Molarity (M): This unit of concentration relates the moles of solute per liter of solution.
is the most common concentration unit involved in calculations dealing with volumetric
Molality (m): This unit of concentration relates the moles of solute per kilogram of solvent.
Molality is often used as the concentration unit involved in calculations dealing with colligative
properties, such as freezing point depression, boiling point elevation and osmotic pressure.
Parts per million (ppm): This unit of concentration may be expressed in a number of ways. It is
often used to express the concentration of very dilute solutions. The "technical" definition of
parts per million is:
Since the amount of solute relative to the amount of solvent is typically very small, the density of
the solution is to a first approximation the same as the density of the solvent. For this reason,
parts per million may also be expressed in the following two ways:
Parts per billion (ppb): This concentration unit is also used for very dilute solutions. The
"technical" definition is as follows:
Owing to the dilute nature of the solution, once again, the density of the solution will be about the
same as the density of the solvent. Thus, we may also express parts per billion as:
Mole fraction (X) and mole percent (%X): A fraction is defined as a part over a whole.
Multiplying this fraction by 100 would give the percent. Thus, a mole fraction involves knowing
the moles of solute or component of interest over the total moles of all components in the solution
You may find it necessary to be able to convert from one concentration unit to another. The key
to solving this type of problem is to realize that you may make an assumption to get started. You
may need to know the density of the solution, which would be given in the problem. Then, by
using dimensional analysis, you try to get to the units of the concentration unit you are seeking to
find. To get started, assume the quanitity of solution found in the denominator unit of the
concentration unit you are trying to convert. For example, if you are trying to convert
weight/weight percent to molarity, assume 100 grams of solution. If you are trying to convert
molarity to weight/weight percent, assume 1 liter of solution.
Let's look at a typical example. Suppose you are given a concentrated solution of HCl which is
known to be 37.0% HCl and has a solution density of 1.19 g/mL. What is the molarity, molality
and mole fraction of HCl?
Begin with the assumption of 100 g of solution. With this assumption, you now know a few other
facts. In 100 g of solution, 37.0 g is due to HCl (grams of solute) and 63.0 g is due to water
(grams of solvent).
To find molarity, we need to determine the moles of HCl (solute) per liter of solution.
First, convert the known amount of HCl (37.0 g) to moles:
Next, convert the known mass of solution, 100 g solution, to liters of solution, using the density
of the solution:
Since the moles of solute (HCl) and volume of solution in liters is now know, calculate the
molarity (M) as the moles of solute per liter of solution:
From the information above, let's find the molality of the HCl solution. The moles of solute is
already known (1.01 mol HCl). We need to find the kilograms of solvent:
Since molality (m) is defined as the moles of solute per kilogram solvent, it becomes easy to find
Finally, let's tackle the mole fraction of HCl. The moles of HCl is known to be 1.01 mole. We
need to find the moles of H2O:
Since the moles of solute (HCl) and moles of solvent (H2O) are known, the mole fraction of HCl may be calculated:
This concludes the tutorial!
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