# 2.2.3: Moles

- Page ID
- 18288

A * mole* of an element (or of a compound) is defined as containing 6.022 × 10

^{23}atoms (or molecules). The number, 6.022 × 10

^{23}, is known as

*. So, one mole of carbon is equivalent to 6.022 × 10*

*Avogadro’s number*^{23}carbon atoms. The scale used to measure atomic mass has changed slightly over time. Today, it is standardized relative to carbon so that the mass of one mole of

^{12}C is exactly 12.0000. Consequently, all atomic masses are given in

*(*

*atomic mass units**), defined as one-twelfth the mass of*

*amus*^{12}C. Both protons and neutrons have equivalent mass, about one amu, and electrons have almost no mass (less than 1/1000

^{th}the mass of protons and neutrons). So, we might expect the mass of an atom to be equal to the mass number (

*, the total number of protons plus neutrons). But for several reasons, not worth going into here, the mass of an atom is generally close to, but not the same as, the mass number.*

*A*Elements are different from atoms. The * atomic mass*, also called the

*, of an element is the sum of the masses of its naturally occurring isotopes weighted in accordance with their abundances. Atomic masses/weights of elements are molal quantities (and often given in units of grams/mole) but they are really dimensionless numbers because they are all calculated relative to the atomic mass/weight of a mole of carbon. Although isotope mass numbers are always integers, atomic weights of elements are not. For example, many tables and charts give the atomic weight of oxygen as 15.999 and that of iron as 55.847. When elements combine to produce a compound, the atomic weight of the compound is the sum of the weights of the elements in the compound. FeO, for example, has atomic weight 71.846 (15.999 + 55.847) grams/mole.*

*atomic weight*Most elements have very small isotopic variation in nature, no matter where they are found. Thus, most quartz (SiO_{2}) contains about the same relative amounts of the three natural oxygen isotopes (mostly ^{16}O) depicted in Figure 2.5 above. Furthermore, isotopic variations have extremely small effects on the properties of minerals. So, mineralogists generally do not worry much about isotopes. Small isotopic variations, however, may be significant to a geochemist trying to determine the genesis of a particular mineral or rock.

Quartz (SiO_{2}) is one of the most common and well-known minerals. A mole of quartz is 6.022 × 10^{23} SiO_{2} molecules, and that sounds like a lot. How much quartz is that?

###### Solution

To answer this question, we use the atomic weights of silicon and oxygen as well as some crystallographic data. Silicon and oxygen have atomic weights of 28.0855 and 15.9994, respectively. The atomic weight of quartz, SiO_{2}, is therefore 60.0843 (= 28.0855 + 15.9994 + 15.9994). This means that a mole of quartz, 6.022 × 10^{23} SiO_{2} molecules, weighs 60.0843 gm.

Crystallographers have determined that quartz crystals are made of fundamental unit cells shaped like trigonal prisms (discussed in detail in later chapters) containing three (\(Z = 3\)) SiO_{2} molecules. Each unit cell has a volume of 112.985 Å^{3}. So we may calculate the volume of a mole of quartz as:

\[V = N_A \times v/Z\]

where \(V, N_A, v\), and \(Z\) are the molar volume, Avogadro’s number, the unit cell volume, and the number of molecules per unit cell, respectively.

So, \(V\) = 6.022 × 10^{23} SiO_{2}/mole × 112.986 Å^{3}/unit cell \(\div\) 3 SiO_{2}/unit cell

= 2.268 × 10^{25} Å^{3} = 22.68 cm^{3}

which is slightly smaller than a golf-ball.

We can, if we wish, then calculate the density (\(\rho\)) of quartz from the molar data:

\(\rho\) = molar weight \(\div\) molar volume = 60.0843 gm/mole \(\div\) 22.68 cm^{3}/mole = 2.649 gm/cm^{3}