# Why titration is a good method for determining concentrations

Hi,

I was wondering why titration is a good method for determining concentrations. For instance to determine the concentraion of a weak acid HAc with a strong base NaOH,

NaOH+HAc --> NaAc+H20

Does this reaction have an equilibrium factor of inifinite or a very big one so that equivalent amounts of weak acid and base just neutralize eachother?

Can u determine the concentration of a weak acid with a weak base? I dont think so because the total reaction doesnt have a very big equilibrium factor.

Kind regards

vulgar

epenguin
Homework Helper
Gold Member

You need to just study the basics in your book as the questions are not very well formulated. E.g. what is 'equilibrium factor'?
However it is more interesting to study the book when you do have some questions, so fine.

You'll find NaAc if it is mentioned, perhaps it is in elementary chemistry, is just a manner of speaking. You get HAc molecules all right and then you get Na+ ions and Ac- ions. Think of NaAc molecules as not really existing.

Also I'd say 'neutralised' is a bit of a metaphor. What does it mean?

What happens in titration of e.g. a weak acid HAc with a strong base NaOH is the first starts not very dissociated mostly in the form HAc but enough is dissociated to give a fairly high concentration of H+ which makes the solution acid, or rather that is what acid solution means. You will probably have to do calculations where you work out the [H+] of such solutions. As you add NaOH which is all dissociated as Na+ and OH- nearly all the added OH- reacts

...........OH- + HAc -> H2O + Ac- ..............(1) .

However at the same time because of the equilibria a small amount of the OH- reacts

....................OH- + H+ -> H2O..............(2)

So the H+ concentration decreases or, we say, the pH increases. The pH increases steadily, most of the added OH being taken up in the first reaction until you have added NaOH to he same amount as the total acetic acid that was there at first, and then there is no more HAc there to yield protons in the first reaction. So then only the second reaction can happen and [H+] diminishes steeply i.e. pH increases steeply, changing quite a lot with the one drop of added base. You can see this happen either with an indicator that changes colour in the right pH range, or by measuring pH with a pH meter. That is what is happening when the strong base 'neutralises' the HAc.

Your question "Can u determine the concentration of a weak acid with a weak base? " is good.

I think you can though it is not so often done, but necessary to understand anyway. The equivalence point would then be the pH exactly halfway between the pKa's of the weak acid and base. This would be the point where pH is changing most steeply (inflection point) as acid or base is added. The nearer the pK's the shallower the slope. If they are far enough apart you could find an appropriate indicator.

If not all this is understandable it is because I'd have to write a textbook chapter. Keep and come back to it when you have gone through the book and lessons.

Hi epenguin,

I will rephrase my question. You want to determine the concentration of HAc with NaOH, so when you precisely add the equivalent amount of NAOH your solution jumps to a much higher pH, which you can visualise with an indicator. My statement is that this can only happen when the equilibrium constant K (not the factor: was an error) of the overall acid base reaction:

OH- + HAc -> H2O + Ac- ..............(1) .

is infinite. If it werent infinite you would have to add a bit more OH- for the HAc to completely react. Ofcourse the K constant isnt infinite for (1) but probably very big, so you make a tiny intrinsic error. My question was: is the assumption of the infinite K-factor right? If the K-constant werent very big then titration would not be a method to determine concentrations.

Thats why I also asked the same question about the weak acid with the weak base. I think the K constant of the overall reaction isnt so big, so you make a bigger intrinsic error in this case because there is no strong acid or base present. Is this also correct? Also there is no sudden jump here, so next to the intrinsic error you make an error because the indicator doesnt register the jump very well.

epenguin
Homework Helper
Gold Member

Hi epenguin,

I will rephrase my question. You want to determine the concentration of HAc with NaOH, so when you precisely add the equivalent amount of NAOH your solution jumps to a much higher pH, which you can visualise with an indicator. My statement is that this can only happen when the equilibrium constant K (not the factor: was an error) of the overall acid base reaction:

OH- + HAc -> H2O + Ac- ..............(1) .

is infinite. If it werent infinite you would have to add a bit more OH- for the HAc to completely react. Ofcourse the K constant isnt infinite for (1) but probably very big, so you make a tiny intrinsic error. My question was: is the assumption of the infinite K-factor right? If the K-constant werent very big then titration would not be a method to determine concentrations.

Thats why I also asked the same question about the weak acid with the weak base. I think the K constant of the overall reaction isnt so big, so you make a bigger intrinsic error in this case because there is no strong acid or base present. Is this also correct? Also there is no sudden jump here, so next to the intrinsic error you make an error because the indicator doesnt register the jump very well.

For all the first part it is hard to answer - you need to formulate the equations then it will be less vague and you will begin to see.

Your last sentence is fairly close and I think I said something related. If the pK's are close together it will be hard to find a suitable indicator, specially as these are themselves acids/bases, and if they are monobasic will change form no more steeply than what you are titrating. You will be able to see an inflection in the pH/acid or base added curve at equivalence. For acetic acid and ammonia for example, the pKa's are far enough apart you could find an indicator for in between.

Borek
Mentor

For acetic acid and ammonia for example, the pKa's are far enough apart you could find an indicator for in between.

Can be difficult. See titration curves - both solutions 0.1M.

Shameless plug: both curves generated and exported from BATE pH calculator with just a few clicks.

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Hi,

For the equilibrium constant K of the reaction

NaOH + HAc -> H2O + NaAc ..............(1) .

I was thinking this, (1) is a combination of the following

HAc -> H+ + Ac- K=Ka
NaOH -> Na+ + OH- K=very big
Na+ + Ac- -> NaAc K=very big
H+ + OH- -> H2O K=1/Kw=1014=very big

Seeing that deltaG=-RTlnK, you can add these reactions for a total deltaG and you will still get a very big overall K factor

K=[NaAc][H2O]/[NaOH][HAc]

So that when you add an equivalent amount of base, all the weak acid will have reacted and you have a pH jump and you can use the formula

N(acid)xV(acid)=N(base)xV(base)

But when you have a weak acid and a weak base, for instance ammonia and HAc:

NH3 + HAc -> NH4+ + Ac- ..............(2) .

(2) is a combination of the following

HAc -> H+ + Ac- K=Ka=not very big
NH3 + H+ -> NH4+ K=Kb=not very big

So now the overal reaction doesnt have a big K constant

K=[NH4+][Ac-]/[HAc][NH3]

So for almost all the HAc to react you need way more NH3, and then you cant use

N(acid)xV(acid)=N(base)xV(base)

Borek
Mentor

It can be done exactly, no need for approximations.

We are looking for the equilibrium constant of the neutralization reaction:

HAc + NH3<-> Ac- + NH4+

$$K = \frac {[Ac^-][NH_4^+]}{[HAc][NH_3]}$$

We know that

$$K_a = \frac {[Ac^-][H^+]}{[HAc]}$$

$$K_b = \frac {[NH_4^+][OH^-]}{[NH_3]}$$

(Kb can be also defined with water concentration in denominator, it doesn't change much)

$$K_w = [H^+][OH^-]$$

From Ka definition:

$$\frac {[Ac^-]}{[HAc]} = \frac {K_a}{[H^+]}$$

from Kb and Kw:

$$\frac{[NH_4^+]}{[NH_3]} = \frac{K_b}{[OH-]} = \frac {K_b[H^+]}{K_w}$$

Substituting into K:

$$K = \frac {[Ac^-]}{[HAc]}\times \frac {[NH_4^+]}{[NH_3]} = \frac {K_a}{[H^+]} \times \frac {K_b[H^+]}{K_w} = \frac {K_a K_b}{K_w}$$

For acetic acid and ammonia K = 3x104, that's not small equilibrium constant.

But the really important thing is how fast does pH change around equivalence point. And I am not going to repeat the discussion that I linked to.

Ok, I see it now, I didnt see that Kw incoming there. I thought to have a sudden pH change, it would be enough to have a large K, but the important thing for a sudden change is the difference in Ka and Kb values? I assume that when you have a sudden change you will always probably find a good indicator. From your HAc-ammonia plots, there is no sudden change at all, you would need and indicator that changes right at pH 7

Borek
Mentor

Ok, I see it now, I didnt see that Kw incoming there. I thought to have a sudden pH change, it would be enough to have a large K, but the important thing for a sudden change is the difference in Ka and Kb values?

Large K yes, but obviously 104 is not enough. Difference between Ka and Kb is not a good indicator, Ka = Kb = 1 is a perfect combination of acid and base.

From your HAc-ammonia plots, there is no sudden change at all, you would need and indicator that changes right at pH 7

No, that won't work either.

Why wouldnt that work? Is the equivalent point pH not always 7 in the case of a weak base and a weak acid?

So determining a weak acid concentration with a weak base is not a good method because the K value isnt large enough for a sudden pH change

Borek
Mentor

Why wouldnt that work? Is the equivalent point pH not always 7 in the case of a weak base and a weak acid?

For the reasons explained on the pages linked to several hours ago.

For now it is enough that you remember a rule of thumb, that for full color change property of the solution that is responsible for the indicator color must change by about 2 units.

I ll go for this one then!

But sticking in a pH meter and titrating untill pH 7 should work though right

Borek
Mentor

But sticking in a pH meter and titrating untill pH 7 should work though right

More or less yes. Unfortunately it is less accurate than it may seem, as pH is also a function of temperature and ionic strength fo the solution. Other techniques should give better results, for example conductometric detection of the equivalence point. Or perhaps pH meter, but combined with a Gran plot.