For convenience, chemicals are sometimes bought and stored as concentrated solutions, which are then diluted before use. Aqueous hydrochloric acid, for example, is sold commercially as a 12.0 M solution, yet it is most commonly used in the laboratory after dilution with water to a final concentration of either 6.0 M or 1.0 M.

Concentrated solution + Solvent → Dilute solution

The main thing to
remember when diluting a concentrated solution is that the number of moles of
solute is constant; only the volume of the solution is changed by adding more
solvent. Because the number of moles of solute can be calculated by multiplying
molarity times volume, we can set up the following equation:

where Mi is the initial molarity, Vi is the initial volume, Mf is the
final molarity, and Vf is the final volume after
dilution. Rearranging this equation into a more useful form shows that the molar
concentration after dilution (Mf) can be found by multiplying the initial
concentration (Mi) by the ratio of initial and final volumes (*V*i > *V*f):

Mf = Mi * (*V*i/*V*f)

Suppose, for example, that we dilute 50.0 mL of a solution of 2.00 M H_{2}SO_{4}
to a volume of 200.0 mL. The solution volume *increases *by a factor of 4 (from
50 mL to 200 mL), so the concentration of the solution must *decrease *by
a factor of 4 (from 2.00 M to 0.500 M):

Mf = 2.00 M * (50.0 mL/200.0 mL) = 0.500 M

In practice, dilutions are usually carried out as shown in figure below. The
volume to be diluted is withdrawn using a calibrated tube called a *pipet*,
placed in an empty volumetric flask of the chosen volume, and diluted to the
calibration mark on the flask. The one common exception to this order of steps
is when diluting a strong acid such as H_{2}SO_{4}, where a
large amount of heat is released. In such instances, it is much safer to add
the acid slowly to the water rather than adding water to the acid.

Source : Mc Murry

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