Molarity:  Concentration of Molecular Intensity

Molarity (a way to determine concentration) is deceptive:  Its formula is simple, but what it attempts to measure is illusive.  Individual molecules are invisible.  And concentration, like all variations of intensity, is not a fundamental aspect of the universe.  Properties like the number of atoms or their diameters really are core concepts.  Yet we have a perception that intensities like the brightness of a green leaf, the loudness of music, the sourness of a pickle, the crowdedness of a busy highway, or the extent of a person’s anger are equally real.  But they are not.  Determining sourness or “how angry” are not as simple as counting or measuring.  (Today we have equipment such as pH meters that sometimes hide the complexities and tricks making such tasks appear deceptively as simple measurements.)  It is that deception and complexity that make concentration difficult.

Because intensities are not fundamental, we must invent relationships that represent the intensity.  Such a creative process takes the insight of genius, yet often looks trivial to hindsight.  We define Molarity as the number of molecules in a give space: the moles of solute divided by the litres of solution.  It is as simple as counting the cars on a given mile of crowded highway.  Only when you try to define the extend of someone’s anger or love does the difficulty of that creative process appear.

Example:

Presume a solution of table salt in water.  This is NOT a pure substance such as an element or a compound.  There is more than one ingredient (eliminating element), and the ratio of salt to water is not fixed.  The amount of salt could be any amount from none up to the limit of its solubility.  (Thus a solution is not a true compound which has a fixed ratio.)  For such materials as solutions, concentration is a valuable invention.

An intensity must compare(at least) two properties.  To determine (note the verb was not MEASURE) concentration, we wish to compare the amount of salt with the amount of water.  There are many units that could be used.  Molarity compares the moles of solute with the litres of total solution.  The salt is the solute, and the entire salt and water is the solution.  The volume of solution can be measured, perhaps with a graduated cylinder.  But since the moles of salt can’t be visibly counted, it must be calculated.  Since pure salt is a solid compound, it can be weighed either before making the solution, after separation from the water, or by a titration.  Table salt has a known formula, NaCl, so we can determine its molecular mass: 23.0 + 35.5 = 58.5g/mole.  Since the molecular mass = mass/mole, we can calculate the moles by dividing the measured mass of salt by its molecular mass of 58.5g/mole.  Once the moles are calculated, it can be divided by the volume to calculate concentration.

Say 2.0g of salt is combined with enough water to make 250mL of solution.  What is the concentration?

Calculations:

moles of salt = mass/molecular mass
moles of salt = 2.0g/58.5g/mole
moles of salt = 0.034mole

concentration = moles solute/litres solution
concentration = 0.034mole/0.25L (note: volume converted from mL as required by formula)
concentration = 0.14M (note: M = mole/L)

Notes:

The concentration determined (0.14M) is based on the formula (NaCl).  In some cases this can be misleading.  In solid table salt, the sodium and chlorine exist as ions in a lattice.  Molecules of NaCl do not exist either in the solid or the solution.  The formula NaCl is based on the emperical ratio between the two ions.  Never the less, the concentration of 0.14M is a useful and meaningful way of measuring the solution.  In solution the sodium and chloride ions dissociate and are each surounded by an entourage of water molecules.  Since there is one sodium ion and one chloride ion for each nominal NaCl, the concentration of each ion is also 0.14M.  Had the substance been CaCl₂, the concentration of chloride ions would have been double that of the calcium ions.  In substances that only partially dissociate (such as citric acid) the concentrations of ions and molecules are even more complicated.  (Skills needed for such systems in flux are developed in a later page on Equilibrium Constants.)  However the concentration based on presumed formula remains a valuable measure even in such complicated cases.

A later page on pH extends the mathematics of determining concentration by hiding the need to use exponential numbers for vastly differing concentrations.  That page presents a procedure for presenting any information that has vast variations.

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