One of the tasks that every science teacher has to do, particularly the chemistry teacher, is to make up solutions - reagents, standard solutions, indicators, test solutions etc. This seems to present problems to trainee teachers and perhaps to others. The lack of technical assistance in Irish schools compounds this problem, since this means that hard-pressed teachers must do it themselves.
It may be that the real source of difficulty is using the mole concept to work out concentrations, dilutions etc., or it may be lack of a 'recipe' book that tells you what to do. This short article can't give all the answers but it may give some useful tips. As with all these 'ChemTips' there's no substitute for practice.
One solution to the time problem is to make up batches of solutions at the start of terms, sufficient to meet most of the projected needs. Stock solutions can readily be diluted as required.

Precise versus imprecise concentrations
We do not always need to know the concentrations of solutions used in the laboratory very precisely e.g. bench reagents, test solutions, indicators etc. It is not worth spending time and effort making up solutions if the required precision does not need it.

Know when to make up solutions approximately and when they need to be precise.

Standard solutions
These are solutions used in analytical determinations, whose concentrations need to be known precisely (within specified limits). They are made either by weighing out a known mass of a standard solid and making up to a specified volume (e.g. sodium carbonate) or by standardisation (after making up approximately) by titration against a known standard (e.g. sulphuric acid against sodium carbonate). A standard solution is one whose concentration is known (to an appropriate number of significant figures, s.f.) and which doesn't go off with time i.e. is stable.

Precision and significant figures
If a solution was made up by weighing out 2.5g solid (to +/- 0.1g) it is known to 2 s.f. and the concentration could only be given to 2 s.f. e.g. 1.2M or 0.12M. If weighed as 2.50g (3 s.f., +/- 0.01g) the concentration is known to 3 s.f. i.e. 1.20M or 0.120M; if weighed out as 2.500g (4 s.f., +/- 0.001g) the concentration would be known to 4 s.f. i.e. 1.200M or 0.1200M. The significant figures are given in bold.

This idea of precision and significant figures is important as it tells us how carefully to make up solutions and how precisely we can quote the final answer.
In school the precision required is usually not very high, certainly for junior classes, as other sources of error are much bigger. Making a solution up to 3 or 4 s.f. is quite adequate i.e. weighing to +/-0.01 or 0.001g, which can be done on a good top-pan balance.
If you weigh out a larger amount the percentage error is less (greater precision) and you can make up a concentrated 'stock' solution and dilute it down as required (providing it is stable). Thus you can do one session of weighings and making up solutions at the start of a year or term to produce a set of stock solutions, which can be stored and diluted down as required. (This is particularly suitable for bench reagents where the exact concentration is not important.)

Suitable chemicals for standard solutions:

An alternative approach is to buy small quantities of standard solutions (ready-made or concentrated) and use these to standardise one's own solutions. Once a solution has been standardised so that we know its concentration precisely, we can use this as a 'secondary standard' to standardise other solutions.
So we can use sodium carbonate to standardise hydrochloric or sulphuric acids, which in turn can be used to standardise sodium hydroxide solutions.

Bench reagents
By bench reagents we mean dilute acids and bases etc. that are routinely used in the laboratory for tests, simple reactions and preparations. The exact concentration is not important and they can be made up with less care and precision, and do not need standardisation. The concentration is usually reported as 0.5M, 1M, 2M, 4M etc., which implies 1 s.f. i.e. not very precise. Such solutions can be made up to +/-10% without affecting practical work. This includes dilute acids, bases, metal salts, water-soluble organics etc.
This precision can be obtained by using a top-pan balance to +/-0.1g or by using a measuring cylinder for liquids. Dilution can be done in the final container, rather than in volumetric flasks, thus saving time.

Example 1.
e.g. 5L of 1M sodium hydroxide is required.
GMM NaOH = 40 g/mol
Thus a 1M solution contains 1 x 40 = 40g/L and 5L would need 5 x 40 = 200g.
200g of NaOH pellets can be weighed out on a top-pan balance and dissolved in ~2L distilled water in a large beaker or clean plastic bucket. This gets very hot and NaOH is very caustic. Care should be taken to wear plastic gloves and full face protection.
Allow the solution to cool. Pour into a 5L plastic bottle and fill up with distilled water and mix well. Keep containers stoppered to reduce reaction with CO₂ in the air. This solution can be used to top up reagent bottles or to make up more dilute solutions. It can be used in titrations as an 'unknown', but needs standardisation if used otherwise.

Example 2.
To make up 2M ethanoic acid start with glacial ethanoic acid (pure CH₃COOH, GMM = 60g/mol). This has a density of 1.05g/mL so that 1L weighs 1,050g i.e. 1050/60 = 17.5M.
To make up 1L of 2M solution measure out 2M/17.5M x 1000mL = 114mL glacial ethanoic acid (Caution: fumes), dissolve in water and make up to 1L in a large stoppered bottle.

N.B. we need the GMM of the starting material to work out what mass we need to make up a solution of specified concentration.

Ammonia solutions are made up in the same way using the concentration of conc. ammonia in wt.%, the density and GMM (see below).

Stock solutions
A stock solution is a concentrated solution (standard or non-standard) whose concentration is known, which can be stored and diluted as required to give solutions of lower concentration. A stock solution should be chemically stable, so that it doesn't change with storage. Keeping suitable quantities of stock solution can save time during term in making up solutions, as they only need dilution. Thus 1L of a 10M solution, for example, would make 10L of 1M solution when diluted. Concentrated acids are one example of a stock solution, which can be diluted as required. When making up bench reagents the stock solution can be measured out with a measuring cylinder; for analytical solutions it should be measured out using a pipette, depending on how precisely the stock solution is known. If the stock solution is only approximate, then it is best to dilute without taking to much care and then standardise the final solution. The exact final concentration is then known.

Dilution
We often need to dilute one solution, whose concentration is known, to give another of known concentration. Although this is a simple task some students find it difficult. The basic idea to remember is that when we dilute a solution the amount of solute stays the same, although its concentration decreases.

In any solution:
moles of solute

= volume (dm³) x concentration (mol/dm³)

= volume (cm³)/1000 x concentration (mol/dm³)

Diluting with water keeps the number of moles constant i.e. the product of volume and concentration is constant.

Thus:
volumei x concentrationi = volumef x concentrationf (i and f stand for initial and final)
or:

V_i x M_i = V_f x M_f

(Any unit can be used for concentration or volume in this expression, providing it is the same on both sides.)
Once you've grasped this, dilution problems couldn't be easier!

Example 1.
1. What is the final concentration if you dilute 15cm³ of 1.00M ethanoic acid to 250cm³?
Using the dilution expression:
15 x 1.00 = 250 x M_f

Thus, M_f = 15/250 x 1.00 = 0.0600M
Diluting 15cm³ 1.00M ethanoic acid to 250cm³ gives a 0.060M solution (to 2 sig. figs.)

Example 2.
You need to dilute 100 volume hydrogen peroxide (H₂O₂) to make 2.5 dm³ 20 volume solution.
(100 and 20 volume are measures of concentration for hydrogen peroxide, see below.)

Using the expression:
V_i x 100 = 2.5 x 20

Thus, V_i = 2.5 x 20/100 = 0.50dm³
You need to dilute 0.50dm³ 100 volume H₂O₂ to 2.5dm³ to make 20 volume H₂O₂.

Example 3.
You need to dilute a stock solution of 1000 ppm calcium carbonate (dissolved in acid) to produce 100cm³ 5.00ppm calcium carbonate. How much stock solution is needed?

Using the general expression:
V_i x 1000 = 100 x 5

Thus: V_i = 100/1000 x 5 = 0.500cm³.

This is a very small volume and would be subject to a large error (unless a micropipette was used) and it is usual to dilute in stages when there is such a large dilution factor (of 200). Thus one would make 100cm³ of 50.0ppm first, which would require 5.0cm³ of 1000ppm solution. 10cm³ of 50ppm diluted to 100cm³ would then give 5.00ppm.

Prepared solutions
It is possible to buy from laboratory or chemical suppliers ready-made solutions either ready to use in their desired concentrations or as concentrated solutions ready to dilute. This is an expensive way to provide solutions (see below) but it is very convenient and saves valuable time, especially in the absence of technical assistance. The ampoules of concentrate are cut open and the contents washed out with water into a standard volumetric flask, and diluted to the mark. This gives a solution of precisely known concentration suitable for analytical purposes. It gives reliable solutions but at quite a high cost.
e.g. Ready-made solutions:
2.5 dm³ of AR 1M HCl costs £8.92 in a catalogue; 2.5 dm³ of AR conc. HCl (35wt.%) costs £11.37 and would make 12x the volume (30 dm³) of 1M acid if diluted oneself, at a cost of around £0.95/dm³ (excluding the cost of the water). There is roughly a factor of ten times in the cost in buying solutions like this.

If small volumes of solutions are used e.g. indicators, then this may be the best way to buy them, rather than having large amounts of pure solid or liquid indicator lasting for years.

Making up solutions
The key steps in making up a solution from a pure solid (or liquid) are:

• weighing (or measuring) out the correct amount of pure solid (or liquid)
• transferring this without loss to a volumetric flask
• dissolving fully and diluting the solution to the mark correctly with water
• thorough mixing of the solution

The procedure is summarised in the box below:

MAKING UP A STANDARD SOLUTION
1. Rinse the volumetric flask first with tap-water and then with distilled water.
2. Weigh out the required mass of solid on a 3/4-figure balance (analytical balance weighing to 3/4 d.p.). Use a weighing bottle. Weigh the bottle empty, add the right amount of solid to get roughly the correct mass*, reweigh and then transfer into the flask. Reweigh the empty weighing bottle - the difference in mass before and after transfer is the exact mass of solid transferred into the flask. This is known as weighing by difference.
* It is NOT necessary to weigh out the amount specified e.g. 1.000g and spend a lot of time adding and subtracting solid. You should weigh out a mass close to the required mass but you should know exactly what it is. This is often referred to as: "Weigh out accurately about 1 g".
You can also weigh using a watchglass or plastic boat - in this case it is best to weigh it clean and dry, and then to wash off all solid into the flask to get 100% transfer.
3. Add the solid to the volumetric flask through a clean funnel placed in the neck of the flask. This ensures that no solid is lost in transfer. Wash the solid down into the flask using distilled water until no trace of solid is left in the funnel. Remove the funnel.
4. Add distilled water until the flask is about 2/3rds, full. Stopper and shake by inversion and swirling about 20-30 times to ensure that the solid dissolves and mixes.
5. When the solid is dissolved add distilled water until the liquid level is 1-2cm. below the mark. Stopper and remix by inversion 20-30 times.
6. Finally, make up to the mark with distilled water using a dropper. Stopper and mix by inversion 20-30 times to ensure the solution is homogeneous.
7. The solution can be now be used from the flask or transferred to a storage vessel or a beaker. IF transferring to a clean container, rinse this 2-3 times with small portions of the solution before filling it up.
8. Label the container with the name of the chemical and its concentration.

Storage of solutions
Plastic bottles (polyethene or polypropene), with screw tops, are a convenient way to store stock or diluted solutions. They are lighter and unbreakable than glass. Plastic bottles should always be used for alkalis, which dissolve glass. For large volumes of stock solution, small aspirators fitted with stopcocks are very useful, so that solutions can be dispensed easily.
All bottles should be clearly and legibly labelled with the correct name, concentration and hazard symbols relevant to the solution in waterproof ink. Running off labels on a laser printer is a good idea (not on an inkjet).
Incorrect or illegible labelling is a major problem in schools and a major safety hazard. The concentration is important and serious accidents can happen if concentrated solutions are used instead of dilute ones.
Always read the label twice and check the concentration and the name are correct.

Diluting concentrated acids
The science teacher often needs to dilute concentrated acids (hydrochloric, nitric and sulphuric acids are most common) to produce diluted solutions (1M, 2M, 4M, 6M etc.). To do this we need to know the approximate molarity of the concentrated acids (each one is different!), and to do this we need the concentration in wt.% and density of the conc. acid (usually on the bottle). Acids are usually sold in Winchester bottles of 2.5L capacity.

Sample calculation for HCl:
Conc. HCl contains 35-37wt.% hydrogen chloride dissolved in water and has a density of 1.18g/ cm³.
Thus if 1dm³ = 1000 cm³ of conc. HCl has a density of 1.18g/cm³ it will have a mass of 1000 x 1.18 = 1,180g.
1L of conc. HCl contains 35/100 x 1,180 = 413g HCl
GMM HCl = 1.008 + 35.5 = 36.508 ~ 36.5g/mol Molarity of conc. HCl = 413/36.5 = 11.3 M HCl
Thus conc. HCl is ~11.3M.

In the same way we can work out the approximate molarities of the other common conc. acids used in laboratories and this data is given below.

General method:
* From the density, work out the mass of 1 litre of acid.
* From the % purity, work out the mass of acid/litre.
* Using the GMM of the acid, work out the no. of moles/litre = molarity.

(Check these calculations in the table above yourself to make sure they're correct and that you can do them!)

Thus if we know that conc. HCl is approx. 11.3M, how do we make up 1 dm³ (1 L) of 1M HCl solution?
When we dilute a volume of concentrated solution to give a dilute solution the number of moles of solute (HCl in this case) stays the same (see above).
Thus: V_conc x M_conc = V_dil x M_dil

This equation can be used for any dilution problem to find out the required final volume for a given concentration, or given the final volume to find out the final concentration (as above).

Thus, V_conc cm³ x 11.3M = 1000 cm³ x 1M
Thus V_conc = 1000/11.3 x 1 = 88. 5 cm³

If we measure out 88.5cm³ of conc. HCl and dilute to 1000 cm³ (1dm³) with distilled water we will get an approx. 1M solution of HCl. It will only be approximate because the initial concentration of HCl is not precise (HCl is lost when the bottle is open) and unless the volume is measured precisely this will also cause an error. Thus it is appropriate to use a measuring cylinder to measure out the conc. HCl, and to standardise afterwards if necessary.

8.8 cm³ of conc. HCl diluted to 100 cm³ would also give ~1M HCl;
354 cm³ diluted to 1 dm³ would give ~4M HCl and so on.

When diluting conc. acids always add the acid to an excess of water, mix to dilute and then make up to the mark.
This precaution is essential for conc. sulphuric acid, which reacts violently with water liberating heat. But it is a good precaution when diluting or dissolving any substance - add it to excess water rather than add water to the concentrated substance, in case there is an exothermic reaction.
If heat is liberated use cold water and allow the solution to cool before making to the mark.
Always add conc. acid to excess water when diluting.

CAUTION: Conc. acids are very corrosive and must be handled with care. Wear goggles or better, a full face shield when pouring conc. acids. Use plastic gloves (not rubber) to handle the bottles - the outsides often get acid drips on them. Wipe the outside carefully after pouring.

Use a measuring cylinder or graduated pipette (with a pipette filler) to measure out the required volume of conc. acid. Always wash out the measuring cylinder or pipette after use by immersing in a large container of water - don't fill them with water.

This method only gives approximate concentrations, suitable for bench reagents. For analytical work all the acids must be standardised against a primary standard such as anhydrous sodium carbonate.

Sodium hydroxide solutions
Sodium hydroxide pellets or concentrated solutions of NaOH are very corrosive. Even dilute alkali solutions can do serious damage to the eye. Solutions of NaOH can be made by dissolving NaOH pellets in water e.g. 40g NaOH dissolved and made up to a litre has an approximate concentration of 1M. NaOH pellets and solutions go 'off' when standing in air as they absorb CO2 and the pellets also absorb water. For analytical work NaOH solutions must be freshly made up and then standardised.
Wear plastic gloves, goggles or full-faced protector and handle the pellets with tweezers or a spatula.
If the bottle has been opened they tend to stick together and can be hard to unlodge. It is a good idea to keep opened bottle in a desiccator.* The pellets or NaOH solutions should not be spilled on the skin. The reaction with water is vigorous and exothermic. Add the pellets to excess water, mix to dissolve and then dilute. It is a good idea to use cold water to make up the solutions. Allow the solution to cool before diluting to the mark.

Do not add water directly to the NaOH pellets.

It is easier to dilute a stock solution than make it up fresh each time, so make up 4M or 6M NaOH and dilute as required. Try to keep bottles as full as possible to avoid contamination from the air.
(Concertina bottles sold for photographic solutions are quite useful for this.)
* A simple, cheap desiccator for storing hygroscopic chemicals (those that pick up water from the air) can be made from a large plastic container with an airtight lid. Put silica gel crystals or packets at the bottom, and store the bottles with the lid tightly closed.

Hydrogen peroxide solutions
Hydrogen peroxide is commonly sold as 30wt% or as '20 volume' H₂O₂. What do these mean and how do we obtain 20 volume H₂O₂ from 30wt% (conc.) H₂O₂?
We need to know what '20 volume' means - it means that 1cm³ solution gives 20cm³ oxygen gas. So how much gas does 30wt% H₂O₂ give per cm³?

The density of conc. H₂O₂ is 1.10g/cm³ so that 1dm³ weighs 1,100g and thus contains 30/100 x 1,100 = 330g H₂O₂.
GMM of H₂O₂ is 34g/mol.
The molarity of 30wt% H₂O₂ is thus 330/34 = 9.7M.

The equation for decomposition is:
H₂O₂ = H₂O + 1/2 O₂
1 mole 1/2 mole
9.7 mole 4.85 mole
1000cm³ ? cm³ gas

1 mole of O2 gas at STP occupies a volume of 22.4dm³ = 22,400cm³.
Thus, 4.85 mole occupies 108,640cm³.
1 cm³ 30wt.% H₂O₂ gives 108,640/1000 cm³ oxygen = 108 cm³ = '100 volume'

'20 volume' H₂O₂ is actually 5-6% H₂O₂ i.e. '18-22 volume'.
To get '20 volume from 30wt% we must dilute by a factor of 5 i.e. 200 cm³ 30wt% diluted to 1000 cm³.

What size to buy?
What size of bottle/how much of a chemical does one buy? This depends on how much you use in a year and how stable the chemical is once opened. Once a bottle is opened it is liable to contamination - it may react with air or moisture or lose water or vapour. Buying a large bottle that lasts for years is a false economy and results in bottles of ill-defined chemicals clogging up prep-room shelves. Buying several smaller bottles e.g. 250g or 500g, rather than 1kg, is better and should only cost slightly more. It is best to buy a year's supply at a time for all except the most stable chemicals and those you use little of, where the smallest size lasts several years.
When you get a new bottle of chemical, write the date on it with a permanent marker so you will know which is the oldest bottle.
(Similar principles apply to the chemistry laboratory and store room that apply to the kitchen and larder - a little commonsense goes a long way!)

Which grade of chemical to buy?
When you look at the chemical catalogues it is very confusing. Each chemical comes in different grades and amounts, all at different prices. Which should you buy? In a catalogue AR grade, Laboratory Reagent grade, Technical Grade etc.
AR stands for Analytical Reagent - this is the highest purity and costs the most. There are also laboratory reagent and technical grade chemicals. Technical grade is the least pure and for most purposes in schools, laboratory or reagent grades are adequate. You don't need to buy AR grade unless the price is hardly any different to laboratory grade or you need it for a specific analytical purpose.

Remember: if making up solutions, careful weighing and measurement is no use if you don't mix the final solution thoroughly to ensure homogeneity.

We haven't covered every possible angle on making up solutions, but you should now have the basics needed to make up most types of laboratory solution. The information given above should enable you to make up many of the solutions needed in a school laboratory safely and efficiently.

If you have queries about ChemTips, or need to know how to do something, or if you have a good ChemTip of your own, please email it to me at: peter.childs@ul.ie