[Henri]

I do not understand the following question: "An acid-base indicator has a pKa value of 4.0. At what pH will this indicator change colour?" The answer is 4.0 but I do not understand how to get it and why?

[Arkcon]

Well, try to take it step-wise.  What causes a pH indicator to change color?

[Henri]

I know this fact:
pKa = [H+][A-]/[HA] => [H+] = pKa [HA] / [A-]
and the colour of indicator change according to [H+]. Is the answer 4.0 because [HA] / [A-] = 1?
ie.  [H+] = pKa [HA] / [A-] = 4.0 * 1 = 4.0 ?

But I do not understand why this simplification could be made? Is it because there are weak-acids and weak-bases in the indicators?

[Arkcon]

The indicator is generally a weak acid or weak base, yes.

[Henri]

I think I should take now -log( ):

p[H+] = -log(4[HA] / [A-]) = p(4[HA]) - p[A-]

I make now an assumption that(because I know the answer, I try to come from the solution to the procedure):

-log(4[HA] / [A-]) = 4
=> 10^-4 = 4[HA] / [A-]
=> [HA] / [A-] = 10^-4 / 4

I do not see why this would be right? Alternatively, my method may be wrong?!

[ARGOS++]

Dear Henri;

Such calculations may be good, but you have to think about that as soon as both forms of the pH-Indicator exist the Indicator is changing its color. 
But our Eye is not able to detect such small changes!

By a Thumb rule you mostly can say that the range where the Indicator changes it Color is ± 1 pH Unit around.
To get you an Idea about the reality you may also read on:  "pH Indicators”

I hope it may be of help to you.

Good Luck!
                    ARGOS⁺⁺

[Henri]

Can someone show me step-by-step procedure including assumptions? I have still not got it. Please, help.

[Borek]

Indicator is a weak acid with two forms - protonated and not protonated - that have different colors. Try to calculate their relative amounts for pH=pKa, pH=pKa-1 and pH=pKa+1. Use just dissociation constant definition for that.

[Henri]

pH=pKa, pH=pKa-1 and pH=pKa+1. Use just dissociation constant definition for that.

I do not understand this part. Why pH=pKa? What do you mean by pH=pKa-1 and pH=pKa+1?

Dissociation constant: Kd = [H+][A-] / [HA], but I do not see what are you looking for? How can you solve the question using the latter information? Are you saying that if you have pKa = X for an indicator, the indicator will always change around pH = X ? I just do not understand why pH = pka?

I know this fact: pKw = pKa + pKb = 14, but it will not help me, will it?

[Borek]

Why pH=pKa?

Because I know you find something interesting there.

What do you mean by pH=pKa-1 and pH=pKa+1?

If pKa=4 then pH=pKa+1=5

Dissociation constant: Kd = [H+][A-] / [HA]

Solve for [A^-]/[HA] - you will have ratio on the LHS and pH with pKa on the RHS.

[Arkcon]

Can someone show me step-by-step procedure including assumptions? I have still not got it. Please, help.

I'm confused, by your confusion, if you will.   I said they were weak acids, or weak bases.  ARGOS⁺⁺: and Borek: have re-iterated, when the pH of the surroundings is successfully deprotonates a colorless acid form, as an example, you get the colored deprotonated form.  The calculation you're doing, I don't see it as necessicary to answer this question, or am I missing something?

[Henri]

I "understood" it when I read this:

"As indicators have a different coulour whn in the molecular form to when in the ionic form it seems logical to assume that the point of changing colour will be when there is 50% of both forms present i.e. the equilibrium HIn  H+ + In- lies exactly in the middle." http://ibchem.com/IB/ibnotes/full/aab_htm/18.6.htm

ie.
Ka =[H+][In-] / [HIn]
=> [In-] =  [HIn]

Thanks for every that have helped me

[Borek]

I "understood" it when I read this:

"As indicators have a different coulour whn in the molecular form to when in the ionic form

It doesn't have to molecular vs ionic, it can be ionic vs ionic as well.

What I prosposed to you was to calculate that at pH 1 unit below pKa there is 10 times more protonated form than non protonated, at pH=pKa thera eidentical cocncentrations of both, at pH one unit over pKa there is 10 times non protonated form. That clearly shows transition from one color to other. It is assumed that color changes at pKa, but in fact color change is a process that is visible in about 2 pH units span.