How to prepare solutions and dilutions

## Calculating a dilution The quantity of substance introduced via a stock solution is the same as that of the final solution ni = nf ### Starting from a solution with a known concentration

Example: prepare 100 mL of a 10-1 mol/L solution of Na+ from a 1 mol/L solution

Starting from the above equation, we obtain:

Where
Ci = stock solution concentration (in mol/L)
Vi = stock solution volume (in L)
Cf = final solution concentration (in mol/L)
Vf = final solution volume (in L)

Thus, the volume to be withdrawn from the the stock solution of known concentration is:

In order to prepare a 100 mL solution of Na+ at 10-1 mol/L from a 1 mol/L solution, we will need to withdraw 10 mL then make it up to 100 mL with the solvent (water or other solution).

### Starting from a commercial solution

Example: prepare a 100 mL solution at 10-1 mol/L of HCl from a commercialised solution. Most labels of commercial solutions do not give the concentration level but instead the molar mass: M (36.46g/mol), the density: d (1.18) and the percentage by mass: %m (0.35) #### Calculating a commercial solution's concentration

µ = volumic mass of the stock solution in kg/m3 (g/L)
µ0 = volumic mass of water = 1 000 kg/m3 (g/L)
Where
Csol = commercial solution concentration
µ0 = water density = 1000 kg/m3 (g/L)
d = commercial solution density
%m = percentage by mass of commercial solution
Msol = molar mass of the commercial solution

#### Calculating the volume to be withdrawn for a dilution

Where
Csol = commercial solution concentration
µ0 = water density = 1000 kg/m3 (g/L)
d = commercial solution density
%m = percentage by mass of commercial solution
Msol = molar mass of the solution

Numerical application:

In order to prepare a 100 mL solution of HCl at 10-1 mol/L from a (pure) commercial solution, we need to withdraw a sample of 883 µl then make up to 100 mL with the solvent (water or other solution).             