Avogadro's Number

Consider one atom of oxygen and one atom of sulfur, and compare their atomic weights.

Oxygen's atomic weight = 15.999 amu

Sulfur's atomic weight = 32.06 amu

The sulfur atom weighs approximately twice as much as the oxygen atom. (32.06 / 15.99 x 2)

Because the sulfur atom weighs twice as much as an oxygen atom, a one gram sample of oxygen contains twice as many atoms as a one gram sample of sulfur. Thus, a two gram sample of sulfur contains the same number of atoms as a one gram sample of oxygen.

From this previous example, one might suggest that a relationship exists between the weight of a sample and the number of atoms in the sample. In fact, scientists have determined that there is a definite relationship between the number of atoms in a sample and the sample's weight. Experimentation has shown that, for any element, a sample containing the atomic weight in grams contains 6.022 x 10²³ atoms. Thus 15.999 grams of oxygen contains 6.022 x 10²³ atoms, and 32.06 grams of sulfur contains 6.022 x 10²³ atoms. This number (6.022 x 10²³) is known as Avogadro's number. The importance of Avogadro's number to chemistry should be clear. It represents the number of atoms in X grams of ~Lny element, where X is the atomic weight of the element. It permits chemists to predict and use exact amounts of elements needed to cause desired chemical reactions to occur.

The Mole

A single atom or a few atoms are rarely encountered. Instead, larger, macroscopic quantities are used to quantify or measure collections of atoms or molecules, such as a glass of water, a gallon of alcohol, or two aspirin. Chemists have introduced a large unit of matter, the mole, to deal with macroscopic samples of matter.

One mole represents a definite number of objects, substances, or particles. (For example, a mole of atoms, a mole of ions, a mole of molecules, and even, theoretically, a mole of elephants.) A mole is defined as the quantity of a pure substance that contains 6.022 x 10²³ units (atoms, ions, molecules, or elephants) of that substance. In other words, a mole is Avogadro's number of anything.

For any element, the mass of a mole of that element's atoms is the atomic mass expressed in units of grams. For example, to calculate the mass of a mole of copper atoms, simply express the atomic mass of copper in units of grams. Because the atomic mass of copper is 63.546 amu, a mole of copper has a mass of 63.546 grams. The value for the atomic mass of gold is 196.967 amu. Therefore, a mole of gold has a mass of 196.967 grams. The mass of a mole of atoms is called the gram atomic weight (GAW). The mole concept allows the conversion of grams of a substance to moles and vice versa.

Figure 2 A Mole of Gold Compared to a Mole of Copper

Figure 2 contains a ball of gold and a ball of copper. The two balls are of different masses and different sizes, but each contains an identical number of atoms.

Example 1:

A silver bar has a mass of 1870 grams. How many moles of silver are in the bar?

Solution:

Since the atomic mass of silver (Ag) is 107.87 amu, one mole of silver has a mass 107.87 grams. Therefore, there is one mole of Ag per 107.87 grams of Ag

. There are 1870 grams of silver.

Example 2:

Mercury (Hg) is the only metal that exists as a liquid at room temperature. It iszsed in thermometers. A thermometer contains 0.004 moles of mercury. How many grams 6 mercury are in the thermometer?

Solution:

Since the atomic mass of Hg is 201 amu, one mole of Hg has a mass of 201 grams of Hg or . There are 0.004 moles of Hg. 1 mole Hg