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Acid-Base Indicator End Point

Key Concepts

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Indicator Concepts

An indicator is a Brønsted-Lowry conjugate acid-base pair of which the acid is one colour and the base a different colour:

indicator in acid form + H2O conjugate base of indicator + H3O+
one colour     a different colour    

In aqueous solution, the indicator molecule in its acid form can donate a proton, H+, to a water molecule which results in the formation of the conjugate base of the indicator and the conjugate acid of a water molecule, H3O+.

Most indicators are organic molecules with very complex structures, so the following abbreviations are commonly used:

The reaction above can now be rewritten:

indicator in acid form + H2O conjugate base of indicator + H3O+
HIn + H2O In- + H3O+

By Le Chatelier's Principle we can see that:

Consider an acid-base titration in which base from a burette (buret) is added to acid in a conical (erlenmeyer) flask containing a drop of indicator as shown in the diagram on the right.

Consider first the reaction between the acid, H+(aq), and the base, OH-(aq), occurring in the conical flask:

H+(aq) + OH-(aq) → H2O(l)

before equivalence point equivalence point after equivalence point
acid in excess neither acid nor base in excess base in excess
moles acid > moles base moles acid = moles base moles acid < moles base

 
← base
 
← acid
 

Now consider what is happening to the indicator molecules in the conical flask as the base is being added to the acid:

acid-base reaction excess H+ moles H+ = moles OH- excess OH-
indicator reaction before end point end point after end point
dominant indicator reaction In- + H+ → HIn neither reaction dominates HIn → In- + H+
dominant indicator species HIn is dominant species neither species dominates In- is dominant species
relative concentration
of species
[HIn] > [In-] [HIn] = [In-] [HIn] < [In-]
observed colour HIn colour mixture of HIn and In- colours In- colour

The end point of the titration as indicated by the indicator is the point during the titration at which the concentration of the acid form of the indicator is the same as the concentration of base form of the indicator.

Why do different indicators change colour at different pH values?
Because different indicators have different values for their dissociation (ionisation) constants.

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Dissociation (Ionisation) Constants for Indicators, KIn

The general equation for the dissociation (ionisation) of an indicator molecule, HIn, is given below:

HIn + H2O In- + H3O+
or
HIn(aq) In-(aq) + H+(aq)

An indicator molecule, HIn, is actually a weak acid.
An aqueous solution of indicator, HIn(aq), will contain the undissociated HIn molecules, as well as the ions In-(aq) and H+(aq).
Therefore we can write an equilibrium expression, an equation to represent this equilibrium condition.
Let KIn represent the dissociation constant for the indicator:

KIn = [In-][H3O+]
[HIn]
or KIn = [In-][H+]
[HIn]

The values of KIn and pKIn1 for a number of different aqueous solutions of acid-base indicators at 25oC are given below:

indicator name pKIn KIn
methyl orange 3.4 4.0 x 10-4
bromophenol blue 3.8 1.6 x 10-4
methyl red 4.9 1.3 x 10-5
chlorophenol red 6.0 1.0 x 10-6
bromothymol blue 7.1 7.9 x 10-8
phenolphthalein 9.4 4.0 x 10-10
thymolphthalein 10.0 1.0 x 10-10
alizarin yellow R 11.2 6.3 x 10-12

Notice that the values of KIn are all small, less than 10-3.
This means that the protonated indicator molecule, HIn, is largely undissociated in aqueous solutions at 25oC, that is, [HIn] is much greater than [In-].

Knowing the value of KIn for a particular indicator allows us to perform calculations.

For example, KIn for bromothymol blue is 7.9 × 10-8, so the chemical equation becomes:

HIn In- + H+
KIn = 7.9 × 10-8

so the equilibrium expression for bromothymol blue becomes:
KIn = [In-][H+]
[HIn]
= 7.9 × 10-8

The equilibrium expression also allows us to predict the colour of an indicator at the end point of an acid-base titration.

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End Point pH

The dissociation (ionisation) of the acid form of the indicator, HIn, is represented as:
HIn + H2O In- + H3O+

and the equilibrium expression for this dissociation (ionisation) reaction is:

KIn = [H3O+][In-]
[HIn]

At the end point, the concentration of undissociated protonated indicator molecules, HIn, is equal to the concentration of its conjugate base, In-, that is

[HIn] = [In-]

So,

KIn = [H3O+][In-]
[HIn]

Therefore, at the end point,

[H3O+] = KIn
or
[H+(aq)] = KIn

and

-log10[H3O+] = -log10KIn
or
-log10[H+(aq)] = -log10KIn

Since pH = -log10[H+]

this means that at the endpoint :

pH = pKIn

So now we can calculate the pH at which any acid-base indicator will change colour, as long as we known the value of its dissociation constant!

indicator name KIn pKIn = -log10KIn = pH at end point
methyl orange 4.0 × 10-4 3.4 3.4
bromophenol blue 1.6 × 10-4 3.8 3.8
methyl red 1.3 × 10-5 4.9 4.9
chlorophenol red 1.0 × 10-6 6.0 6.0
bromothymol blue 7.9 × 10-8 7.1 7.1
phenolphthalein 4.0 × 10-10 9.4 9.4
thymolphthalein 1.0 × 10-10 10.0 10.0
alizarin yellow R 6.3 × 10-12 11.2 11.2

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Indicator Colour

The dissociation (ionisation) of the acid form of the indicator, HIn, is represented as:
HIn + H2O In- + H3O+

and the equilibrium expression for this dissociation (ionisation) reaction is:

KIn = [H3O+][In-]
[HIn]

We can rearrange this expression to express the ratio of [In-] to [HIn]:

  KIn  
[H3O+]
= [In-]
[HIn]

The colour of the indicator at any pH is determined by the ratio [In-]:[HIn]

As base is added to a mixture of indicator and acid, [H3O+] decreases, so the value of [In-]:[HIn] increases, so the indicator has increasingly more of the colour of the base form and less of the acid form.
That is:


At low pH, the colour of HIn will be dominant.
At high pH, the colour of In- will be dominant.

Tables of KIn and/or pKIn also include the colour of the solution at low and high pH.

indicator name KIn pKIn = -log10KIn low pH colour
(HIn doninant)
high pH colour
(In- dominant)
methyl orange 4.0 × 10-4 3.4 red yellow
bromophenol blue 1.6 × 10-4 3.8 yellow blue
methyl red 1.3 × 10-5 4.9 red yellow
chlorophenol red 1.0 × 10-6 6.0 yellow red
bromothymol blue 7.9 × 10-8 7.1 yellow blue
phenolphthalein 4.0 × 10-10 9.4 colourless pink
thymolphthalein 1.0 x 10-10 10.0 colourless blue
alizarin yellow R 6.3 × 10-12 11.2 yellow violet

At the end point, [HIn] = [In-] so we expect the colour of the solution at the end point to be an equal mixture of the HIn colour and the In- colour.

indicator
name
KIn pKIn low pH
colour
end point
colour
high pH
colour
methyl orange 4.0 × 10-4 3.4 red orange yellow
bromophenol blue 1.6 × 10-4 3.8 yellow green blue
methyl red 1.3 × 10-5 4.9 red orange yellow
chlorophenol red 1.0 × 10-6 6.0 yellow orange red
bromothymol blue 7.9 × 10-8 7.1 yellow green blue
phenolphthalein 4.0 × 10-10 9.4 colourless pale pink pink/purple
thymolphthalein 1.0 × 10-10 10.0 colourless light blue blue
alizarin yellow R 6.3 × 10-12 11.2 yellow pinky-orange violet

No two people "see" colour the same way, they will use different terms to refer to the same colour, and they will detect the "end point" differently, depending on their ability to discriminate between colours.
For these reasons, the pH for the colour change of an acid-base indicator is given as a range of pH values rather than as a single value:

indicator
name
KIn pKIn low pH
colour
pH range for
colour change
high pH
colour
methyl orange 4.0 × 10-4 3.4 pH < 3.1 3.1 - 4.4 pH > 4.4
bromophenol blue 1.6 × 10-4 3.8 pH < 3.0 3.0 - 4.6 pH > 4.6
methyl red 1.3 × 10-5 4.9 pH < 4.4 4.4 - 6.2 pH > 6.2
chlorophenol red 1.0 × 10-6 6.0 pH < 5.2 5.2 - 6.8 pH > 6.8
bromothymol blue 7.9 × 10-8 7.1 pH < 6.2 6.2 - 7.6 pH > 7.6
phenolphthalein 4.0 × 10-10 9.4 pH < 8.3 8.3 - 10.0 pH > 10.0
thymolphthalein 1.0 × 10-10 10.0 pH < 9.4 9.4 - 10.6 pH > 10.6
alizarin yellow R 6.3 × 10-12 11.2 pH < 10.0 10.0 - 12.0 pH > 12.0

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1. Relationship between KIn and pKIn:
pKIn = -log10KIn
KIn = 10-pKIn