Solutions, Concentrations, and Dilutions

Most reactions dealt with in the laboratory are carried in liquid form, or in solution. For the most part liquids are homogeneous (unlike solids), can be well contained (unlike gas), and can be easily measured by volume.

Amount

Chemical reactions are controlled by concentration of reagents – a number of molecules of reagent in a volume of solution.  The number of molecules determines the amount of reagent - a large volume of diluted solution may contain the same amount as a small volume of concentrated solution. Amount is measured in moles, or weight in grams equal to molecular weight in Daltons. One mole always contains the same number of molecules equal to Avogadro’s number – approximately 6x10²³.

Concentration

Concentration represents is the number of molecules in a volume, or how frequently a molecule of a particular substance can be encountered. Concentration of a substance is measured in moles per liter which represents molarity and is measured in units of molar or M. This is the key measure because rates of many chemical reactions in the solution are proportional to molar concentrations of reagents, but not to concentration in weight per volume, weight or volume fractions etc. Common derivatives of molar concentration are milli-molar (mM, mmol/L) and micro-molar (mM, mmol/L), which make small concentrations more manageable in calculations.

Note that volume used in determining concentration represents volume of solute and solvent after solute has been dissolved. Do not confuse this with volume of solvent or sums of volumes, although (with proper understanding) volume of diluted solutions can sometimes be approximated to the volume of solvent. General rule is that for accurate concentration all solutes must be fully and homogeneously dissolved in 80-90% of solvent before total volume is adjusted to 100%. Do not forget to mix solution after topping up with solvent.

Concentrations are commonly abbreviated by letter C or square brackets:  C = 1M or [NaCl]=1M.

 Dilutions

When two solutions are mixed, concentration all reagents change. This is a common situation when reagents are made out of concentrated stock solutions, for example. It is important to accurately keep track of individual concentrations after mixing, which is done separately for each chemical.  

If a particular substance was present in all initial solutions at the same concentration, this concentration will not change after mixing. Preparation of phosphate buffer from 0.4M stock solutions of monobasic and dibasic phosphate salts is a common example where concentration of phosphate ion in both initial components and in the buffer after mixing remains 0.4M.

To calculate final concentration of a chemical that was present only in one reagent R1, first calculate its amount A in the volume V_in of concentration C_in that you are adding:

One can notice that in this case concentration will decrease by the same factor as volume increases, which is called dilution factor. Dilution factor is dimensionless and will not change concentration units if initial and final volumes are in the same units.

Pay close attention to keeping units consistent: do not mix amount in moles with mM concentrations. Errors by few orders of magnitude are the most common.

If a chemical is present in two or more reagents, calculate its amount in each reagents for the volume that you are adding, add amounts together and divide by total volume as above