pH, titrations and indicators Notes

The Definition of pH

1. The pH of an aqueous solution is a measure of how acidic or basic it is.
2. It is directly linked to the concentration of hydrogen ions, H⁺(aq), in the solution
3. Mathematically, it is defined as the negative logarithm of the hydrogen ion concentration: $$ \text{pH} = -\log_{10}[\text{H}^+] $$ where $[\text{H}^+]$ is in $\text{mol dm}^{-3}$.
   1. Lower pH → higher $[\text{H}^+]$ → more acidic
   2. Higher pH → lower $[\text{H}^+]$ → more basic
4. This also means that each unit change in pH corresponds to a tenfold change in $[\text{H}^+]$.
   1. pH 3 has 10× more $[\text{H}^+]$ than pH 4.
   2. pH 2 has 100× more $[\text{H}^+]$ than pH 4.

Concentration Solution in Dilute Acids

1. For a strong acid like HCl, we often assume it dissociates completely in water: $$\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})$$
2. So: $\left[\mathrm{H}^{+}\right] \approx \text { acid concentration }$
3. When we dilute an acid:
   1. The total number of moles of acid stays the same.
   2. The volume increases, so the concentration decreases.
   3. As $[\text{H}^+]$ decreases, pH increases (solution becomes less acidic).
4. If we dilute by a factor of $F$:
   1. $[\text{H}^+]$ decreases by factor $F$.
   2. pH increases by $\log_{10}{F}$.

Indicators and the pH Scale

How Indicators Work

1. An indicator is a substance that changes colour depending on the pH of the solution.
2. This allows us to see whether a solution is acidic, neutral or basic.
3. In many cases:
   1. The acidic form of the indicator (HIn) has one colour.
   2. The basic form (In⁻) has a different colour.
4. As pH changes, the ratio of HIn to In⁻ changes, and so does the colour.
5. For MYP level, you mainly need to know:
   1. Which colour means acid?
   2. Which colour means base?
   3. In which pH range does each indicator change colour?

Common Laboratory Indicators

Investigating the pH of Everyday Substances

Acid–Base Titrations

What Is a Titration?

In acid–base titrations, we react an acid with a base until neutralisation is complete.

1. The known solution is called the titrant (in the burette).
2. The unknown solution is called the analyte (in the flask).

We use an indicator to show when the reaction is complete (the end point).

Apparatus

1. Burette – delivers measured volumes of titrant accurately.
2. Pipette + pipette filler – measures a fixed volume (aliquot) of the analyte.
3. Conical flask – holds the analyte and indicator.
4. Volumetric flask – prepares accurate standard solutions.

Basic Titration Procedure (Acid–Base)

1. Prepare a standard solution of known concentration in a volumetric flask.
2. Rinse and fill the burette with the titrant (e.g. NaOH solution).
3. Use a pipette to transfer a fixed volume of the analyte (e.g. HCl solution) into a conical flask.
4. Add 1–2 drops of a suitable indicator.
5. Slowly add the titrant from the burette while swirling the flask.
6. Near the expected end point, add titrant drop by drop until the indicator just changes colour.
7. Record the final burette reading and subtract the initial reading to find the volume of titrant used.
8. Repeat until you have concordant results (two or three volumes within 0.10 cm³).

Why Is an Indicator Needed?

The indicator tells us when we have added exactly enough acid to neutralise the base (or vice versa):

1. At this point the solution is at or very near the equivalence point, where moles of acid and base react according to the balanced equation.
2. The indicator’s transition range must overlap the pH at the equivalence point.

Titration Curves (pH Curves)

1. A titration curve shows how pH changes as we add titrant during a titration.
   1. x-axis: volume of titrant added
   2. y-axis: pH of the solution
2. Key features:
   1. Initial pH – depends on the strength of the acid or base in the flask.
   2. Equivalence point – where stoichiometric amounts of acid and base have reacted.
   3. Steep pH change – near the equivalence point (especially for strong acid–strong base).
   4. Final pH – depends on the excess titrant.

1. Strong Acid + Strong Base (e.g. HCl + NaOH)

1. Initial pH: low (~1).
2. pH rises slowly at first, then shows a very steep jump near the equivalence point.
3. Equivalence point pH ≈ 7.
4. After equivalence, pH rises more slowly as base is in excess.

2. Weak Acid + Strong Base (e.g. CH₃COOH + NaOH)

1. Initial pH: higher (weak acid, maybe pH ~3).
2. Curve shows a buffer region where pH changes gradually.
3. Equivalence point pH > 7 (basic salt formed).
4. Phenolphthalein is a good indicator (changes in basic pH range).

3. Strong Acid + Weak Base (e.g. HCl + NH₃)

1. Initial pH: low (strong acid).
2. Curve rises gradually; equivalence point pH < 7 (acidic salt formed).
3. Methyl orange is a good indicator (changes in acidic pH range).

4. Weak Acid + Weak Base (e.g. CH₃COOH + NH₃)

1. Initial pH: weakly acidic.
2. No very steep jump at any point.
3. Equivalence pH near neutral but hard to detect with an indicator.
4. A pH meter is usually needed to follow this titration accurately.

Real-World Uses of Titrations

Water Quality Testing

1. Environmental scientists use titrations to measure acidity, alkalinity, or the amount of dissolved substances in water.
2. For example, titrations can determine how much alkali is needed to neutralise acidic wastewater before it is released into rivers.

Food Production

1. The acidity of vinegar, soft drinks or dairy products is often measured by titration.
2. Controlling pH is important for:
   1. Flavour
   2. Preservation (slowing bacterial growth)
   3. Texture and coagulation in dairy products like yoghurt or cheese.

Medicine and Pharmaceuticals

1. Titrations can be used to determine the concentration of active ingredients in medicines (quality control).
2. Blood and urine tests in hospitals sometimes use titration-based methods to measure substances like bicarbonate or calcium, related to pH balance.