Acid-Base Indicator End Point

Key Concepts

• An acid-base indicator is a dye that changes colour when pH changes.⁽¹⁾
• An acid-base indicator can be modelled as a weak Arrhenius acid or base in which the undissociated molecule (eg, HIn(aq)) is a different colour from its ion (In^-(aq)):⁽²⁾

  HIn(aq)

  ⇋

  In-(aq)

  +

  H+(aq)

• An acid-base indicator can be modelled as a Brønsted-Lowry conjugate acid-base pair in which the acid, HIn(aq), is a different colour to the base, In^-(aq):

  HIn(aq)

  +

  H2O(l)

  ⇋

  In-(aq)

  +

  H3O+(aq)

• K_In is the value of the dissociation constant (ionisation constant) of an acid-base indicator⁽³⁾:

  Arrhenius model	KIn	=	[H+][In-] [HIn]
  Brønsted-Lowry model	KIn	=	[H3O+][In-] [HIn]

• The colour of an acid-base indicator solution is determined by the ratio of the concentration of undissociated molecules to the concentration of its ions:

  [HIn]/[In^-] > 10 then solution is the colour of HIn molecules

  [HIn]/[In^-] < ¹/₁₀ then solution is the colour of In^- molecules

• The end point (or end-point) of an acid-base titration is when the indicator changes colour during a titration.⁽⁴⁾

  The colour at the end point is referred to as the middle tint.

• At the end point (end-point):

  This condition is met: [HIn] = [In^-] and the colour of the indicator is an equimolar mix of the colour of HIn and the colour of In^-

  Therefore: K_In = [H⁺]   or   K_In = [H₃O⁺]

  So : pK_In = pH

• The colour-change interval, or pH range, of an indicator can be predicted:

  pH = pK_In ± 1

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What is an Acid-Base Indicator?

An acid-base indicator is a substance, a dye or pigment, that changes colour when the pH of the solution changes.

The dye or pigment making up the acid-base indicator is commonly an organic molecule that is either a weak acid (HIn) or a weak base (InOH or In).

If the acid-base indicator is a weak acid, then the undissociated molecule (HIn) is in equilibrium with the products of its dissociation: hydrogen ions (H⁺) and its corresponding anion (In^-) as shown in the balanced chemical equation below:

Weak acid (HIn) acting as an indicator: HIn(aq) ⇋ H⁺(aq) + In^-(aq)

If the acid-base indicator is a weak base, then the undissociated molecule (InOH) is in equilibrium with the products of its dissociation: hydroxide ions (OH^-) and its corresponding cation (HIn⁺) as shown in the balanced chemical equation below:

Weak base (InOH) acting as an indicator: InOH(aq) ⇋ OH^-(aq) + In⁺(aq)

If the acid-base indicator is a weak base that does not include hydroxide in its structure, then the indicator molecule (In) hydrolyses in water and is in equilibrium with the products of this reaction: hydroxide ions (OH^-) and its corresponding cation (HIn⁺) as shown in the balanced chemical equation below:

Weak base (In) acting as an indicator⁽⁵⁾: In(aq) + H₂O(l) ⇋ OH^-(aq) + HIn⁺(aq)

We could use Brønsted-Lowry theory of acids and bases instead of the Arrhenius definitions above to write chemical equations for the proton-transfer reactions between weak acids or weak bases in solvent water as shown below:

The corresponding descriptions of acid-base indicators would then be:

• An acid-base indicator that is a Brønsted-Lowry acid is in equilibrium with its conjugate base.
• An acid-base indicator that is a Brønsted-Lowry base is in equilibrium with its conjugate acid.

Because undissociated acid-base indicator molecules exist in equilibrium with their ions, we can write an expression for this dissociation.

Let K_In represent the equilibrium constant for the dissociation of the indicator molecule, then :

• A weak acid (HIn) acting as an acid-base indicator:

  HIn ⇋ In- + H+					HIn +H2O ⇋ In- + H3O+
  KIn	=	[In-][H+] [HIn]		or		KIn	=	[In-][H3O+] [HIn]

• A weak base (In) acting as an acid-base indicator:

  In + H2O ⇋ HIn+ + OH-
  KIn	=	[HIn+][OH-] [In]

You can find published tables that give the value of K_In⁽⁶⁾ for different acid-base indicators at 25°C.
The table below provides some examples:

Notice that the values of K_In are all small, less than 10^-3.
This means that the protonated, or acid, indicator molecule, HIn, is largely undissociated in aqueous solutions at 25°C, that is, [HIn] is much greater than [In^-].
Ofcourse, this is just another way of saying that the indicator is a weak acid (in this case).

For example, we could represent the dissociation (ionisation) of the acid-base indicator phenolphthalein (HIn) into hydrogen ions (H⁺) and its ions (In^-) as shown below:

Since K_In is very small, the equilibrium position lies well to the left favouring the undissociated HIn molecules (unionised HIn molecules).
In an aqueous solution of phenolphthalein at 25°C, the concentration of HIn molecules will be much greater than the concentration of In^-, and also much greater than the concentration of H⁺.

Why do Acid-Base Indicators Change Colour?

The first useful theory for why acid-base indicators change colour was proposed by W. Ostwald in 1891:

We can represent this as shown below:

This means that the colour of the acid-base indicator in an aqueous solution is a mixture of 2 colours: the colour of the undissociated molecule and the colour of its product ions.

• If the concentration of undissociated indicator molecules is much larger than the concentration of its ions, then we see the colour of the undissociated molecules.

  Weak acid acting as an indicator: [HIn] >> [In^-] then the colour of the solution is the colour of HIn

  Weak base acting as an indicator: [InOH] >> [HIn⁺] then the colour of the solution is the colour of InOH

• If the concentration of undissociated indicator molecules is much smaller than the concentration of its ions, then we see the colour of the ions.

  Weak acid acting as an indicator: [HIn] << [In^-] then the colour of the solution is the colour of In^-

  Weak base acting as an indicator: [InOH] << [HIn⁺] then the colour of the solution is the colour of HIn⁺

Let's consider a weak acid (HIn) acting as an acid-base indicator in order to understand why an acid-base indicator changes colour.

If we increase the concentration of H⁺(aq) by adding acid, then, by Le Chatelier's Principle, the equilibrium position shifts to the left to consume some of the added H⁺(aq).
This means that some of the In^-(aq) molecules will also be consumed so the concentration of In^-(aq) decreases.
It also means that more HIn(aq) molecules will form, so the concentration of [HIn(aq)] increases.
So, increasing [H⁺(aq)] increases the ratio of [HIn]:[In^-] and we see more colour due to undissociated HIn molecules than we see colour due to the In^- ions.

If, on the other hand, we decrease the concentration of H⁺(aq) by adding some base (such as OH^-) to react with the H⁺, then, by Le Chatelier's Principle, the equilibrium position shifts to the right to produce more H⁺.
This means that some of the HIn(aq) must dissociate to produce H⁺(aq) and more In^-(aq), so concentration of HIn(aq) decreases and the concentration of In^-(aq) increases.
So, decreasing [H⁺(aq)] decreases the ratio of [HIn(aq)]:[In^-(aq)] and we see more of the colour due to the In^- ions.

We could model the behaviour of a weak acid acting as an indicator in aqueous solution using the Brønsted-Lowry theory of acids and bases.
The indicator molecule (HIn) acts as a Brønsted-Lowry acid by donating a proton (H⁺) to a water molecule (H₂O) to produce the oxidanium ion (H₃O⁺, also known as the oxonium or hydronium ion) and the conjugate base of the acid (In^-) in a proton transfer reaction.
The acid molecule (HIn) is a different colour its conjugate base (In^-).

Using Le Chatelier's Principle:

• increasing [H₃O⁺] increases ratio [HIn]:[In^-]

  colour due to HIn increases, and due to In^- decreases

• decreasing [H₃O⁺] decreases ratio [HIn]:[In^-]

  colour due to In^- increases, and due to HIn decreases

Let's use phenolphthalein indicator as an example.
Phenolphthalein is colourless in acidic aqueous solution (high concentration of H⁺) but pink in basic or alkaline aqueous solution (low concentration of H⁺).
For the reaction: HIn(aq) ⇋ In^-(aq) + H⁺(aq)
If the concentration of H⁺(aq) is increased the equilibrium position shifts to the left favouring the production of undissociated HIn(aq) molecules.
Undissociated phenolphthalein molecules must therefore be colourless (because solution is colourless in acidic solution).
Similarly, when the concentration of H⁺(aq) is decreased the equilibrium position shifts to the right favouring the production of In^-(aq) ions.
The ions produced by the dissociation of phenolphthalein molecules must be pink (because phenolphthalein is pink in basic solutions).
We can summarise all this information as shown below:

An acid-base indicator changes colour when the concentration of H⁺(aq) changes because this shifts the equilibrium position to the right or left and varies the ratio of [HIn]:[In^-]

Since we calculate pH using the concentration of hydrogen ions as shown below:

pH = −log₁₀[H⁺]     or     pH = −log₁₀[H₃O⁺]

then we can also say that an acid-base indicator changes colour when the pH of the solution changes.

At What pH Does An Acid-Base Indicator Change Colour?

Let's continue to use phenolpthalein as an example of acid-base indicator:

In acidic solution ([H⁺] is high), the solution is colourless because [HIn(colourless)]>>[In^-(pink)]
In basic or alkaline solution ([H⁺] is low), the solution is pink because [HIn(colourless)]<<[In^-(pink)]

So when does the phenolphthalein indicator change colour from colourless to pink?
What is the concentration of hydrogen ions at the point when phenolphthalein changes colour?
At what pH does phenolphthalein change colour?

Let's start by examining the equilibrium expression for the dissociation (ionisation) of phenolphthalein:

Recall that for aqueous solutions at a given temperature K_In is a constant, and we know that changing H⁺(aq) concentration changes the ratio of [HIn]:[In^-], so let's rearrange the expression for K_In to isolate the [H⁺] term:

In an acidic solution, in HCl(aq) for example, [HIn] >> [In^-], that is, [HIn]/[In^-] > > 1, and the solution appears colourless.
As we decrease [H⁺] by addinga little NaOH(aq) for example, [HIn] decreases, [In^-] increases, that is [HIn]/[In^-] decreases and approaches 1.
If we add an excess of OH^-, the [H⁺] becomes very small indeed (K_w=[H⁺][OH^-]= 10^-14 at 25°C), so [HIn] << [In^-], and [HIn]/[In^-] < 1 and the solution is pink.

The point at which the phenolphthalein changes colour is the point at which there is an equimolar mixture of both HIn and In^-, that is, [HIn]/[In^-] = 1, or put another way:

[HIn] = [In^-]

or

So, the expression for the point at which phenolphthalein indicator changes colour becomes:

When the concentration of hydrogen ions in solution is the same as the value of the dissociation constant for the indicator, then the indicator has changed colour.
When [H⁺] > K_In, the solution is "acidic" and the colour of the solution is the colour of undissociated HIn molecules.
When [H⁺] < K_In, the solution is "basic" and the colour of the solution is the colour of the ions, In^-.
When [H⁺] = K_In the colour of the solution is half-way between the colour of HIn molecules and the colour of In^- ions. This colour is referred to as the middle tint of the indicator.

If we take the negative logarithm (base 10) of both sides of the equation above, we produce another useful result:

An acid-base indicator changes colour when the pH of the solution is the same as pK_In.
And it is this result which makes acid-base indicators useful in acid-base titrations.
It tells us that, if we choose the right indicator, we can match the pH of the "neutralised" solution with the pH of the middle tint of the indicator.
The colour change of the indicator tells us to end the titration, to stop adding any more base to the acid because the solution has been "neutralised".
Hence the pH at which the acid-base indicator has reached its middle tint is referred to as the end point of a titration.

In the table below we have calculated the pK_In, and hence pH at the end point of a titration, for some different acid-base indicators. You might like to confirm the results of these calculations for yourself.

Notice that different indicators have different values for pK_In, and hence the pH at which they achieve their middle tint colour is different.
In the table below we show the colours of these indicators at low pH and high pH values as well as the pH of the middle tint (pH = pK_In):

In the table above, "low pH" refers to a pH less than pK_In, and, "high pH" refers to a pH greater than pK_In:

• low pH : pH < pK_In
• high pH : pH > pK_In

Phenolphthalein, for example, is colourless at "low pH" when pH < 9.4, and it is pink at "high pH" when pH > 9.4
At pH = 9.4 the phenolphthalein solution is half-way between colourless and pink, that is, it is a pale pink colour.

Look carefully at the colours in the table above. Could you pick out exactly when phenolphthalein, for example, is half-way between colourless and pink?
Can you actually pin-point the line at which alizarin yellow R is mid-way between yellow and violet?
Ask a few people to point to where these positions are on the table, I bet you get a whole range of answers!!

Acid-Base Indicator Colour-Change Interval (pH Range)

The change from the low pH colour to the high pH colour of an acid-base indicator is gradual, and the exact middle tint can be hard to determine visually.⁽⁷⁾

In general, the human eye has only a limited ability to detect either of the two colours when one of them is dominant.

In general, experience tells us that the acid-base indicator appears to have the:

• low pH colour if [HIn]/[In^-] > 10
• high pH colour if [HIn]/[In^-] < ¹/₁₀

We can use this information to calculate a range of pH values over which we see a change from the "low pH" colour to the "high pH" colour.

In the section above we arrived at an expression for the relationship between [H⁺], [HIn]/[In^-], and K_In as shown bellow:

If we take the negative logarithm (base 10) of each term in the expression we get the result:

So, if we take the "low pH" case, we will see the colour-change when [HIn]/[In^-] > 10:
Let's find the lower pH limit by using the minimum value of [HIn]/[In^-] = 10
then

pH = pK_In − log₁₀10

pH = pK_In − 1

Colour change at low pH occurs between pK_In and pK_In − 1

Now let's find the upper limit for the pH of the colour-change, that is, [HIn]/[In^-] = ¹/₁₀ :

pH = pK_In − log₁₀(¹/₁₀)

pH = pK_In − −1

pH = pK_In + 1

Colour change at high pH occurs between pK_In and pK_In + 1

So now we can define a pH range over which the colour of indicator changes from one colour to the other as:

(pK_In − 1) < pH(middle tint) < (pK_In + 1)

which can also be written more concisely as:

pH range = pK_In ± 1

So, for phenolphthalein with a K_In = 4.0×10^-10 :

pH of middle tint = pK_In = −logK_In = −log(4.0×10^-10) = 9.4

pH range = pK_In ± 1 = 9.4 ± 1

Since phenolphthalein changes colour from colourless to light pink to pink between 8.4 and 10.4, this is referred to as the "colour-change interval", or as the "pH range" of the indicator.

Calculation of pH Range vs Published Values

No two people "see" colour the same way, they will use different terms to refer to the same colour, and they will detect the "middle tint" at different pH values, depending on their ability to discriminate between colours.
Added to that problem are others: the concentration and the intensity of the colour of the "acidic" and "basic" forms of the acid-base indicator can vary, altering our perception of the pH at which the "end point" or "middle tint" occurs.
Hence the published "pH range" of an indicator can be different to our predicted ranges calculated above.

Compare our calculated values (pK_In ± 1) with published values for the pH range of indicators shown in the table below:

In general, predicted pH ranges are 2 pH units but the published results for pH range are smaller than this. Some examples are given below:

Methyl red : published 3.1 to 4.4 (total interval 1.3 pH units)

bromophenol blue: published 3.0 to 4.6 (total interval 1.6 pH units)

When it comes to answering questions in an exam, use the information you are provided with.
If you are given a table of values for acid-base indicators for "low pH colour", "high pH colour" and a pH range for the colour change then use the pH range given to you to answer the question.
If the table gives you K_In (or pK_In) and the "low pH colour" and "high pH colour" of the indicator, then you will need calculate the pH range (pH range = pK_In ± 1)

Problem Solving: Acid-Base Indicator End Point