Chemistry

The mole

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# Avogadro constant

## Mole and number of formula units

One mole of a substance is its gram formula mass (GFM).

One mole of a substance contains 6.02 x 1023 formula units.

This number is known as the Avogadro constant.

The Avogadro constant can be found in the SQA data booklet, and is expressed as 6.02 x 1023 mol-1.

The term formula unit is a general term that relates to the type of particles that make up a substance. In general, it refers to the formula normally used for the substance.

• In diamond, one formula unit is a carbon atom [atom: An atom is the smallest part of an element that still has the properties of that element, comprising electrons surrounding a nucleus of protons and neutrons. (C).
• In oxygen, one formula unit is an oxygen molecule (O2).
• In sodium chloride, one formula unit is one sodium ion and one chloride ion (Na+Cl-).
• In silicon dioxide, one formula unit is one silicon atom and two oxygen atoms (SiO2).

Equimolar quantities of substances contain equal numbers of formula units.

The idea of the mole links the mass of a substance to the number of formula units it contains.

The calculations below involve calculating number of formula units, given number of moles, and vice versa.

The link here is:

1 mole ↔ 6.02 × 1023 formula units

Question

How many molecules are contained in 0.65 mole of sulphur dioxide, SO2?

Answer

Find: m molecules from 0.65 mole of SO2

Link: 6.02 × 1023 formula units ↔ 1 mole

Convert: 6.02 × 1023 molecules ↔ 1 mole

Proportion: There are 6.02 × 1023 molecules in 1 mole. Hence, in 0.65 mole:

m = 0.65 × (6.02 × 1023)

m = 3.91 × 1023

Answer: 3.91 x 1023 molecules are in 0.65 mole of SO2.

Question

How many moles of hydrogen contain 5.5 x 1024 molecules of H2?

Answer

Find: m moles from 5.5 x 1024 molecules

Link: 1 mole ↔ 6.02 × 1023 formula units

Convert: 1 mole ↔ 6.02 × 1023 molecules

Proportion: There is 1 mole for every 6.02 × 1023 molecules. Hence, for 5.5 x 1024 molecules:

m = (5.5 x 1024) ÷ (6.02 × 1023)

m = 9.14

Answer: 9.14 moles contain 5.5 x 1024 molecules of H2.

## Mass and number of formula units

The examples involve calculating number of formula units from a given mass, and vice versa.

The link here is:

mass of 1 mole ↔ 6.02 × 1023 formula units

As the mass of moles is involved, it is necessary to calculate the GFM of the substance.

Question

How many molecules are in 150 g of water, H2O?

Answer

GFM: 2 x H and 1 x O

2 × 1.0 = 2.0

1 × 16.0 = 16.0

GFM = 18.0 g

Find: m molecules from 150 g

Link: 6.02 × 1023 formula units ↔ 1 mole

Convert: 6.02 × 1023 molecules ↔ 150 g

Proportion: There are 6.02 × 1023 molecules in 150 g. Hence, in 150 g:

m = (150 × 6.02 × 1023) ÷ 18

m = 5.02 × 1024

Answer: 5.02 x 1024 molecules are in 150 g of water, H2O.

To work out the number of atoms, multiply the number of molecules by three, which is the number of atoms in one molecule.

Question

What mass of carbon disulphide (CS2) contains 2.04 x 1022 molecules of CS2?

Answer

GFM: 1 x C and 2 x S

1 × 12.0 = 12.0

2 × 32.1 = 64.2

GFM = 76.2g

Find: m grams from 2.04 x 1022 molecules

Link: 1 mole ↔ 6.02 × 1023 formula units

Convert: 76.2 g ↔ 6.02 × 1023 molecules

Proportion: There are 6.02 × 1023 molecules in 76.2 g. Hence, for 2.04 x 1022 molecules:

m = (76.2 × 2.04 x 1022) ÷ (6.02 × 1023)

m = 2.58

Answer: 2.58 g contains 2.04 x 1022 molecules of CS2.

Question

What mass of sodium chloride (NaCl) would contain 9.03 x 1021 ions?

Answer

GFM: 1 x Na and 1 x Cl

1 × 23.0 = 23.0

1 × 35.5 = 35.5

GFM = 58.5g

Note that one formula unit of NaCl contains two ions.

Find: m grams from 9.03 x 1021 ions

Link: 1 mole ↔ 6.02 × 1023 formula units

Convert: 58.5 g ↔ 2 × (6.02 × 1023) ions

Proportion: 2 × (6.02 × 1023) ions are in 58.5 g. Hence, 9.03 x 1021 ions are in:

m = (58.5 × 9.03 x 1021) ÷ (2 × (6.02 × 1023))

m = 0.44

Answer: 0.44 g of NaCl contains 9.03 x 1021 ions.

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