Conversion of Concentration Units

There are instances when we are given a solution concentration in one unit and we need it in another.  There are two kinds of concentration units, those that involve mass-mass ratios such as mass percentage, molality and mole fraction, and those that involve mass-volume ratios, such as molarity grams per 100 mL etc.  It is relatively easy to convert one type of mass-mass concentration to another mass-mass unit of concentration.  It is slightly more complex to convert concentration units from mass-mass type to concentration units that are mass-volume, since we have the additional task of converting mass to volume or vice versa.  This is usually done through density.  Let's look at some examples now.

Conversion of Molality to Mole Fraction

Example

What is the mole fraction of each component in a 0.500 m aqueous solution of NaCl? 

From the definition of molality we know that this solution contains 0.500 mol of NaCl in 1.00 kg of water.  So let's assume we have enough solution to contain 0.500 mol NaCl.  This means that the solution will have 1.00 kg of water, convert this to moles.

Conversion of Molality to Mass Percent

Again assume that you have enough solution, that it contains 0.500 mol NaCl and therefore 1.00 x 10³ g of water. Convert 0.500 mol of NaCl into mass.

 Conversion of Mole Fraction to Molality

Example

What is the molality of NaCl in an aqueous solution in which the mole fraction of NaCl is 0.100?

Let's assume we have 1.00 mol of solution.  This means that the solution will contain 0.100 mol of NaCl and 0.900 mol of water.  Convert 0.900 mole of water to kilograms.

Conversion of Molarity to Molality

Example

What is the molality of NaCl in an aqueous solution which 4.20 M? The density of the solution is 1.05 x 10³ g/L.

Let's assume we have 1.00 L of solution.  This means that the solution will contain 4.20 mol of NaCl.  Convert this to mass.

mass water = 1050 g solution - 245 g NaCl = 805 g water

Conversion of Molality to Molarity

Example

What is the molarity of NaCl in an aqueous solution which 4.50 M? The density of the solution is 1.05 x 10³ g/L.

Let's assume we have enough solution to contain 4.50 mol NaCl, which means that we will have 1.00 kg of water.  Convert 4.20 mol of NaCl to mass.

mass solution = 1000 g water + 263 g NaCl = 1263 g solution

Next use the density to calculate the volume of solution.