The Mole

The mole is a unit of measurement used in both chemistry and physics. It represents a numerical quantity and is based on Avogadro’s Number, named after Amedeo Avogadro. It is a constant 6.02 x 1023. The following relationship will better clarify what it means:

1 dozen = 12, 1 mole = 6.02 x 1023

The idea behind these two terms is basically the same. You could say you have one dozen eggs, meaning you have 12 eggs, and the same way you could say that you have one mole of eggs meaning you have 6.02 x 1023 eggs.

x 10 n notation is referred to as scientific notation. It is used to compactly write very large numbers. Avogadro’s Number is actually 602 followed by 21 zeros - a very large number.

The atomic mass listed for carbon, about 12.01 u, is an abundance-weighted average over naturally occurring isotopes. It is not the exact mass of every individual carbon atom. A carbon-12 atom has mass 12 u by definition. For an ordinary sample of carbon with the tabulated isotopic composition, we can use a molar mass of about 12.01 g mol⁻¹ in our sample calculations.

Using the mole offers a very useful relationship that will help us to better understand weights and amounts of elements and compounds:

1 mol C = 6.02 x 1023 C atoms = 12.01 g

Look at the image on the left carefully - the number on the top right demonstrates the relative weight of the element, but can carry two different units: amus (atomic mass units) or atomic weight (grams per mole). Meaning, one mole of carbon (6.02 x 1023 atoms) weighs 12.01 grams. How much do you think one mole of Carbon Dioxide (CO2) weighs?

This relationship applies to all elements in the periodic table, because it provides easier measurement.

Similarly, molarity (M) is a measure of how many moles (mol) of solute are dissolved in a liter (L) of solution.

Recall the difference between, solute, solvent, and solution from Chapter 1

Therefore, if we are told we have a solution with 0.50 M NaCl, that simply means there are 0.50 moles of NaCl for every 1 liter of solution.

To facilitate conversion between moles, grams, and liters, we will use a process called dimensional analysis.

Example Problem 2.1.1

This process of dimensional analysis depends on making ratios (as fractions) to cancel out certain units and end up with the correct unit and numerical quantity at the end of the calculation.

One mole counts the same number of specified entities for any substance: exactly 6.02214076 × 10²³. State what you are counting. For water, the entities can be H₂O molecules; for sodium chloride solid, formula units; for dissolved sodium chloride under a complete-dissociation model, Na⁺ and Cl⁻ ions. The compound formula tells us the corresponding number of each kind of atom or ion.

Example Problem 2.1.2

How much does one molecule of water weigh?

Knowing how to find atomic weights on the periodic table, how to correctly set-up and calculate in dimensional analysis, and how to take “inventory” for compounds will help you answer almost any question dealing with moles or weights. Let’s try something even more difficult

Example Problem 2.1.3

Reviewed numeric example: a60.0mL final NaCl solution has analytical concentration0.200M. UsingM(NaCl)=58.44g mol⁻¹, find its dissolved salt mass and the number of formula units represented. n=0.0120mol, mass=0.701g, and formula units=7.23×10²¹. Under complete dissociation there are that manyNa⁺ions and that manyCl⁻ions. When converting NaCl to a particle count, use formula units, not NaCl molecules. One mole of solid NaCl represents one mole of Na⁺ ions and one mole of Cl⁻ ions in the lattice. If that amount dissolves completely in water, the same ion amounts are dispersed through the solution; dissolution does not change the sodium-to-chloride ratio.