Preparing dilutions

Making a single dilution
In analytical work, you may need to dilute a standard solution to give a particular mass concentration or molar concentration. Use the following procedure.

1. Transfer an appropriate volume of standard solution to a volumetric flask, using appropriate equipment (Table 3.1).
2. Make up to the calibration mark with solvent - add the last few drops from a Pasteur pipette until the bottom of the meniscus is level with the calibration mark.
3. Mix thoroughly, either by repeated inversion (holding the stopper firmly) or by prolonged stirring, using a magnetic stirrer. Make sure that you add the magnetic flea after the volume adjustment step.

For general-purpose work using dilute aqueous solutions where the higher degree of accuracy is not required, it may be acceptable to substitute conical flasks, beakers or test tubes for volumetric flasks and use measuring cylinders for volume measurements. In such cases you would calculate the volumes of 'stock' solutions (usually 'bench' reagents) and diluent required, with the assumption that the final volume is determined by the individual volumes of stock solution and diluent used. Thus a two-fold dilution would be prepared by using one volume of stock solution and one volume of diluent. The dilution factor is obtained from the initial concentration of the stock solution and the fmal concentration of the diluted solution. The dilution factor can be used to calculate the volumes and stock and diluent required in a particular instance. For example, suppose you wanted to prepare 100mL of a solution of NaOH at 0.lmolL^-1. Using the bench reagent, commonly containing 2.0molL-] (2.0 M), the dilution factor is 0.1 &divide 2.0 = 0.05 = 1/20 (a twenty-fold dilution). Therefore the amount of stock solution required is 1/20th of 100mL = 5mL and the amount of diluent needed is 19/20th of 100mL =95 mL.

Preparing a dilution series
Dilution series are used in a wide range of procedures including the preparation of standard curves for the calibration of analytical instruments. A variety of different approaches can be used but the most common is a linear dilution series.

In a linear dilution series the concentrations are separated by an equal amount, e.g. a series containing cadmium at 0, 0.2, 0.4, 0.6, 0.8, 1.0mmol L^-1 might be used to prepare a calibration curve for atomic absorption spectroscopy when assaying polluted soil samples. Use [C₁] V₁ = [C₂]V₂ to calculate the volume of standard solution for each member of the series and pipette or syringe the calculated volume into an appropriately sized volumetric flask as described above. Remember to label clearly each diluted solution as you prepare it, since it is easy to get confused.

The process is outlined below.
*Note: Make all the dilutions from the working stock solution to the required solution. Do not make a solution of lower dilution from one already prepared: if you have made an error in the first dilution, it will be repeated for the second dilution.

Process: How to make a linear dilution series for use in quantitaive analysis
The experimental protocol states: 'Prapare a standard solution (250.00mL; 0.01M) of cadmium ions using cadmium nitrtate and use this solution to produce a linear dilution series of solutions (100.00mL) of accurately known concentrations of approximately 0.0, 0.2. 0.4, 0.6, 0.8, 1.0mmolL^-1.

1. Calculate the amount of cadmium nitrate required for the standard soluion: cadmium nitrate is supplied as the tetrahydrate Cd(NO₃)₂.4H₂O; M_r = 308.47g mol_-1. Therefore, using eqn [4.1], you should calculate 250.00mL of an 0.01M solutuion of cadmium ions requires 0.01 &times 0.25 = 0.0025mol = 0.0025 × 308.47 = 0.07712g of Cd(NO₃)₂.4H₂O. Remember: this solution will contain 0.0025 moles of 'cadmium nitrate' or 0.0025 moles of cadmium ions and 0.005 moles of nitrate ions.
2. Make the standard solution by the quantitative method described in the above procedure and calculate its concentration to four decimal places.
3. Calculate the volume of solution required for the dilution series using [C₁]V₁ = [C₂]V₂, where V₁ = volume (mL) os standard solution; V₂ = volume of diluted solution (100.00mL) and C₂ concentration of diluted solution.
4. Express the concentrations in the same units, the most convinient in this case being molL_-1. Therefore, C₁ = 0.01M = 1 × 10_-2molL_{- 1} and for the distilled solution of concentration 0.2mmolL_-1, c₂ = 0.2 &times 10₃molL_-1. By arragement
   V₁ = {[C₂]V₂} &divide [C₁]
   

   =	0.2 × 103molL-1 × 100.00mL		= 2.00mL
   	1 × 102molL-1

5. Transfer the standard solution (2.00mL) to the volumetric flask (100.00mL) and make up to the mark with distilled water.
6. Repeat the calculation for each of the other diluted solutions as required , but note that a short cut is possible in this case: since you require stock solution (2.00mL) for the diluted solution of concentration 0.2mmolL^{- 1}, you will need 4.00mL for the 0.4mmolL^-1 solution etc. Use pure distilled water for the solution of conbentration 0.0molL^-1.
7. Calculate the exact concentrations of the diluted solutions using [C₁]V₁ = [C₁]V₁, since the concentration of the standard solution is most unlikely to be exactly 0.0100molL^-1. For example, if the concentration of the standard solution [C₁] is actuaaly 0.00987 molL^-1 = 9.87 × 10³molL^-1, then for the dilute solution of approximately concentration 0.2mmolL^-1, the actual concentration [C₂] is:
   [C₂] = {V₁ × [C₁]} ÷ V₂
   

   =	0.2ml × 9.87 × 10-3molL-1
   	100.00ml

   =	2 × 9.87 × 10-5molL-1 = 0.1974mmolL-1

   
   *Note: It is much simplier to measure out whole-number volumes (2.00mL, 4.00mL, etc.) using a pipette and procedure diluted solutions of accurately known concentrations (but not necessarily whole numbers) rather than to try to produce whole-number concentrations by measuring out non-whole-number volumes.

Storing chemicals and solutions
Chemicals which decompose easily (labile chemicals) may be stored in a fridge or freezer. Take special care when using chemicals which have been stored at low temperature: the container and its contents must be allowed to warm up to room temperature before use, otherwise water will condense onto the chemical. This may render accurate weighing impossible and you may ruin the chemical.

Chemicals and solutions to be stored at low temperatures must be in stoppered or sealed vessels. Do not store aqueous solutions below 0 QCsince freezing can occur and, with the resulting expansion of the volume, the vessel may crack. Solutions containing flammable solvents should only be stored in specialized 'spark-proof fridges: consult your laboratory instructor.

You must be aware of the particular problems of storing solutions in flasks with ground-glass joints. If you are using aqueous solutions you should lightly grease the joint and stopper with petroleum jelly, since the water will not dissolve the grease as it is poured from the flask. The stopper can be removed easily and the solution will be uncontaminated.

Conversely, if you are using solutions made up from organic solvents, you should not grease the joints since the organic solvent will dissolve the grease as you pour it from the flask and contaminate the solution. Moreover, you should not allow the solution to come in contact with the ungreased joints, since the solvent will evaporate and leave the solute to 'weld' the stopper to the flask. Fill the flask with solution, using a filter funnel with the stem of the funnel positioned well below the joint.

*Note: Always label all stored chemicals clearly with the following information: the name (if a solution, state solute(s) and concentratlonlsl], plus any relevant hazard warning information, the date made up, and your name.