We have already been introduced to solutions. Several chapters ago molarity (M) was introduced. Molarity is measured in moles per liter, or mol/L. A 0.30 M NaCl solution means that there is 0.30 mol NaCl in every liter of solution.
Often chemists have to make solutions; so, doing the calculations necessary to make a certain amount of solution become second nature.
For example:
Make 250 mL of a 0.30 M NaCl solution.
To make the solution we need to calculate the amount of NaCl to dissolve to make 250 mL of solution.
start with 250 mL
The solution is made by adding 4.38 g NaCl to a 250-mL volumetric flask. About 100 mL of water are added and when all the NaCl dissolves water is added up to the line on the volumetric flask.
But molarity is not the only unit we use; so, we need to be able to convert between different units...
Common units of concentration include
<==> <==><==>
% wt.
% vol
molarity (M)
molality (m)
mol fraction
That is, the mol fraction of "a" is the number of moles of "a" present divided by the total number of moles of material in the solution (including the solvent).
There is no simple formula for converting from one concentration unit to the next. In general the first step is to pick a convenient sample size. Then work to change each part of the concentration unit to the new unit. Do not try to do the conversion all at once.
For example,
HCl comes in bottles marked 37 % HCl by weight. The density of the solution is 1.200 g/cm-1. What is the molarity of the solution?
A conveneint sample size is 100 g of solution; convenient because 100 g x 37% = 37 g HCl.
This is the key...you must know the definitions for all the concentration terms
First, convert number of grams of HCl in your sample to number of moles in your sample (the 100 g of solution).
Second, convert g of solution to L of solution.
Third, divide moles by liters and you have molarity.
What is the molality of this solution?
Going from M to m. Since the concentration is in M a convenient sample size is 1 L.
OK, so the first conversion is not a conversion...there are 12 mol HCl present in 1 L of solution.
The second conversion is not as easy as it first appears. Let's use the density of the solution to perform a conversion from volume to mass.
This is NOT the mass that is used in molality. We just determined the mass of the solution; molality uses the mass of the SOLVENT!
The solution is made of a solvent and a solute. So, the mass of solvent can be found by subtracting the mass of the solute from the mass of the solution.
