Concentration and Titrations

What Is Concentration?

Concentration measures how much solute is dissolved in a given volume of solution.

A concentrated solution has a large amount of solute per unit volume. A dilute solution has a small amount of solute per unit volume.

Units of Concentration

Concentration can be expressed in two ways:

1. Grams per decimetre cubed ($\text{g/dm}^3$): $c = \frac{\text{mass of solute (g)}}{\text{volume of solution (dm}^3\text{)}}$

2. Moles per decimetre cubed ($\text{mol/dm}^3$): $c = \frac{\text{moles of solute}}{\text{volume of solution (dm}^3\text{)}}$

Volume Conversions

$1 \text{ dm}^3 = 1000 \text{ cm}^3 = 1 \text{ litre}$

To convert cm³ to dm³: divide by 1000

To convert dm³ to cm³: multiply by 1000

Converting Between Units

$\text{Concentration (g/dm}^3\text{)} = \text{concentration (mol/dm}^3\text{)} \times M_r$

$\text{Concentration (mol/dm}^3\text{)} = \frac{\text{concentration (g/dm}^3\text{)}}{M_r}$

Example 1: g/dm³

Question: 5.0 g of NaCl is dissolved in 250 cm³ of water. Calculate the concentration in g/dm³.

Solution: Convert volume: $250 \text{ cm}^3 = 0.250 \text{ dm}^3$ $c = \frac{5.0}{0.250} = 20 \text{ g/dm}^3$

Example 2: mol/dm³

Question: Calculate the concentration of a solution containing 0.1 mol of NaOH in 500 cm³.

Solution: Convert volume: $500 \text{ cm}^3 = 0.500 \text{ dm}^3$ $c = \frac{0.1}{0.500} = 0.2 \text{ mol/dm}^3$

Example 3: Converting Units

Question: A solution of HCl has a concentration of 3.65 g/dm³. Calculate the concentration in mol/dm³. ($M_r$ of HCl = 36.5)

Solution: $c = \frac{3.65}{36.5} = 0.1 \text{ mol/dm}^3$

What Is a Titration?

A titration is an accurate experimental technique used to find the exact volume of a solution needed to react completely with another solution. It is commonly used for acid-base reactions.

Equipment

Common Indicators

Titration Method

1. Use a pipette to measure exactly 25.0 cm³ of alkali into a conical flask
2. Add a few drops of indicator
3. Fill a burette with acid and record the initial reading
4. Add acid from the burette slowly, swirling the flask
5. When the indicator changes colour permanently, stop adding acid
6. Record the final burette reading
7. Calculate the titre (volume of acid added) = final − initial reading
8. Repeat until you get concordant results (within 0.10 cm³ of each other)
9. Calculate the mean titre using concordant results only (ignore anomalous results)

The Method

1. Write the balanced equation
2. Calculate moles of the substance you know (using concentration × volume)
3. Use the molar ratio to find moles of the unknown
4. Calculate the concentration of the unknown

Key Formula

$n = c \times V$

where $n$ = moles, $c$ = concentration (mol/dm³), $V$ = volume (dm³)

Worked Example

Question: 25.0 cm³ of 0.10 mol/dm³ NaOH is exactly neutralised by 20.0 cm³ of HCl. Calculate the concentration of HCl.

$\text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O}$

Step 1: Moles of NaOH: $n = c \times V = 0.10 \times \frac{25.0}{1000} = 0.0025 \text{ mol}$

Step 2: Molar ratio NaOH : HCl = 1 : 1 $n(\text{HCl}) = 0.0025 \text{ mol}$

Step 3: Concentration of HCl: $c = \frac{n}{V} = \frac{0.0025}{0.020} = 0.125 \text{ mol/dm}^3$

Example Results Table

• Run 1 is a rough titre (first attempt to find approximate volume)
• Concordant results: Run 2 and Run 3 (within 0.10 cm³)
• Mean titre = $\frac{23.30 + 23.30}{2} = 23.30$ cm³

Important: Don't include the rough titre or anomalous results in the mean.

• Always convert cm³ to dm³ before calculating (÷ 1000)
• Write the balanced equation and molar ratio as your first step
• Show all working clearly — units at every step
• In practical questions, mention concordant results, swirling, and reading the meniscus
• Remember the formula triangle: $n = c \times V$

• Concentration = amount of solute per volume of solution
• Units: g/dm³ or mol/dm³
• $c = \frac{n}{V}$ where $V$ is in dm³
• Titrations accurately determine unknown concentrations
• Use concordant results for the mean titre
• Follow: balanced equation → moles of known → ratio → moles of unknown → concentration