Measuring Concentrations

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Learning Outcomes

When you have mastered this topic, you will:

A note on mass & volume

The SI unit of mass is the KILOGRAM, kg, while the unit of length is the METER, m. It follows that the SI unit of volume is the cubic meter (m³). These units are far too large for practical work in molecular biology, so one use smaller compatible units: the GRAM, g, (1×10^-3kg) and the cubic decimeter (dm³). For all intents and purposes, the LITRE, l is equivalent to 1 dm³, and that is the volume unit we will use.

You should be familiar with the use of SI prefixes:

Mass		Volume
1 mg	1×10-3g	1 ml	1×10-6l
1 µg	1×10-3g	1 µl	1×10-6l
1 ng	1×10-9g	1 nl	1×10-9l
1 pg	1×10-12g	1 pl	1×10-12l

In your laboratory work, you will become used to equipment capable of measuring masses with accuracies down to 1 µg and volumes as small as 1 µl.

Concentration & standard solutions

The quantity of solute present in a solution is called the CONCENTRATION of the solute in that solution. A solution with an accurately known concentration of a particular solute is referred to as a STANDARD SOLUTION.

There are several ways in which concentrations may be expressed. Molecular biologists most frequently refer to the MOLARITY of a solution. This is the amount (number of moles) of solute present in 1dm³ (1000 cm³).

[NaCl] = 1.00 mol.dm^-3 is a molar solution of sodium chloride. When “[ ]” are used to denote concentrations, the units of the concentrations are always mol.dm^-3.

The symbol M is used to denote molarity. A 1.00 m NaCl is a solution of NaCl with concentration 1.00 mol.l ^-1. Since the relative formula mass (M_r) of sodium chloride is 58.5, one mole of NaCl expressed in grams in is 58.5 g, and a 1.00 m NaCl solution will contain 58.5 g of NaCl in 1.00 lof that solution.

Note that the following concentrations are all equal: 1 M = 1 mol.l^-1 = 1 mmol.ml^-1 = 1 µmol.µl^-1.

Other ways of expressing concentrations are:

• Percentage by volume: 8% ethanol (8 volumes of ethanol in 100 volumes of solution). Usually written (v/v).
• Percentage by mass: 10% sucrose (10 g sucrose in 100 ml of solution). Usually written (w/v).
• Mass per volume: g.ml^-1(mass of solute per unit volume of solvent).
• Mass per mass: g/100g (mass of solute per 100 g of solvent).
• Molality: Number of moles of solute per 1000 g of solvent.

Preparing Standard Solutions

This page will help you to master the practical details involved in preparing standard solutions.

Preliminary calculations

A 0.050 m solution will contain 0.050 moles of solute in 1.00 l of solution. Now, sodium chloride has a M_r = 58.44, so the solution will contain 58.44 x 0.050 = 2.922 g.l^-1. Since we only want 500 ml (i.e. ½ l, we will only require 1.461 g of NaCl.

These calculations should be entered in your laboratory workbook.

Equipment and reagents required

You will need:

Method

Step 1:

Tip about 3 g of the sodium chloride into the small beaker. (As a rule, do not put spatulas into bottles of analytical grade reagents. This is important in order to maintain the purity of their contents. Close the bottle as soon as you have finished with it.

Step 2:

Place a square of glassine paper on the pan of the balance. Adjust the reading to 0.00 g. Using the spatula, gradually add small quantities of the sodium chloride from the beaker until a reading of 1.46 g is obtained. Switch off the balance. Make sure that no reagent has been spilled onto the pan. If you see any reagent, clean the pan and start over.

Step 3:

Pour the contents of the glassine paper CAREFULLY into the volumetric flask. If any crystals stick to the paper, wash them in with the wash bottle.

Step 4:

Add about 200 ml distilled water to the flask, and swirl it gently until all crystals are dissolved.

Step 5:

Add distilled water carefully up to 2-3 cm below the mark on the flask. Make up to the final volume with the wash-bottle (Do not overfill!). Stopper the flask and turn it upside down a few times to thorougly mix the contents.

Step 6:

Pour the contents of the flask into a clean, dry blue-top reagent bottle.

Make sure that you label the bottle with its contents, your name, and date of preparation.

Stock solutions

Rather than preparing small quantities of a standard solution every time you require it, it is better to prepare a relatively large volume of a concentrated stock solution, and dilute it as required. For example, suppose you have made up 2 l of a 3 M sodium carbonate solution, as described above. Then, if you need 100 ml of a 0.01 M Na₂CO₃ solution, you would need to dilute this solution 300 times:

Pipette 0.33 ml of your stock solution, using a Gilson pipette, into a 100 ml volumetric flask, and make up to the mark with distilled water. Use what you need, and discard the rest.

The use of Gilson pipettes is discussed .

Serial dilution

Suppose you have a stock solution of a reagent, at 1.0 m. If you take 1.0 ml of that solution, and dilute it to 10.0 ml in a volumetric flask, you will have a new stock solution which will have 1/10th the concentration of the original solution. This process can be repeated, each time obtaining a solution which is 10 times more dilute than the previous one. Great care must be taken that the volumes are accurately dispensed, as errors increase exponentially as one makes several dilutions in this way.