3.3: Counting Atoms

How do I count and calculate the mass of atoms?

Counting Atoms• Atoms are far too small to be counted individually, so we

use the concept of a weighted average.

• Suppose you need 1000 mints. • Each mint weights 1 gram.• How could you gather 1000 mints

without actually counting each

individual mint?

Atomic Number• Atoms of different elements have different numbers of

protons.• Atoms of the same element all have the same number of

protons!!!

• The atomic number (Z) of an element is the number of protons of each atom of that element. It also indicates the number of neutrons (in a normal atom).

• Atomic number identifies an element!

• For all neutral atoms: protons = electrons

Isotopes• Isotopes are atoms of the same element that have

different masses.• Meaning they have varying number of neutrons. • Most elements exist as a mixture of different isotopes.

Three isotopes

of hydrogen

Mass Number• The mass number is the total number of protons and

neutrons that make up the nucleus of an isotope.

Atomic Number(protons)

Number of Neutrons

Mass Number(p+ + n0)

Protium 1 0 1

Deuterium 1 1 2

Tritium 1 2 3

Designating Isotopes• Hydrogen isotopes are unusual in that they have names.• Isotopes are usually identified by specifying their mass

number. • Two methods for specifying isotopes:

1. Hyphen notation hydrogen-3 ( 3 is the mass number (number of p+ and n0))

2. Nuclear symbol

Uranium-238

Finding the number of particles in Isotopes

Example:

How many protons, electrons, and neutrons are there in an atom of chlorine-37?

•The mass number is 37•It indicated the number of protons and neutrons in the nucleus

Solution

We know:• atomic number of chlorine = number of protons

and = number of electrons

(atomic number is found on the periodic table.)

• mass number = protons + neutrons

# neutrons = mass number - protons

Solution• Number of protons = atomic number = 17• Number of electrons = atomic number = 17• Number of neutrons = mass number – atomic number

= 37 – 17

= 20

Protons = 17

Electrons = 17

Neutrons = 20

Learning Check – Left side

1. How many protons, electrons, and neutrons are there in an atom of bromine-80?

2. Write the nuclear symbol for carbon-13

3. Write the hyphen notation for the isotope with 15 electrons and 15 neutrons.

Learning Check- Left side

Fill in the following table.

Element Protons Neutrons Electrons NuclearSymbol

Carbon

11 12

Lithium 4

Relative Atomic Masses• The mass of an individual atom, expressed in grams, is very,

very small.• One atom of oxygen-16 = 2.656 x 10-23 g.

= .00000000000000000000002656 g• So, the standard measurement chemists use atomic mass

units or amu.• One amu = 1/12 the mass of a carbon-12 atom.

Atomic Mass (amu)

Average Atomic Masses of Elements• Why are atomic masses not whole numbers?• Average atomic mass is the weighted average of the

atomic masses of the naturally occurring isotopes of an element.

Calculating Average Atomic Mass• What is the average atomic mass, in amu, of copper?

Naturally occurring copper consists of 69.15% copper-63, which as an atomic mass of 62.929 601 amu; and 30.85% copper-65, which has an atomic mass of 64.927 794.

.6915 (62.929601) + .3085 (64.927794) =

• When you average the masses and adjust for percentage, you get an average atom’s mass of 63.55 amu.

Summary• Atomic number = # p+ = # e-

• Mass # - atomic # = # n0

• # of neutrons varies with the isotope

How many atoms are in a given mass of a compound?

• How can we relate the number of atoms in a sample to a samples mass?

• We need an equality statement to use in the conversion of mass to # of atoms when we use dimensional analysis.

• Our equality statements are:• The Mole• Avogadro’s Number• Molar Mass

The Mole• A mole, mol, is the amount of a substance that contains

as many particles as there are atoms in exactly 12 g of carbon-12.

• A counting unit.

• 1 mol = 6.022 x 1023 atoms

Avogadro’s Number• Avogadro’s number – 6.022 141 79 x 1023 – is the number

of particles in exactly one mole of a pure substance.

• IT IS RIDICULOUSY LARGE!!!!!

602,214,179,000,000,000,000,000

• If every person living on Earth (6 billion) worked to count the atoms in one mole of an element, and if each person counted continuously at a rate of atom per second, it would take about 3 million years for all the atoms to be counted.

Molar Mass• The mass of one mole of a pure substance is called the

molar mass of that substance.

• Units of molar mass = g/mol

• Numerically equal to the atomic mass found on the periodic table.

• What is the molar mass of Lithium?

Comparison of 1-Mol Samples