# The Avogadro Constant

Submitted by ChemPRIME Staff on Wed, 12/08/2010 - 23:44

Although chemists usually workA mechanical process in which energy is transferred to or from an object, changing the state of motion of the object. with moles as units, occasionally it is helpful to refer to the actual number of atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. or molecules involved. When this is done, the symbol N is used. For example, in referring to 1 mol of mercury atoms, we could write

nHg = 1 mol      and      NHg = 6.022 × 1023

Notice that NHg is a pure number, rather than a quantity. To obtain such a pure number, we need a conversion factorA relationship between two units of measure that is derived from the proportionality of one quantity to another; for example, the mass of a substances is proportional to its volume and the conversion factor from volume to mass is density. which involves the number of particles per unit amount of substanceA material that is either an element or that has a fixed ratio of elements in its chemical formula.. The appropriate factor is given the symbol NA and is called the Avogadro constant. It is defined by the equation

$N_{\text{A}}\text{ = }\frac{N}{n}$            (1)

Since for any substance there are 6.022 × 1023 particles per mole, NA =6.022 × 1023/1 mol = 6.022 × 1023 mol–1.

EXAMPLE Calculate the number of O2 molecules in 0.189 mol O2.

SolutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. Rearranging the above equation, we obtain

N = n × NA = 0.189 mol × 6.022 × 1023 mol–1 = 1.14 × 1023

Alternatively, we might include the identity of the particles involved:

$\text{N}=\text{0}\text{.189 mol O}_{\text{2}}\times \frac{\text{6}\text{.022}\times 10^{\text{23}}\text{ O}_{\text{2}}\text{ molecules}}{\text{1 mol O}_{\text{2}}}$

$=~\text{1}\text{.14}\times \text{10}^{\text{23}}\text{ O}_{\text{2}}\text{ molecules}$

Notice that the above equation, which defines the Avogadro constant, has the same form as the equation which defined density. The preceding example used the Avogadro constant as a conversion factor in the same way that density was used. As in previous examples, all that is necessary is to remember that number of particles and amount of substance are related by a conversion factor, the Avogadro constant.

$\text{Number of particles }\overset{\text{Avogadro constant}}{\longleftrightarrow}\text{amount of substance}$

$N\overset{\text{N}_{\text{A}}}{\longleftrightarrow}n$

As long as the units mole cancel, NA is being used correctly.