Review of Fundamentals

The Mole

A mole is a unit for counting atoms, molecules, ions, electrons, etc. It is used in the same sense that a dozen is a convenient unit for donuts, eggs, etc.

One dozen is a small integer number because donuts, eggs, etc, are large objects. One mole is a large integer because atoms, molecules, ions, electrons, etc, are really small objects.

The international convention is that a mole is equal to the number of atoms contained in an exactly 12 gram sample of pure ¹²C isotope. With this definition of a mole we further define:

Gram Atomic Weight:

weight of one mole of atoms. For example, Carbon has a gram atomic weight of 12.011

Gram Molecular Weight:

weight of one mole of molecules. For example, CO₂ has a gram molecular weight of 44.01

Gram Formula Weight:

weight of one mole of a given stoichiometry. For example, NaCl has a gram formula weight of 58.44. NaCl is not really a molecule so we use the more general term formula.

Concentration Units

Molarity

A concentration given in units of molarity is calculated according to:

The unit volume is most commonly in liters. The abbreviation for molarity is M.

helpful hint:

Let's look at some examples:

1.26 g of AgNO₃ is dissolved in H₂O and the solution is diluted to 250 mL. What is the molarity?

First step: Determine the G.F.W. of AgNO₃

Second step:

Try this one at home:

Starting with this 0.0297 M solution, calculate how much volume of it you would need to prepare 100 mL of a 0.01 M solution of AgNO₃.

To do this problem you will need to (1) calculate the number of moles needed in 100 mL of solution, and (2) calculate the volume of 0.0297 M solution that contains the number of moles needed. You should obtain 33.7 mL as your final answer.

Formality

Many compounds undergo dissociation of complex formation when dissolved. For example, the solute acetic acid, CH₃CO₂H discociates slightly when dissolved in H₂O according to:

If we dissolve 0.100 moles of CH₃CO₂H in 1.000 L of H₂O we find that 1.3% of it dissociates according to:

Because of dissociation the final CH₃CO₂H concentration is less than 0.100 M. Thus, we use the term formality (F) to indicate the total number of moles of a solute in one liter of solution.

In this example the solution is a 0.0987 M solution of acetic acid, and at the same time is a 0.100 F solution of acetic acid. If there is no dissociation then molarity and formality are equivalent.

Molality

Molality is a convenient unit because molal concentrations are not temperature dependent. Only at 3.98°C, where the density of water is 1.0000 g/mL will 1000 g of water have a volume of 1 liter. That is, volume changes with temperature, but mass will not. Thus, molality has the advantage that it is independent of temperature, whereas Formality and Molarity both depend on temperature.

Normality

Normality only has meaning in the context of a chemical reaction. The number of equivalents is number of reacting units in a species times the species' concentration in Molarity. That is,

where n is the number of reacting units, such as H⁺, e^-, univalent cations, etc. For example, when dealing with acids and bases we consider the H⁺ or OH^- ions as reacting units. Thus, the acid H₂SO₄ contains two reacting H⁺. So, a 2 M H₂SO₄ solution is a 4 N H₂SO₄ solution.

In reduction/oxidation (redox) reactions it is the electrons that are counted as reacting units. For example, consider the oxidation of the oxalate ion by permanganate:

For this reaction the change in oxidation number of Mn is 5. This is known by looking at the reduction half-reaction involving Mn:

where it is clear that Mn accepts 5 electrons. Thus, a 1M KMnO₄ solution is a 5 N solution when used in the oxidation of oxalate ions.

It is important to emphasize that normality only has meaning in the context of a chemical reaction. For example, the permanganate ion could also be involved in chemical reactions with different half reactions:

and the normality of a KMnO₄ solution would be different in each case.

Other Concentration Units

Amount of solid samples

weight percentage (%):

This is one of the most common units for solids.

For example, if a 100 g sample of limestone contains 3 g of iron then the concentration of iron is

Trace concentrations are given in smaller units

weight parts-per-thousand (ppt):

weight parts-per-million (ppm):

weight parts-per-billion (ppb):

Amount of liquid samples

Weight/volume (g/mL) is also a common unit.

weight/volume (%):

weight/volume (ppt):

weight/volume (ppm):

weight/volume (ppb):

It is important to specify (w/w) or (w/v) when reporting results in %, ppt, ppm, or ppb.