How many moles of solute per litre of solution? The importance of visualisation.
The term concentration refers to how crowded are solute particles in solution (on average) - and does not depend on the volume of the solution of interest: it is an intensive property.
There are a number of different ways that the concentration of solutions can be expressed. In this module, I will focus on the most common of these, called the molarity.
Real understanding (rather than simply substitution into mathematical equations) can be enhanced by visualising how close, on average, are the molecules of solute in a solution.
The molarity of a solution (also called the molar concentration), for which we use the symbol c, is defined as the amount (in moles) of solute per litre of solution – expressed by the relationship
in which V is the volume of the solution, and n is the amount (in moles) of solute in that volume of solution.
The unit of this measure of concentration is mol L-1, although sometimes the shorter form, M, is used.
So, for a 0.100 molar solution of sucrose in water, we write
and the label that we would put on the container would be
The mechanics of calculations using equation (1) are straightforward. However, teachers are aware of two common problems that students have in application of this equation (and the alternative form, n = c × V):
The essence of this module is that these problems can be minimised by visualising the molecules of solute dispersed among the molecules of solvent.
And this can be enhanced by thinking about the concept of concentration not mathematically through the definition given above, but visually in terms of how close the solute molecules are, on average.
The closer the solute molecules are to each other (on average), the higher is the concentration.
With this in mind, perhaps it is easier to recognise the following:
So, for a given volume of solution (500 mL in the graphic below), the more dissolved solute in the solution, the higher is the concentration:
And, to achieve a given concentration of solute (say 0.020 mol L-1, as in the graphic below), the larger the volume of solution, the more dissolved solute it must contain:
Beware! Complexity lies ahead .... Doesn't it always?
In this module, I have deliberately considered only aqueous solutions of sucrose (C12H22O11, table sugar) because sucrose is a non-electrolyte: the molecules that comprise the solid solute retain their identity when they dissolve in water. This is not the case with some other molecular substances called electrolytes whose molecules break apart in solution to form ionic species. (See 0908 Chemical species, speciation, and 0909 Solutes: Electrolytes or non-electrolytes).
In these cases, it is often more important to consider the concentrations of the ions (the species concentrations), rather than the solution concentration (which is based on how much solute is dissolved in water, rather than on how much is actually in solution after ionisation). See Module 0912 Species concentration vs. solution concentration.