Working with Solutions
Solutions are uniform mixtures on the molecular level of 2 or more substances. The
substance present in largest amount is called the solvent (usually water) and any substance
dissolved in the solvent is called a solute.
The molar concentration or molarity, M, of a solution is used to indicate the number of moles
of solute per liter of solution:
mol (no.of moles solute)
L (no. of liters of solution)
The molarity of a solution is often used as a conversion factor between moles of solute and
volume of solution: it is a “molar density”.
One common type of “lab assistant” problem is the preparation of a dilute solution from a
more concentrated solution. For example, we might want to prepare 250 mL of a 0.500 M
NaOH solution from a 6.00 M NaOH solution as in exercise 5 below. There is a shortcut way to
work dilution problems which is based on the knowledge that the # of moles of solute you need
for the dilute solution all come from the concentrated solution. Thus
# moles concent rat ed #moles dilute and since M(mol L-1) x V(L) = n (mol), it follows that
Mconcent rated Vconcent rated Mdilute Vdilute
or, in the notation of Chang,
Minit ial Vinit ial Mfi nal Vfi nal
In the laboratory this equation is often used to determine the Vconcent rat ed that needs to be diluted
to give the desired volume of a more dilute solution.
Stoichiometry of Reactions in Solution
Problems involving solutions are very similar to the chemical stoichiometry problems we
have discussed earlier. The only difference is that the moles of reactant or product may need to
be calculated from a solution volume using the molarity (M = mol/L) as a conversion factor
between volume and moles.
Lab Assistant Problems
The problems below will introduce you to calculations involving molarity. I call these “lab
assistant problems” since we do this kind of calculation all the time when setting up labs! When
working these problems, it is useful to recall that 1 L = 1000 mL.
1. What is the molarity of a solution containing 21.0 g NaCl in 200 mL of solution?
Answer: 1.80 M NaCl
2. What ions exist in a 0.245 M Na2CO3 solution? Give the molar concentration of each ion.
Answer: 0.490 M Na+ and 0.245 M CO32-
3. How many mL of a 0.420 M NaCl solution should be measured out to provide 1.5 g NaCl?
Answer: 61 mL of 0.420 M NaCl
4. How many grams of CaCl2 are needed to make 200 mL of a 0.500 M Cl- solution? (Note:
CaCl2 is a soluble salt. The molar mass of CaCl2 is 110.98 g/mol.)
Answer: 5.55 g CaCl2
5. How do you prepare 250 mL of a 0.500 M NaOH solution from a 6.00 M NaOH solution?
Answer: Take 20.8 mL of 6.00 M NaOH and dilute to a total volume of 250 mL.