Say you have 500 mL of a solution (HCl and water, for example) in a volumetric flask, and the concentration of HCl is 5 mol/L.
If you want to dilute this solution to 2 mol/L, first you use the equation:
Concentration
initial * Volume
initial = Concentration
final * Volume
final Or shortly put: C
iV
i = C
fV
fSince our final concentration will be 2 mol/L, we know that C
f is
2. C
i is
5 (don't worry about the units) and V
i is 500.
(5)(500) = (2)(
Vf)
Vf = 2500/2 = 1250 mL
What does this number mean?
In order to dilute the 5 mol/L into 2 mol/L, we need 1250 mL of solution. We already have 500 mL, so we'll need 750 mL of water added onto the 500 mL (750 mL = 1250 mL - 500 mL). This will give us a diluted solution of HCl to the concentration we want.
- Here's another method or way of thinking about it...
If we want to prepare 500.0 mL of a 0.0540 mol/L NaOH solution, begin by thinking what the number means. That is, in one L there are 0.0540 moles of NaOH. NaOH has a
molar mass of 40.01 g/mol, so 0.0540 moles is a very small mass.
So we need to begin by calculating how much NaOH is required:
Step 1: Convert 500.0 mL to litres. (= 0.500 L)
Step 2: Convert litres to moles using molarity as the conversion factor.
(0.500 L x 0.0540 mol/L = 0.027 mol)
Step 3: Convert moles of NaOH to mass of NaOH (in grams) using molar mass as the conversion factor.
(0.027 mol x 40.01 g/mol = 1.08 g)
Thus, we need to weigh out 1.08 grams of NaOH on an electronic balance, add it to a 500 mL volumetric flask, add approximately 300 mL of distilled water, swirl to dissolve the solid NaOH and add more distilled water until the 500 mL mark is reached on the volumetric flask (see diagram below).