Mole concept

Definition

The scientific definition of a mole is as follows:

• 1 mole of pure ¹²C is exactly 12 grams.
• 1 mole of any substance contains 6.022 x 10²³ particles (rounded to 4 significant figures).

6.022 x 10²³ is known as Avogadro's number.

From the above definition, it follows that there are 6.022 x 10^{23 12}C atoms in one mole of ¹²C atoms.

A mole is used to express a mass quantity and a counting quantity for very small particles such as atoms, protons, electrons etc. In general, one mole of any particles contains 6.022 x 10²³ particles.

Magnitude of Avogadro's Number, 6.022 x 10²³

How does the magnitude 10²³ compare to other large numbers?

Example

1. Distances
   • 10⁷ meter is the diameter of Earth
   • 10⁸ meter is the diameter of Jupiter
   • 10¹⁶ meter is the distance light travels in a year
   • 10²¹ meter is the diameter of the Milky Way
   • 10²⁶ meter is the diameter of the universe
2. Masses
   • 10²³ kilograms is the mass of Mercury
   • 10²⁴ kilograms is the mass of Earth
   • 10²⁷ kilograms is the mass of Jupiter
   • 10³⁰ kilograms is the mass of the sun
3. Other big numbers
   • 10⁹ people is the world population
   • 10¹⁰ years is the age of the universe
   • 10²¹ is the estimated number of stars in the universe

External link

World population clock

A counting quantity

All measurements are always given in reasonable units. A reasonable unit for counting everyday items like apples, eggs, and bananas is to group them by the dozen (count by 12). A reasonable unit for counting very tiny particles like electrons, protons, neutrons, atoms and molecules is to group them by the mole (count by 6.022 x 10²³).

Dozen	a dozen is counting by 12. used to count typical visible quantities eg - marbles, oranges, pencils ... etc
Mole	a mole is counting by 6.022 x 1023. used to count extremely small particles eg - atoms, molecules, ions, electrons, protons, formula units ... etc

Counting by the mole is convenient. Using our eyes, we cannot see a single atom, or a single molecule, but if we scale up to the mole and count in the unit of a mole, we can see these compounds in bulk form. For example,

• We cannot see a molecule of water, but a mole of water is about 18 mL.
• We cannot see a formula unit of table salt, but a mole of table salt is about a palm-full of table salt.
• We cannot see a molecule of oxygen gas, but a mole of oxygen gas will expand a balloon to a diameter of 35 cm at room temperature.

For counting, Avogadro's number has units of:

 6.022 x 1023 ions/mole 

 6.022 x 1023 atoms/mole

 6.022 x 1023 molecules/mole

A mass quantity

Atoms and molecules are very tiny particles. Therefore, counting the number of atoms or molecules in a sample is an impossible task. Since 1 mole of pure ¹²C is, by definition, exactly 12 grams, we can count by weighing.

• One mole of water is about the equivalent of 18 grams.
• One mole of table salt is about the equivalent of 58 grams.

Scaling up to the mole enables us to bridge the gap of the microscopic world of atoms and molecules with the macroscopic world. In the laboratory, a molecule of water cannot be weighed, but a mole of water can be weighed easily because it weighs 18 grams.

Scaling up to the mole allows the chemist to handle chemicals in the laboratory.

Example

Count by weighing is carried out in everyday life. It is similar to buying nails in a hardware store. Although each nail does not have the exact same mass, it is too time consuming to count the number nails at the check out. So, nails are usually purchased by weighing. Chemistry is more exact than buying nail from a hardware store because, unlike nails, atoms of the same types have the EXACT same mass.

• 1 mole hydrogen atoms (or 6.022 x 10²³ hydrogen atoms) has an equivalent mass of 1.008 grams. So, instead of counting 6.022 x 10²³ hydrogen atoms, we weigh out 1.008 grams. When a sample of hyrogen atoms that weighs 1.008 grams is obtained, there must be 6.022 x 10²³ hydrogen atoms, or 1 mole in the sample.
• 1 mole of oxygen atoms (or 6.022 x 10²³ oxygen atoms) has an equivalent mass of 15.999 grams. So, instead of counting 6.022 x 10²³ oxygen atoms, we weigh out 15.999 grams. When a sample of oxygen atoms that weighs 15.999 grams is obtained, there must be 6.022 x 10²³ oxygen atoms, or 1 mole of oxygen atoms in the sample.

Content suitability

BCIT courses: CHEM 0011