Density and percent by mass concentrations

Substances used in chemical reactions may be solids, liquids or gases.  Reactants may also be added in solution.
Solutions are mixtures which one or more substances (solute) is mixed with a solvent such as water. 
Solutions that have water as the solvent are referred to as aqueous solutions.
 
d = m
V
When working with pure liquids or solutions, it is convenient to measure volume.  However it may be necessary to relate that volume to the mass in grams of the substance when, for example, calculating amounts in moles. This can be done through the density which is a measure of mass per unit volume.  This is expressed mathematically as shown at the right.

The unit of density depends on the unit of mass and the unit of volume.  For common pure liquids and aqueous solutions the unit is commonly g
.
g
is read grams per
.  Per means “divide by”;  therefore saying the unit reminds you that density equals mass divided by volume.
 
The mass of liquid, gas or solution can be calculated from a given volume if the density is known by multiplying the two together.
Example using these ideas:
Concentrated hydrochloric acid is a solution of the gas hydrogen chloride in water.  The density of hydrochloric acid is 1.19 g
.
What is the mass of 50
of this solution?
m(hydrochloric acid solution) = 1.19 g
× 50

m(hydrochloric acid solution) = 59.5 g

The concentration of a solution is the amount of solute in a specified volume of solution.  One way of expressing concentration is by mass percentages:  20% w/w.  This means that there is 20 g of the specified solute in 100 g of solution (or 0.2 g solute per 1 g solution).  If the mass of the solution is known, then the % by mass concentration can be used to calculate the mass of solute present.
Example using these ideas:
The above solution of hydrochloric acid is 37.5% w/w HCl.
This means that there is 0.375 g HCl per gram of solution.
Therefore in the 59.5 g of solution above there are 22.3 g of HCl (0.375 g HCl per g solution × 59.5 g solution)