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# CALCULATING MOLAR MASSES AND AVOGADRO’S PRINCIPLE

The atomic masses are given for each element in the periodic table in amus or atomic mass units. The mass number of a given isotope of an element is the sum of the number of protons and the number of neutrons in its nucleus. Recall that in Example 1.1, the mass numbers of the three isotopes of uranium were given as U-234, U-235, and U-238. However, this is not equivalent to the atomic weight. Most elements have more than one isotope, so the natural distribution of the isotopes of an element must also be taken into consideration. Using the carbon-12 isotope as the standard for mass, atomic masses can then be assigned to all the elements. For each element, this number must be a number that is averaged over all of its isotopes according to their relative percent natural abundance. The atomic weight of an element, then, is the average atomic mass of all of the element’s naturally occurring isotopes. The molecular mass then becomes the sum of the atomic weights comprising the molecule, according to the number of each kind of atom occurring in the molecule. In other words, the molecular mass is the sum of the weights of the atoms represented in a molecular formula. Molecular masses (also called molecular weights) are the masses of molecules, which consist of essentially covalent compounds, while formula masses (also called formula weights) are the masses of formula units, which are essentially ionic compounds. The unit, in either case, is the amu, but often converted to the more useful grams/mole, which has the same numerical value.

To get from the microscopic level to the macroscopic scale, a quantity known as “the mole” (abbreviated mol) is defined. A mole of items, regardless of size, shape, or color, all of which are assumed to be identical, is equal to 6.022 x 1023. This is a constant and is referred to as Avogadro’s number. When one mole of atoms of an element is collected, the atoms have a collective mass (molecular mass for a molecule, or a formula mass

for a formula unit) in grams. For comparison sake, one dollar bill or one small paper clip has a mass of about 1 g. The more general term used to refer to either molecular mass or formula mass is molar mass.

Example 1.5

Compute the molar masses of carbon dioxide and calcium nitrate.

Solution

For CO2: The atomic weight of carbon is 12.0 g/mol. The atomic weight of oxygen is 16.0 g/mol.

Hence, the molar mass of carbon dioxide = 12.0 g/mol * 1 + 16.0 g/mol * 2 = 44.0 g/mol

For Ca(NO3)2: The atomic weight of calcium is 40.1 g/mol;

the atomic weight of nitrogen is 14.0 g/mol; atomic weight of oxygen is 16.0 g/mol

Hence, the molar mass of calcium nitrate = 40.1 g/mol * 1 + 14.0 g/mol *

2 + 16.0 g/mol * 6

= 164 g/mol

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