Solutions and Titration

Lessons

Senior 5 · Chemistry

Solutions and Titration

5 lessons

Lesson 1 of 5

Standard Solutions and How to Prepare Them

25 min

How do you know a concentration to four figures?

Every titration compares an unknown solution with one whose concentration is already known exactly. A water-quality laboratory checking hardness, a pharmaceutical company checking the strength of tablets, or a school testing vinegar all need that reference solution first. But you cannot simply weigh out sodium hydroxide and trust the label: its pellets absorb water and carbon dioxide from the air while they sit on the balance. This lesson is about choosing a substance you can trust, and about turning it into a solution of accurately known concentration.

Definition

Standard solution: a solution whose concentration is accurately known, e.g. 0.1000 mol dm⁻³ sodium carbonate.

Primary standard: a substance pure and stable enough that a standard solution can be made from it by weighing alone, e.g. anhydrous sodium carbonate, $\mathrm{Na_2CO_3}$ .

Standardisation: finding the exact concentration of a solution by titrating it against a primary standard. A solution standardised this way is a secondary standard, e.g. NaOH(aq) standardised with potassium hydrogen phthalate.

Concentration: $c = \frac{n}{V}$ in $\mathrm{mol\,dm^{-3}}$ ; mass concentration in $\mathrm{g\,dm^{-3}}$ = $c \times M$ .

Aliquot: an accurately measured portion of a solution, usually taken with a pipette.

What makes a good primary standard?

Requirement	Why it matters
Very high purity (at least 99.9 %) and a known formula	the mass weighed is the mass of the substance
Stable in air: not hygroscopic, not oxidised, does not absorb $\mathrm{CO_2}$	the mass does not change on the balance or in storage
High molar mass	a larger mass is weighed, so the balance error is a smaller percentage
Soluble in water, and reacts rapidly and completely by one known equation	sharp, reproducible end points

Good primary standards (M / g mol⁻¹)	Not primary standards, and why
anhydrous sodium carbonate, $\mathrm{Na_2CO_3}$ (105.99), for acids	sodium hydroxide: absorbs water and $\mathrm{CO_2}$
potassium hydrogen phthalate, $\mathrm{KHC_8H_4O_4}$ (204.22), for alkalis	hydrochloric acid: concentrated acid loses HCl gas
ethanedioic acid dihydrate, $\mathrm{H_2C_2O_4{\cdot}2H_2O}$ (126.06)	potassium manganate(VII): contains $\mathrm{MnO_2}$ , decomposes in light
sodium ethanedioate, $\mathrm{Na_2C_2O_4}$ (134.00), for $\mathrm{KMnO_4}$	sodium thiosulfate: crystals lose water, solution decomposes slowly
potassium dichromate(VI), $\mathrm{K_2Cr_2O_7}$ (294.18)	iodine: volatile
potassium iodate(V), $\mathrm{KIO_3}$ (214.00), for thiosulfate

Method 1: dissolving a weighed solid

Calculate the mass needed: $m = c \times V \times M$ .
Weigh by difference: weigh the weighing bottle with the solid, tip the solid into a clean beaker, and reweigh the bottle. The difference is the mass transferred, so solid left in the bottle does not matter.
Dissolve in a beaker with about half the final volume of distilled water, stirring with a glass rod. (Never dissolve directly in the flask: you cannot stir it, and dissolving can change the temperature.)
Pour through a funnel into the volumetric flask. Rinse the beaker, rod and funnel with distilled water into the flask, two or three times, so that every particle reaches the flask.
Add water until near the mark, then dropwise until the bottom of the meniscus sits on the mark, viewed at eye level (Figure 11.1).
Stopper and invert the flask at least ten times to mix.

Figure 11.1: Making up to the mark. Viewing from above or below the mark (parallax) gives a wrong volume.

Method 2: dilution

A known volume of a standard solution, measured with a pipette (or burette), is transferred to a volumetric flask and made up to the mark. The amount of solute does not change, only the volume:

$c_1 V_1 = c_2 V_2 \qquad \text{dilution factor} = \frac{V_2}{V_1} = \frac{c_1}{c_2}$

Worked example

Problem. Calculate the mass of anhydrous sodium carbonate needed to make 250.0 cm³ of 0.1000 mol dm⁻³ solution, and the percentage uncertainty if the balance reads to ±0.001 g and the 250 cm³ flask is accurate to ±0.15 cm³.

Solution.

$n = cV = 0.1000 \times \frac{250.0}{1000} = 0.02500\,\mathrm{mol} \qquad m = nM = 0.02500 \times 105.99 = 2.650\,\mathrm{g}$

Weighing by difference uses two readings, so the mass is uncertain by ±0.002 g:

$\frac{0.002}{2.650} \times 100 = 0.075\,\% \qquad \frac{0.15}{250} \times 100 = 0.060\,\%$

Answer: 2.650 g; total uncertainty about 0.075 + 0.060 = 0.14 %. A substance with a larger molar mass, weighed in a larger amount, would reduce the first term.

Worked example

Problem. Concentrated sulfuric acid is 98.0 % $\mathrm{H_2SO_4}$ by mass and has density 1.84 g cm⁻³. (a) Calculate its concentration. (b) What volume is needed to make 500 cm³ of 0.500 mol dm⁻³ acid?

Solution. (a) 1.000 dm³ has mass $1000 \times 1.84 = 1840\,\mathrm{g}$ , of which $0.980 \times 1840 = 1803\,\mathrm{g}$ is $\mathrm{H_2SO_4}$ :

$c = \frac{1803}{98.07} = 18.4\,\mathrm{mol\,dm^{-3}}$

(b) $V_1 = \frac{c_2 V_2}{c_1} = \frac{0.500 \times 500}{18.39} = 13.6\,\mathrm{cm^{3}}$

Answer: 18.4 mol dm⁻³; 13.6 cm³, added slowly to about 300 cm³ of water, then cooled and made up to 500 cm³. Because concentrated acid is not a primary standard, the diluted acid must then be standardised.

Warning

Always add acid to water, never water to acid. Diluting concentrated sulfuric acid releases a lot of heat; water poured onto the acid can boil instantly and spray acid out. Wear goggles and gloves.

First aid (CDC/NIOSH Pocket Guide, sulfuric acid): eye contact, irrigate with water immediately; skin contact, flush with water immediately and remove contaminated clothing; swallowed, get medical attention immediately.

Common mistakes: rinsing the volumetric flask with the solution (rinse it only with distilled water); shaking the flask sideways instead of inverting it; filling past the mark and pouring some out, which loses solute. If you overshoot, start again.

Tip

Each piece of glassware is rinsed with what it is about to hold or deliver: pipette and burette with the solution they will measure; volumetric flask and conical flask with distilled water only, because any extra solute left in them would change the amount.

Royal Society of Chemistry: Preparing a standard solution. Watch for weighing by difference, the rinsings poured into the flask, and the final drops added with a dropping pipette at eye level.

✦

Practice

Calculate the mass of potassium hydrogen phthalate needed to make 250.0 cm³ of a 0.0500 mol dm⁻³ solution.
Give two reasons why solid sodium hydroxide is not a primary standard.
25.0 cm³ of 0.200 mol dm⁻³ HCl is diluted to 500 cm³. Calculate the new concentration and the dilution factor.
What volume of 2.00 mol dm⁻³ $\mathrm{H_2SO_4}$ is needed to make 250 cm³ of 0.100 mol dm⁻³ acid?
3.15 g of ethanedioic acid dihydrate is dissolved and made up to 500.0 cm³. Calculate the concentration in mol dm⁻³ and in g dm⁻³.
A student makes up a sodium carbonate solution but forgets to rinse the beaker into the flask. Will the true concentration be higher or lower than the calculated one? Explain.
Explain why potassium hydrogen phthalate (M = 204.22) is a better primary standard than ethanedioic acid dihydrate (M = 126.06) for standardising alkalis, other things being equal.

Show answersHide answers

$0.0500 \times 0.2500 \times 204.22 = 2.553\,\mathrm{g}$ .
It is hygroscopic (absorbs water from the air) and it absorbs $\mathrm{CO_2}$ to form sodium carbonate, so its mass and purity are uncertain.
$c_2 = \frac{0.200 \times 25.0}{500} = 0.0100\,\mathrm{mol\,dm^{-3}}$ ; dilution factor 20.
$V_1 = \frac{0.100 \times 250}{2.00} = 12.5\,\mathrm{cm^{3}}$ .
$n = \frac{3.15}{126.06} = 0.02499\,\mathrm{mol}$ ; $c = \frac{0.02499}{0.5000} = 0.0500\,\mathrm{mol\,dm^{-3}}$ ; mass concentration $\frac{3.15}{0.5000} = 6.30\,\mathrm{g\,dm^{-3}}$ .
Lower: some solute stays in the beaker, so fewer moles reach the flask than were weighed.
For the same number of moles, a larger mass of KHP is weighed, so the fixed balance error is a smaller percentage of the mass. KHP is also not a hydrate, so it cannot gain or lose water of crystallisation.

Sources and credits

Relative atomic masses: IUPAC standard atomic weights (abridged). Density of concentrated sulfuric acid: CRC Handbook of Chemistry and Physics.
First aid: NIOSH Pocket Guide to Chemical Hazards: Sulfuric acid, US Centers for Disease Control and Prevention.
Image: Brand volumetric flask 100ml detail.jpg by Lucasbosch, via Wikimedia Commons, licensed under CC BY-SA 3.0.
Video: Preparing a standard solution, Royal Society of Chemistry, embedded from YouTube.
The text, Figure 11.1, the tables, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1How do you know a concentration to four figures?

2What makes a good primary standard?

3Method 1: dissolving a weighed solid

4Method 2: dilution

How do you know a concentration to four figures?

What makes a good primary standard?

Method 1: dissolving a weighed solid

Method 2: dilution