyprotic acid and a strong acid.

Sorry, it is not something that can be explained in a single post. That's why I linked to the lectures.

I see I don't want to bother you either, I just want a way to obtain the tuples in the curve so I can make my plots. I need several points so I can't use a calculator and I have to hard-code the algorithm to obtain that tuples.

There's no easy way to obtain the pH in this particular case? I know that there're three kind of mixtures in this case:
Na₂CO₃ + NaHCO₃
NaHCO₃ + H₂CO₃
H2CO3 + HCl
But I don't know a method to obtain the pH other than in a strong acid strong base solution.

[Borek]

Have you seen the amphoteric salt pH page? There is a formula derived there.

I took a look but I couldn't understand much

Don't worry about details, only the final formula derived.

I've also been reading Chang's "general chemistry"  but I couldn't find the approach with a solution of a salt of a polyprotic acid and a strong acid.

That's because these are not simple systems.

In general - you need a different approach for initial pH and for end points (both the final and the middle), and different approach in between. Close to end point there is no simple method.

http://www.titrations.info/titration-curve-calculation

http://www.titrations.info/acid-base-titration-curve-calculation

Na₂CO₃ + NaHCO₃

Use Henderson-Hasselbalch equation.

NaHCO₃ + H₂CO₃

Use Henderson-Hasselbalch equation.

H2CO3 + HCl

This is one is quite tricky. The simplest approach calls for ICE table with initial H⁺ from the HCl and change being carbonic acid dissociation. Unfortunately, this approach doesn't take CO₂ loses into account.

[guidob]

Thank you so much!
This is what I have so far:

This is one is quite tricky. The simplest approach calls for ICE table with initial H+ from the HCl and change being carbonic acid dissociation. Unfortunately, this approach doesn't take CO2 loses into account.

Could you explain this better?

Nevermind I used a calculator for the last points.
Thank you for helping me When I have time I'll read to the lectures you gave to me. It's an interesting topic.



Now I only need to edit that plot, but the important part was the data.