0907 Solution concentration

How many moles of solute per litre of solution? The importance of visualisation.

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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.

KEY IDEAS
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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.
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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):

• Understanding what are the values of c, n, and V in particular situations (particularly when samples of a solution are diluted) can be difficult.
• Sometimes students confuse the concentration of solute in a solution and the amount of solute.

 

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.
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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:

• If two samples taken from a given solution have different volumes (let’s say, a 20 mL sample and a 100 mL sample), nothing has been done to change the closeness of the solute molecules: the samples have the same concentration – and this is the same as the concentration of the solution from which they were taken. This is because the 100 mL sample contains five times the amount of solute that is in the 20 mL sample, so the ratio n/V is the same in both samples.
• If a sample of a solution is diluted (by adding water), the same number of solute molecules will be dispersed over a larger volume of (new) solution. So the solute molecules will be further apart (on average): the concentration is less than before.

 

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:
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​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:

Some notes:

• Although it is common to refer to “the concentration of solution”, it is more technically correct to think of “concentration of solute in the solution”. This can certainly aid visualisation.
• The opposite of concentrated is dilute. The less concentrated a solution is, the more dilute it is (and the solute molecules are further from each other, on average).
• There is no value of concentration that is a crossover from “concentrated solution” to “dilute solution”. Rather, these terms are generally used in a comparative sense: “This solution is more concentrated than that one.”
• The concentration of an aqueous solution measured as moles per litre of solution is not the same value as moles per litre of solvent (that is, per litre of water in the solution).
• Solution concentration is what is called an intensive property: it’s value does not depend on the amount of the sample. Other examples of intensive properties are (i) the temperature of a substance, and (ii) density.​

​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.

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