0912 Species concentration vs. solution concentration

Module 0912
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Species concentration vs. solution concentration

"Concentration of a species" is not the same as "Concentration of the solution"

The label on the reagent bottle says 0.100 M HF solution, but the concentration of HF molecules is 0.0092 M.

The label says 1.00 M NaCl solution, but there is no NaCl in solution.

What is going on?

Labelled concentration vs. species concentration.
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Does this video provide some answers?

Prof Bob clarifies the important distinction between solution concentration (or 'labelled concentration' and 'species concentration.

Prior knowledge

Understanding this module depends on prior understanding of some other modules, such as:

• Module 0908: Chemical species, speciation. It’s not what we put into a solution that matters, it’s is what is in there. The label on a bottle doesn’t tell us what species are in the solution.
• Module 0907 Solution concentration. How many moles of solute per litre of solution?

 
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APOLOGY: The editor programme used to create these pages does not allow superscripts and subscripts. So in the text, superscripts and subscripts are in-line.
                         For example:   The solution concentration is 0.100 mol L-1
Subscripts are made a little more obvious by using a smaller font: eg  c(C12H22O11) = 0.100 mol L-1
Symbols and formulas that have both superscripts and subscripts can be clumsy: eg, CO32-
On occasions, I have retained superscripts and subscripts by posting images of equations or text.

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KEY IDEAS - Species concentration vs. Solution concentration

Step by step ........

​When we refer to the concentrations of aqueous solutions, it is important to distinguish between

• the solution concentration (or labelled concentration), indicated by the label on a reagent bottle, and
• the concentration of particular species (molecules or ions) in the solution.

Why is it important to distinguish? See below (at end).
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Solution concentration

Solution concentration, or labelled concentration, refers to the amount of solute that is put into (and dissolved in) water, per defined volume of the solution. It is the value that you see on the labels of solution bottles.
 
Perhaps this would better be called the solute concentration.
 
The symbol used is c(solute). See Module 0907 Solution concentration.
 
Solution concentrations can be specified in various units, but let’s just focus here on the unit  mol L-1  (for which the abbreviation M is used) – that is, moles (of solute dissolved) per litre of solution.

The concentration of a sample of solution does not depend on its volume: so concentration is an intensive property.
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Some examples: Solutions of sucrose (C12H22O11), potassium sulfate (K2SO4), hydrogen chloride (HCl), and methanoic acid (HCOOH).
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In all of the following solutions, the solution concentration is 0.100 mol L-1 : ie, c(solute) = 0.100 mol L-1
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• Dissolve 0.100 mol of sucrose in water and make up to 1.00 L: c(C12H22O11) = 0.100 mol L-1
• Dissolve 0.025 mol of sucrose in water and make up to 0.250 L: c(C12H22O11) = 0.100 mol L-1
• Dissolve 0.200 mol of potassium sulfate in water and make up to 2.00 L: c(K2SO4) = 0.100 mol L-1
• Dissolve 0.010 mol of hydrogen chloride in water and make up to 0.100 L: c(HCl) = 0.100 mol L-1
• Dissolve 0.250 mol of methanoic acid in water and make up to 2.50 L: c(HCOOH) = 0.100 mol L-1

 

​[OK, in the cases of the sucrose solution and the hydrogen chloride solution, we have less than 1.00 L of solution, so the above definition might seem odd (since we can’t take a 1.00 L sample of solution). So, getting precise and technical, we might define the solution concentration to be 0.100 mol L-1 if 1.00 L of a solution with the same concentration has 0.100 mol of dissolved solute.]

Species concentration

What is actually present in the solutions described above? What species (molecules or ions) are present, and what is the concentration of each of them? The symbol used for the concentration of each species is [….]. where the formula of the particular species is put inside the square brackets.

Let’s consider some examples to make sense of this:

A 0.100 mol L-1 ​ sucrose solution, ie, a solution with 

Sucrose is a non-electrolyte: the molecules of sucrose retain their identity when they dissolve in water. So the concentration of the sucrose molecules (the species present) is also 0.100 mol L-1, and we write

Yes, in this solution, c(C12H22O11) = 0.100 mol L-1  and   [C12H22O11] = 0.100 mol L-1.
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That might seem trivial, but this is not always the case: in fact, this is the case only for solutions of non-electrolytes.

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​For example ……

A 0.100 mol L-1 potassium sulfate solution, ie, a solution with c(K2SO4) = 0.100 mol L-1 

Like all soluble ionic salts, the ions in the solid lattice separate from each other on dissolving in water, and the ions are aquated (or hydrated). See Module 0905 Dissolution of ionic salts in water.  This ionisation process can be represented by the following chemical equation:

So, what species are in solution? There is none of a species with composition K2SO4, because all of the K+ and SO42- ions have separated from each other. So .....

But we can see from the equation that for every mole of the substance K2SO4 dissolved, twice as many moles of  K+(aq) ions are formed (and are present in solution). So the concentration of K+(aq) ion species is 0.200 mol L-1 
                                                 

And, by corresponding logic ... ​

​More cases ......

A 100 mol L-1 hydrogen chloride solution, ie, a solution which we would label c(HCl) = 0.100 mol L-1 

Hydrogen chloride gas is a molecular solute which is also a strong electroyte: all of the HCl molecules ionise when it is dissolved in water (See Module 0910 Electrolytes - strong or weak?). This can be represented by the chemical equation:

This process is alternatively, and better, represented as a competition between water molecules and choride ions for H+ ions (See Module 0909 Solutes: Electrolytes or non-electrolytes?):

There are no molecular species identifiable as HCl in solution. So,  [HCl] = 0 mol L-1 

The chemical equation tells us that for every HCl molecule that dissolves, one H3O+(aq) ion and one Cl-(aq) ion are formed. So, species concentrations are:
              [H3O+(aq)] = 0.100 mol L-1 
              [Cl-(aq)] = 0.100 mol L-1 

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​A 0.100 mol L-1 methanoic acid solution, ie, a solution with c(HCOOH) = 0.100 mol L-1  .
The solute methanoic acid is a weak electrolyte: some (but not all) ionizes to the point of reaching a state of dynamic chemical equilibrium:   

See Module 0910 Electrolytes – strong or weak?
 

​So, the concentration of HCOOH molecules (the species concentration) is lower than 0.100 mol L-1    
                      [HCOOH] < 0.100 mol L-1 
And [H3O+(aq)] and [HCOO-(aq)] are non-zero: there is some of each of these species in solution.
 
In fact, (you will have to believe me on this) at 20 °C, at equilibrium:

• 96% of HCOOH molecules remain (are un-ionised)
• 4% of HCOOH molecules are ionised

That is, 0.0096 mol L-1  of HCl molecules remain un-ionised,  and 0.004 mol L-1 ionise
So, the various species concentrations are:

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​A 0.100 100 mol L-1 hydrogen fluoride solution, ie, a solution with c(HF) = 0.100 mol L-1 
Dissolved in water, hydrogen fluoride is a weak electrolyte, depicted by the chemical equation:

Hydrogen fluoride is a stronger weak electrolyte than methanoic acid: 92% of HF molecules retain their identity, and 8% are ionized at equilibrium.

So, at equilibrium, the species concentrations are:

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​WHY DOES THIS MATTER?
In chemistry, there are many mathematical relationships concerning properties of solutions that depend on concentrations.

Always, the dependence is on species concentrations – not on labelled solution concentrations.
 
For example (foreshadowing), chemical equilibrium in HF solutions can be represented as

For all solutions that contain these species (no matter how they are  made), we can define an expression Q:

Remarkably, the numerical value of Q is the same in all HF solutions at the same temperature, and the numerical value is called the equilibrium constant (symbol K).
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This is called the law of equilibrium:   For any number of HF solutions (solutions 1, 2, 3, ….) at a given temperature, no matter how they are made up:

[See Module 1103 Equilibrium constants]
 
For the purposes of this module, the important thing is that the values in the expression for Q are species concentrations, […]
 
For example, in a 0.100 M HF solution at 20° C, using data from above, at equilibrium, the species concentrations are:

So, in this solution .....

Then, in accordance with the law of equilibrium, in all solutions at 20° C that contain these species - no matter how matter how they are made - the numerical value of the expression Q is  7.0 ×  10-4. This value (called the equilibrium constant) is the same in every solution containing these species at 20° C.

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For another example, taking this idea further, see Module 0908 Chemical species, speciation. If we have a solution of a weak acid HX, and we change the concentration of the species H+(aq) ions, ie, we change [H+], then the concentrations of the species HX(aq) molecules and X-(aq) ions, also change.

If we increase [H+], then [HX] increases, and [X-] decreases. The relative concentrations of HX(aq) and X-(aq) change in a way consistent with the law of equilibrium:

The ratio of the two species, for any specified concentration of H+(aq) ions,  is shown by re-arranging …..

These very important equations show relationships among the changing species concentrations in a solution in which the solution concentration, c(HX), does not change.

SELF CHECK: Some thinking tasks
 

Have you made it to the next level? A few to go ..... Check your progress.

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​1.            Consider the following solutions:
                            Solution A: c(sucrose) = 0.20 mol L-1
                            Solution B: c(sucrose) = 0.05 mol L-1
                            Solution C: c(sucrose) = 0.02 mol L-1
 
Which of the following statements are correct?
(a)           Solution B is more concentrated than solution C, and more dilute than solution A.
(b)           Solution A is more concentrated than either of solution B or solution C.
(c)           In each of the solutions A, B, and C, c(sucrose) = [sucrose]
(d)           Solution C may have been made by dissolving 0.01 mol of sucrose and making the volume up to 500 mL.
(e)           Solution C is more dilute than either of Solution A or solution B.
(f)           Solution A may have been made by dissolving 1.0 mol of sucrose and making the volume up to 5.0 L.
(g)           In solution B, the concentration of sucrose molecules is 0.05 mol L-1

​2.            Consider three hypothetical water-soluble weak acids with formulas HX, HY, and HZ.
               The ionisation to equilibrium of each of them can be generalised by the following equation:

In 0.080 M solutions of each weak acid, all at 20 °C, at equilibrium:
                             20% of HX is ionised
                             10% of HY is ionised, and
                             5% of HZ is ionised.
Which of the following statements are correct?
(a)           c(HX)  =  c(HY)  =  c(HZ)
(b)           [HX] in the HX solution  =  [HY] in the HY solution  =  [HZ] in the HZ solution
(c)           [X-] in the HX solution  >  [Y-] in the HY solution  >  [Z-] in the HZ solution
(d)           [H3O+] in the HX solution  <   [H3O+] in the HY solution  <   [H3O+] in the HZ solution
(e)           HX is the weakest of the three weak acids.
(f)           [HX] in the HX solution  =  0.016 mol L-1
(g)           [Y-] in the HY solution  = 0.008 mol L-1
(h)           [H3O+] in the HZ solution  =  0.004 mol L-1

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3.           
(a)           Specify a solution in which [a species]  =  c(solution). Name the species.
(b)           Specify a solution in which [a species]  <  c(solution). Name the species.
(c)           Specify a solution in which [a species]  >  c(solution). Name the species.
 

4.           
(a)    In a sodium chloride solution whose concentration is c(NaCl) = 0.238 mol L-1, what are  (i) [NaCl],  (ii) [Na+],             and   (iii) [Cl-]?

(b)    In a magnesium chloride solution with concentration c(MgCl2) = 0.060 mol L-1, what are (i) [MgCl2],                            (ii) [Mg2+], and (iii) [Cl-]?

(c)    In a sodium sulfate solution whose concentration is c(Na2SO4) = 0.120 mol L-1,  what are  (i) [Na2SO4],
        (ii) [Na+], and (iii) [SO42-]?

(d)    In a glucose solution whose concentration is c(C6H12O6) = 0.200 mol L-1, what are (i) [C6H12O6],                                (ii) [any other species]?

(e)    In a solution of methanoic acid whose concentration is c(CH3COOH) = 0.200 mol L-1, in which about 4% of               this weak acid is ionised at equilibrium, what are (i) [CH3COOH], (ii) [CH3COO-], and (iii) [H3O+]?

(f)     An aqueous solution is made by dissolving both sodium chloride and magnesium chloride such that
         c(NaCl) = 0.100 mol L-1  and   c(MgCl2) = 0.250 mol L-1
        In this solution, what are (i) [NaCl], (ii) [MgCl2], (iii) [Na+], (iv) [Mg2+], and (v) [Cl-]?

ANSWERS
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