pH curves and indicators

In a nutshell

During acid-base titrations, the point of neutralisation can be determined by the colour change from an indicator. Titration curves for acid-base titrations are produced using a pH meter to take pH readings. The pH of an acid can be increased by dilution, reducing the concentration of $H^+$ .

Equations

WORD equation	symbol equation
$pH=-log_{10}\ (concentration\ of\ acid)$	$pH=-log_{10}[acid]$
$pH=-log_{10}\sqrt{acid\ dissociation \ constant\times conc.\ of\ acid}$	$pH=-log_{10}\sqrt{K_a\times [acid]}$

Using pH meters

A pH meter allows you to measure the pH of a solution using a pH probe. Prior to recording the pH of a solution, the pH meter must be calibrated.

The calibration is carried out by immersing the pH probe in a solution of deionised water which will have a neutral pH of $7.0$ . Allow the reading to stabilise, then set the reading to $7.0$ . The calibration should be repeated with standard solutions of pH $4.0$ and $10.0$ . Rinse the probe after each calibration.

A reading can then be taken for the solution with unknown pH, by immersing the probe in to the solution and allowing the reading to set. If you are measuring multiple pH levels, the probe should be rinsed after each reading.

Acids and pH changes

The pH of an acid can be altered by diluting the solution as this will reduce the concentration of $H^+$ . A lower concentration of $H^+$ will increase the pH of an acid.

Strong acids

Strong acids can be diluted by factors of $10$ to increase the pH by $1$ as the concentration of $H^+$ is equal to the concentration of a strong acid.

$[H^+]=[strong\ acid]$

$pH=-log_{10}[H^+]$

$pH=-log_{10}[strong\ acid]$

Example

Sulfuric acid can be diluted in factors of $10$ to alter the pH. If $[H^+]=[acid]$ , for a concentration of $1\ mol\ dm^{-3}$ :

$pH=-log_{10}[strong\ acid]$

$pH=-log_{10}[1]$

$pH=0$

For a concentration of $0.1\ mol\ dm^{-3}$ :

 $pH=-log_{10}[strong\ acid]$

$pH=-log_{10}[0.1]$

$pH=1$ 

Concentration of sulfuric acid	pH
$1\ mol\ dm^{-3}$	$0$
$0.1\ mol\ dm^{-3}$	$1$
$0.01\ mol\ dm^{-3}$	$2$
$0.001\ mol\ dm^{-3}$	$3$

Weak acids

Weak acids can be diluted by factors of $10$ to increase the pH by $0.5$ as the concentration of $H^+$ is not equal to the concentration of a weak acid. The formula for acid dissociation constant can be rearranged to find the concentration of $H^+$ , therefore determine the pH of a weak acid.

$K_a=\frac{[H^+]^2}{[weak\ acid]}$

$[H^+]^2=K_a[weak\ acid]$

$H^+=\sqrt{K_a[weak\ acid]}$
$pH=-log_{10}[H^+]$

$pH=-log_{10}\sqrt {K_a[weak\ acid]}$

Example

Ethanoic acid has an acid dissociation constant of $K_a=1.7\times 10^{-5}\ mol\ dm^{-3}$ . For a concentration of $1\ mol\ dm^{-3}$ :

$pH=-log_{10}\sqrt {K_a[weak\ acid]}$

$pH=-log_{10}\sqrt {1.7\times 10^{-5}\times 1}$

$pH=2.38$

For a concentration of $0.1\ mol\ dm^{-3}$ :

$pH=-log_{10}\sqrt {K_a[weak\ acid]}$ 

 $pH=-log_{10}\sqrt {1.7\times 10^{-5}\times 0.1}$ 

$pH=2.88$ 

concentration of ethanoic acid	pH
$1\ mol\ dm^{-3}$	$2.38$
$0.1\ mol\ dm^{-3}$	$2.88$
$0.01\ mol\ dm^{-3}$	$3.38$
$0.001\ mol\ dm^{-3}$	$3.88$

Determining the concentration of an acid or base

Titrations can be used to find out the concentration of acids and bases.

Example

To find the concentration of an acid:

Chemistry; Acid-base equilibria; KS5 Year 12; pH curves and indicators — Apparatus for a titration.
The base (1) is added to a burette and clamped with a clamp stand (2). Acid (3) is measured using a pipette and indicator added into a conical flask. The base is added to the acid until the indicator shows a change in colour.

Acid-base titration for an unknown concentration of acid:

1.	Pipette a known volume of acid into a conical flask and add indicator.
2.	Wash the burette with the standard base solution then add the base.
3.	Carry out a rough titration to determine the volume of base required to neutralise the acid. There will be a permanent change in colour which is the end point.
4.	Carry out an accurate titration by adding the base to the acid, then a few $cm^3$ before the end point, add the base drop-wise until you reach the end point.
5.	Record the volume of base needed to neutralise the acid.
6.	Repeat the accurate titration multiple times until you obtain a reading within $0.1\ cm^3$ to calculate the mean titre.

Titration curves

You can determine an exact amount of acid required to neutralise a base using titration curves (pH curves). A titration curve is a plot of the volume of acid (or base) added on the $x$ -axis and the pH of the mixture on the $y$ -axis.

The pH meter is used to record pH readings by inserting the probe in the conical flask and taking readings each time a certain volume of acid is added. The shape of titration curves vary depending on the strength of the acid and base:

Chemistry; Acid-base equilibria; KS5 Year 12; pH curves and indicators

The equivalence point is point at which the acid/base has been neutralised. This is the midpoint of the vertical part of the curve.

The half-equivalence point is the point at which half of the acid/base has been neutralised as half of the base/acid has been added. At this point the $pK_a$ will be equal to the pH.

Indicators

An indicator is used during a titration to show when neutralisation has taken place via a colour change. As the indicator must change colour at the end point of the titration, you must select an indicator that has a small pH range within the vertical section of a titration curve.

There are two common indicators:

INDICATOR	COLOUR IN ACIDIC CONDITIONS	Colour in basic conditions	PH RANGE OF COLOUR CHANGE
Phenolphthalein	Colourless	Pink	$8.3-10.0$
Methyl orange	Red	Yellow	$3.1-4.4$

Phenolphthalein is chosen for a weak acid/strong base titration as the pH will rapidly change in basic conditions (high pH). Methyl orange could be chosen for a strong acid/weak base titration as the pH will rapidly change in acidic conditions (low pH).

Either indicator can be used for strong acid/strong base titrations as the pH change occurs over a large pH range. An indicator cannot be used for weak acid/weak base titrations as there isn't a sharp pH change, therefore a pH meter can be used instead.

Using pH charts

When adding an indicator to a solution, the colour of the solution can be compared to the pH chart of an indicator to estimate the pH.

Example

If you add phenolphthalein and the solution is a light pink colour, it indicates that the pH is between $7$ and $9$ .

Chemistry; Acid-base equilibria; KS5 Year 12; pH curves and indicators