pH Range (Indicators) question

[Henreezy]

I've just been looking back at some of the earlier chapters we've covered, and I've realised that I don't fully understand how indicators function. Do they change colour once the pH is below or above the pH range to their respective acid-base form, or do they change based on the middle of the pH range e.g. for Phenolphthalein 8.2-10 the middle number is 9.1, above that number it could be the base form, and below it, the acid form. From a logical standpoint it would make more sense if the indicators changed at the lower and upper limits of the range. i.e. <8.2 and >10 (base form) respectively for phenolphthalein

[lzxnl]

An acid-base indicator is really just a weak acid or a weak base that changes colour depending on if it is protonated or not. Let us assume that the indicator in its neutral form is an acid and denote it by HA, so that the conjugate base is A-. The Henderson-Hasselbalch equation tells us that pH=-log (Ka)+log([A-]/[HA]) where Ka is the acid dissociation constant of HA
Therefore, where pH=-log (Ka)=pKa, the concentrations of A- and HA are equal and this is the middle of the colour change region of the indicator. Now if we increase pH by one, then log([A-]/[HA]) must increase by one as well, so the ratio [A-]/[HA] increases by a factor of ten, meaning that the base form is more predominant. It has been established that we can first see a colour change when the ratio [A-]/[HA] is from 0.1 to 10, i.e. pH is within one point of the pKa either side. This is where the leeway comes from; the fact that enough of HA forms to just see the colour of HA or vice versa with A-.

Remember, acid base reactions with weak acids and bases are equilibrium questions; the reaction HA+H2O <=> A- + H3O+ goes both ways, and from Le Chatelier's principle, if there is too much H3O+ disturbing an equilibrium, the reaction will reverse, producing more acid HA. Le Chatelier's principle can be used to understand why the colour even changes; when the pH changes, [H3O+] changes and so the amounts of HA and A- will change, thereby giving a colour change.

Of course, this reasoning could equally apply to an indicator that was a base in its neutral form as B and in acid form appear as HB+. The point is, the reason why indicators are used for different ranges is due to their acid/base strength and this determines at what pH the acid and base forms are present in equal concentrations, the pKa.

Now what happens with phenolphthalein is that it evidently has a pKa of around 9. This means that the acid form first changes into the base form noticeably at pH=8.2 as you've mentioned. The reason why we can use this indicator for any titration that has an equivalence point at 8.2<pH<10 is because if we are doing a proper titration, one between a strong base and a weak acid, the endpoint will be sharp and although the colour will first change at pH=8.2, even if the equivalence point is at pH=9, for instance, the sharp nature of the endpoint means that the difference in volume between a pH of 8.2 and a pH of 9 is...miniscule. It really doesn't affect the results to four significant figures. This is why the indicators can be used for that range.

If the titration equivalence pH is outside this range, however, then the ratio [A-]/[HA] is either too large or too small, meaning that we will only predominantly have one colour. Therefore, when the equivalence point does arrive, we will either not see it because the colour hasn't changed or because the colour has changed for too long. This is why the right indicator needs to be chosen.

I hope this long-winded and admittedly poorly structured rant helps

[Henreezy]

I liked the explanation and I understood most of what was said but the use of acidity constants in your explanation was pretty confusing to me; I'm pretty sure in our textbook it doesn't make an appearance until Chapter 17.

[lzxnl]

I know; I apologize for that, but using acidity constants makes explanations easier.
As the book may tell you, Ka, the acid dissociation constant for a reaction HA+H2O<=>A- + H3O+, Ka=[A-]*[H3O+]/[HA] at equilibrium. Clearly, if you increase Ka, then more of the acid is ionized and hence the acid strength is larger. Like with H+ concentrations, Ka values may vary across several degrees of magnitude, so we use a pKa system, where pKa=-log Ka, just like with pH and this is where the pH and pKa link comes in.
If we take negative logs of both sides of the Ka equation, we obtain pKa=-log([A-]*[H3O+]/[HA])=-log[H3O+]-log([A-]/HA])
Rearranging and noting that pH=-log[H3O+], we get pKa+log([A-]/[HA])=pH as I stated above.
I hope this now makes a bit more sense.

[gfernandez95]

An acid-base indicator is really just a weak acid or a weak base that changes colour depending on if it is protonated or not. Let us assume that the indicator in its neutral form is an acid and denote it by HA, so that the conjugate base is A-. The Henderson-Hasselbalch equation tells us that pH=-log (Ka)+log([A-]/[HA]) where Ka is the acid dissociation constant of HA
Therefore, where pH=-log (Ka)=pKa, the concentrations of A- and HA are equal and this is the middle of the colour change region of the indicator. Now if we increase pH by one, then log([A-]/[HA]) must increase by one as well, so the ratio [A-]/[HA] increases by a factor of ten, meaning that the base form is more predominant. It has been established that we can first see a colour change when the ratio [A-]/[HA] is from 0.1 to 10, i.e. pH is within one point of the pKa either side. This is where the leeway comes from; the fact that enough of HA forms to just see the colour of HA or vice versa with A-.

Remember, acid base reactions with weak acids and bases are equilibrium questions; the reaction HA+H2O <=> A- + H3O+ goes both ways, and from Le Chatelier's principle, if there is too much H3O+ disturbing an equilibrium, the reaction will reverse, producing more acid HA. Le Chatelier's principle can be used to understand why the colour even changes; when the pH changes, [H3O+] changes and so the amounts of HA and A- will change, thereby giving a colour change.

Of course, this reasoning could equally apply to an indicator that was a base in its neutral form as B and in acid form appear as HB+. The point is, the reason why indicators are used for different ranges is due to their acid/base strength and this determines at what pH the acid and base forms are present in equal concentrations, the pKa.

Now what happens with phenolphthalein is that it evidently has a pKa of around 9. This means that the acid form first changes into the base form noticeably at pH=8.2 as you've mentioned. The reason why we can use this indicator for any titration that has an equivalence point at 8.2<pH<10 is because if we are doing a proper titration, one between a strong base and a weak acid, the endpoint will be sharp and although the colour will first change at pH=8.2, even if the equivalence point is at pH=9, for instance, the sharp nature of the endpoint means that the difference in volume between a pH of 8.2 and a pH of 9 is...miniscule. It really doesn't affect the results to four significant figures. This is why the indicators can be used for that range.

If the titration equivalence pH is outside this range, however, then the ratio [A-]/[HA] is either too large or too small, meaning that we will only predominantly have one colour. Therefore, when the equivalence point does arrive, we will either not see it because the colour hasn't changed or because the colour has changed for too long. This is why the right indicator needs to be chosen.

I hope this long-winded and admittedly poorly structured rant helps

Wow, how do you know all of this already? Have you been reading ahead? Just wondering.

[lzxnl]

I went to the Australian Science Institute's Chemistry Summer School in January this year and the school taught me a wealth of chemistry which really serves to highlight what VCE does not cover.