Molar Concentrations and Solutions
The concentration of a substance in solution is the amount of the
substance in a given volume of the solution. The term concentrated is
used to describe a solution with a relatively high concentration of solutes
(dissolved substances). To describe a relatively low amount of solute in a
solvent, we use the term dilute. These terms are not clearly defined so
they have no precise meanings. The term saturated solution is more
precise. It means that the solvent cannot dissolve anymore solute so that
adding any more solute will result in a precipitate (visible, undissolved
solid).
The molar concentration, or molarity, is defined as the number of moles
in 1 L of solution measured in mol/L or M (read molar). We can use the
following formula to express molar concentration.
Molar concentration = moles/volume
c = n/V
c = molar concentration (mol/L or M)
n = number of mole (mol)
V = volume (L)
Example: If a 1.0 L of solution contains 2.5 mol of NaCl, the molar
concentration can be expressed in the following ways.
Molar concentration of NaCl = [NaCl] = 2.5 mol/L = 2.5 M
The molarity of NaCl is 2.5 molar
Practice: What is the [NaCl] in a solution containing 5.12 g of NaCl in
250.0 mL of solution?
Practice: What mass of NaOH is contained in 3.50 L of 0.200 M NaOH?
Practice: What is the actual experimental procedure you would use to
prepare 2.75 L of 0.0120 M NaOH?
Dilutions
Dilution is the act of making a solution less concentrated. Since
concentration is the number of moles per volume, the more volume of
solvent we have, the less concentrated, or more dilute, the solution
becomes.
By adding more volume of solvent, the number of moles of the solute
does not change.
c = n/V
So n does not change but V increases, resulting in a decreased c.
Example: If 200.0 mL of 0.500 M NaCl is added to 300.0 mL of water,
what is the resulting [NaCl] in the mixture?
Practice: If 20.0 mL of 0.75 M HBr is diluted to a total volume of 90.0 mL,
what is [HBr] in the resulting solution?
Mixing Two Solutions of the Same Chemical with Different
Concentrations
When performing calculations with concentrations, a good strategy is to
always calculate the number of moles of the substances in question and
then divide by the total volume for the final concentration.
Example: If 300.0 mL of 0.250 NaCl is added to 500.0 mL of 0.100 M NaCl,
what is the resulting [NaCl] in the mixture?
First find the number of moles of NaCl in each solution then divide by the
total volume (in L) to get the final concentration.
You can check to see that the answer makes sense because the
concentration should be between that of the two original solutions.
Practice: What is [KOH] resulting from mixing 55 mL of 0.15 M KOH and
75 mL of 0.25 M KOH?