# Dilution of Solutions Techniques and Calculations

(dilution equation: c_{1}V_{1}=c_{2}V_{2})

## Key Concepts

- Dilution means to reduce the concentration of a solution.
- A solution is produced when a solute dissolves in a solvent.
term description example solute: substance which dissolves solid sodium chloride, NaCl(s) solvent: substance which enables the solute to dissolve liquid water, H _{2}O(l)solution: prepared by dissolving a *solute*in a*solvent*NaCl _{(aq)}is NaCl(s) dissolved in H_{2}O(l) - Concentration refers to the amount of solute dissolved in a given volume of solution.
amount of solute volume of solution concentration units of

measurementmoles

mollitres

Lmoles per litre (molarity)

mol L^{-1}(mol/L or M)concentration of a stock solution in mol L

^{-1}= moles of solute ÷ volume of solution in litresc

_{1}= n_{1}÷ V_{1}

c_{1}= molarity of stock solution (concentration of stock solution in mol L^{-1})

n_{1}= moles of solute dissolved (in mol)

V_{1}= volume of stock solution (in L) - A solution can be diluted by adding more solvent to the stock solution (the starting solution before dilution) in the same vessel.

The dilution equation (dilution formula or dilution expression) is:c

_{1}V_{1}= c_{2}V_{2}c

_{1}= concentration of stock solution (before dilution) in mol L^{-1}

V_{1}= volume of stock solution present before dilution in L

c_{2}= concentration of new dilute solution (after more solvent added) in mol L^{-1}

V_{2}= total volume of the new dilute solution in L*Note: V*_{2}> V_{1}and c_{2}< c_{1}find calculation determine concentration of dilute solution c _{2}=c _{1}V_{1}÷ V_{2}determine volume of dilute solution V _{2}=c _{1}V_{1}÷ c_{2}determine concentration of stock solution before dilution c _{1}=c _{2}V_{2}÷ V_{1}determine volume of stock solution used (before dilution) V _{1}=c _{2}V_{2}÷ c_{1} - A solution can be diluted by using a pipette to transfer some of the stock solution to a volumetric flask and then adding solvent up to the mark:

The dilution equation (dilution formula or dilution expression) is:c

_{1}V_{1}= c_{2}V_{2}c

_{1}= concentration of stock solution (before dilution) in mol L^{-1}

V_{1}= volume of pipette used to transfer the stock solution in L

c_{2}= concentration of new dilute solution (after water added) in mol L^{-1}

V_{2}= volume of volumetric flask used to prepare the dilute solution in Lfind calculation determine concentration of dilute solution c _{2}=c _{1}V_{1}÷ V_{2}determine volume of dilute solution V _{2}=c _{1}V_{1}÷ c_{2}determine concentration of stock solution c _{1}=c _{2}V_{2}÷ V_{1}determine volume of pipette used V _{1}=c _{2}V_{2}÷ c_{1}