Final answer:
To dilute a 1 mol/dm³ solution to one-tenth of its concentration, perform a logarithmic dilution by adding nine times the original volume of solvent, resulting in a final concentration of 0.1 mol/dm³.
Step-by-step explanation:
To dilute a 1 mol/dm³ solution to one-tenth of its original concentration, you must perform a logarithmic dilution. This can be achieved by taking a unit volume of the original solution and adding enough solvent to it to increase the total volume to ten times the original volume. For example, if you take 1 dm³ (which is equivalent to 1000 mL) of the solution, you will add 9 dm³ (9000 mL) of solvent to it, making the total volume 10 dm³ (10000 mL). By doing this, the concentration of the solution is reduced to 0.1 mol/dm³.
The molarity of the solution becomes one-tenth of its original value because the number of moles of solute remains constant while the volume increases tenfold. This dilution step can be repeated to achieve further logarithmic dilutions. For instance, performing the dilution process twice would result in a 100-time dilution, and thrice would result in a 1000-time dilution.