Calculate pH of Citric Acid at Various Concentrations

[[-Log10H+]]

Hello, i would really appreciate it if someone could help me with this problem. I would like to know the pH of citric acid at various concentrations.

2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 15%, 20%.

From what i have read it has something to do with its pKa value which for citric acid is: 3.06. The formulas i have seen on wikipedia and other places are too complicated for me to solve and although i have found an on-line calculator it seems very inaccurate.

http://www.sensorex.com/support/education/pH_calculator.html

It gives results of:
5% citric acid = 1.87 pH - Lemon juice is 5% and has a pH of around 2.3

Could someone please work these out for me or show me how to do it.

p.s. 50g per litre is 5% right? or 50g per 0.950 litre... (of water)

Also this is not for my homework.

 

[[-Log10H+]]

That calculator gives accurate results for vinegar and 25% citric acid with water but doesn't seem to give an accurate result for lemon juice which is often cited as:

"a 5-7% solution of citric acid with a pH of 2.3"

The calculator say 5% citric acid has a pH of 1.87, the calculator matches the results of another calculator i downloaded so i doubt its an error. Can someone please tell me what's going on is the calculator accurate? why the discrepancy?

Perhaps there is something basic in lemon juice that increases its pH to 2.3? If so what is it?

Please help.

 

[symbolipoint]

Easy suspect could be differences between molarity and activity due to ionic strengths. (...but from which direction?)

 

[chaoseverlasting]

http://en.wikipedia.org/wiki/Citric_acid

That shows citric acid has a basicity of 4. So if its a 5% solution, we can say 5 grams in 100 grams of water. It has a molar mass of 192 gms, so 5/192 = no of moles present.

If the density isn't give, we can assume it to be 1gm/ml.

Therefore, 5/192 moles in 100 ml of soln.

1 mole gives 4 moles of H+, therefore 5*4/192 moles of H+ present in 100 ml.

5*4*10/192 moles of H+ in 1 litre.

-log(200/[192*1000]) should be your pH. Which comes out to be 2.98.

 

[[-Log10H+]]

Thankyou very much for your reply, i should have said at the beginning that I'm not studying chemistry or anything and i only have a gcse in it so I'm about as smart as rodney :rofl:. At the moment what i basicaly want to know is why the discrepancy between the reported pH values for lemon juice (2.3), and the calculator which gives 1.84 for 5% citric acid, also now you have done a calculation that gives 2.98.

I hope you can see my predicament, who's right:

a) the chemist (2.98)
b) the calculator (1.84)
c) the masses (2.3)

Also if only one is right why do the others get it wrong?

EDIT: You said citric acid has a basicity of 4, i can't find that on the wikipedia page you posted, are you saying its part acid part basic? i thought basicity was dependant upon concentration? sorry for the millions of questions but i think I'm more confused now than when i started! :)

 

[Borek]

1.86 or something close is the right answer (ionic strength taken into account) for the 5% citric acid. 5.000% citric acid solution is exactly 0.2650 M. You may check these results using my pH calculator (see signature; I don't remember if free trial version contains citric acid in the database, but even if not, you can enter its three pKa values manually). Calculator shows equilibrium concentrations of all ions present in the solution, so it is not hard to check that result is consistent with all equations describing solution equilibria.

chaoseverlasting calculation assumes full dissociation (wrong) then he divides the final result by 1000 (wrong) probably to convert mL to L - but he already did the conversion earlier multiplying by 10. After two errors his result is completely off. Not to mention the fact that citric acid has three protons only, not four. Fourth proton can dissociate only in very specific situations, when citric acid is a part of multicore complex.

Lemon juice is most likely not only citric acid, but also contains some citrates mixture (ie part of the acid is neutralized, which rises juice pH). Note also that lemon juice pH is not a constant thing, it depends on the fruit ripeness. In fact first modern pH meter (Model G) was designed to help decide if lemons are ready to be harvested :)

 

[[-Log10H+]]

Excellent! thankyou for your explanation. I have a couple more questions but these are comparatively easy.

First off 5% acetic acid has a ph of 2.42 so i take it citric acid must be a much stronger acid? This may sound like a daft question but i read somewhere that there was a difference between acidity and ph but i didn't understand what it meant. So just checking.

Second, a ph of 1.84 seems rather strong would this burn on contact with skin? Do you know of any data regarding safety of acid's what ph is safe for skin contact.

 

[Borek]

Citric acid is stronger than acetic. pH is a measure of equilibrium H+ concentration - trick is, weak acids (ie most acids you will deal with) are not strong enough to be fully dissociated, thus pH of their solutions is higher (concentration of H+ lower) than you may expect. All these formulas that you didn't understood deal with the equilibrium calculations.

pH 2 acid is not strong enough to be really dangerous - as long as the contact is not prolonged. That's about pH of gastric juice - if you have ever vomited you know it didn't kill your mouth. Just rinse skin with water and you'll be OK.

 

[chaoseverlasting]

chaoseverlasting calculation assumes full dissociation (wrong) then he divides the final result by 1000 (wrong) probably to convert mL to L - but he already did the conversion earlier multiplying by 10. After two errors his result is completely off. Not to mention the fact that citric acid has three protons only, not four. Fourth proton can dissociate only in very specific situations, when citric acid is a part of multicore complex.

Thank you. I didnt know the basicity was 3, but should have seen it cause the 4th OH group forms a Hydrogen bond with the carbonyl group to form a stable six membered ring. As for the dividing by 1000, sorry, that was a completely careless mistake.

 

[[-Log10H+]]

Thanks for all your help Borek. Just a quick question, i was wondering whether in your opinion electronic pH meters are accurate?