[hybris]

Hi I have a small problem, I need to find out what happens in a solution with the following ingredients and calculate the pH for the solution.

The solution contains:

1 litre of water
100 g NaCl
10 g Citric Acid (pka1=3,128, pKa2=4,761, pKa3=6,396, Molarweight = 210,14)
5g SodiumBensoate (pKb = 9,78, molarweight = 144,11)
4g Potassium Sorbate (pKa of sorbic acid is = 4,76 (pkb=?) molar weight= 150,22)

How do I put up the equation and what formulas should i use?
Do the citric acid dissolve in 2 steps or only the first H+?
I recon this will be sort of a buffered solution but how do i calculate the equivalence when i have one weak acid and in the soultion i will have atleast 3 bases (H2A-) from citric acid and bensoate- ions and sorbate- ions?
Also the sodium bensoate <==> Na+ + bensoate- reaction... will it be affected by the addition of NaCl???
It was 3 years since i studied chemistry last time and I completly forgot :..(

Any help would be greatly apriciated.

[Borek]

I would start calculating amount of bases (that is benzoate and sorbate) added and assuming they have stoichiometrically neutralized citric acid. That's not necesarilly true, but at least that will give some idea about what is going on in the solution.

Well, to be honest - I lied. I would not even try to calculate these things manually. I would start pH calculator (the one built in Buffer Maker)

Sad truth is that it is not possible to calculate pH of this solution - too high ionic strength. You can evaluate pH, but you won't ever get accurate result.

[hybris]

Hi again and thank You for Your fast answer Borek.

If I would like to give it a try anyway how would i set up the equation? (if i skip the salt part).

I can only find how to calculate equivalence between a weak acid and its own corresponding base.. how do i make the calculation for an acid and another weak acids corresonding base.

How do i set up the equation for equiv. with one acid and 2 different corresponding bases?

If I look at the solution i have (in moles):
citric acid 0,0476m
sodiumbensoate 0,0347m
potassiumsorbate 0,0357m

pKa1 of citric acid = 3,13 so it would "easily" give away those H+
pKa2 of citric acid = 4,76 and bensoic acid = 4,21 and sorbic acid 4,76;
this would to me mean that bensoic and sorbic "acid-"ions would take up "all" H+ from the first step in citric acid. If you add the moes of the bases (Sodium&potassium) you would get 0,0704m ( > 0,0476.)
For the remaining part the citric acid would have to let go of its second H+ and since the pKa for bensoic acid is lower than pKa2 for citric acid i would imagine that reaction is skewed towards bensoic acid. As for the pka of sorbic acid its equal to pKa2 of citric acid so i would imagine this is closer to 50/50 balance?

is the above correct or is my brain on vacation?

If it would be easier how would i calculate the balance for a solution that had (in moles)
citric acid 1 mole
sodium bensoate 0,5 mole
potassium sorbate 0,3 mole
that would give the 1 mole - 0,8 mole and the citric acid would only leave one of its H+ (greatly simplified since i know there is alway a balance relationship between all possible forms of the acid).

[Borek]

General approach:

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

For the remaining part the citric acid would have to let go of its second H+ and since the pKa for bensoic acid is lower than pKa2 for citric acid i would imagine that reaction is skewed towards bensoic acid. As for the pka of sorbic acid its equal to pKa2 of citric acid so i would imagine this is closer to 50/50 balance?

If by "skewed towards" you mean that benzoic acid is dissociated further, and if I understand what you mean - you are right.

Take a look at the equation (2):

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

(ignore Ind, it holds for every weak acid).

[hybris]

Hi again,

I have another question. Say I cheated and measured the pH of that solution and the pH was 3,3. Is it possible to calculate all equilibrium states for the different components independant of eahother then?
Like how much is H3A, H2A-...Sodium bensoate, bensoate-... and so on if i know the pH is 3,3?

Could i set up equations like
a mol citric acid added...at ph 3,3 I have x ions H3A, y ions H2A-, z ions HA2-...
b mol sodium bensoate.. at ph 3,3 i have a ions sodium bensoate, b ions sodium-b ions bensoate..

Like I just treat each component separatly since i know the pH (and what equation should i use then)?

Thanks.