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Mole Concepts

3.2 Mole Concept - Chemistry Form 4
CHEMISTRY • Form 4 • Chapter 3: The Mole Concept, Chemical Formula and Equation

3.2Mole Concept

In everyday life, counting large numbers of items is simplified using grouping units such as a pair (2 items) or a dozen (12 items). In chemistry, because atoms, molecules, and ions are unimaginably tiny and exist in immense quantities, chemists use the unit mole (symbol: mol) to measure the amount of substance. A mole acts as a counting bridge that connects microscopic particles to measurable laboratory quantities like mass in grams and gas volume in cubic decimetres.

Learning Objectives

  • Define mole.
  • Interrelate the Avogadro constant, \(N_A\), the number of particles, and the number of moles.
  • State the meaning of molar mass.
  • Interrelate the molar mass, mass, and the number of moles.
  • State the meaning of molar volume.
  • Interrelate the molar volume, volume of gas, and the number of moles.
  • Solve numerical problems involving the number of particles, number of moles, mass of substances, and volume of gases.

The Mole Conversion Map

The number of moles is the central medium connecting mass, volume of gas, and number of particles.

Brief Explanation

Understand the mole, Avogadro constant, molar mass and molar volume.

Mole (mol) is the SI unit of amount of substance. One mole of substance contains \(6.02214076 \times 10^{23}\) elementary entities of the substance. This number is a fixed value known as the Avogadro constant, \(N_A\), expressed in \(\text{mol}^{-1}\). For calculations at this level, \(N_A\) is taken as \(6.02 \times 10^{23}\text{ mol}^{-1}\).

1. Definition of Mole and Avogadro Constant

One mole of any substance contains \(6.02 \times 10^{23}\) representative particles.

  • Atomic substance: \(1\text{ mol}\) of copper, \(\text{Cu} = 6.02 \times 10^{23}\text{ Cu}\) atoms.
  • Molecular substance: \(1\text{ mol}\) of water, \(\text{H}_2\text{O} = 6.02 \times 10^{23}\text{ H}_2\text{O}\) molecules.
  • Ionic substance: \(1\text{ mol}\) of sodium chloride, \(\text{NaCl} = 6.02 \times 10^{23}\text{ NaCl}\) formula units.

\[\text{Number of moles, } n = \frac{\text{Number of particles}}{N_A}\]

\(\text{Number of particles} = \text{Number of moles } (n) \times N_A\)

2. Number of Moles and Mass of Substances

Molar mass is the mass of one mole of substance, with the unit \(\text{g mol}^{-1}\). Its numerical value is identical to the relative atomic mass (RAM), relative molecular mass (RMM), or relative formula mass (RFM).

  • Copper, \(\text{Cu}\) (RAM = 64) → Molar mass \(= 64\text{ g mol}^{-1}\).
  • Water, \(\text{H}_2\text{O}\) (RMM = 18) → Molar mass \(= 18\text{ g mol}^{-1}\).
  • Sodium chloride, \(\text{NaCl}\) (RFM = 58.5) → Molar mass \(= 58.5\text{ g mol}^{-1}\).

\[\text{Number of moles, } n = \frac{\text{Mass (g)}}{\text{Molar mass (g mol}^{-1}\text{)}}\]

\(\text{Mass (g)} = \text{Number of moles } (n) \times \text{Molar mass (g mol}^{-1}\text{)}\)

3. Number of Moles and Volume of Gases

Molar volume is the volume occupied by \(1\text{ mol}\) of any gas under specific temperature and pressure conditions.

  • STP: \(0^\circ\text{C}, 1\text{ atm}\) → \(22.4\text{ dm}^3\text{ mol}^{-1}\).
  • Room conditions: \(25^\circ\text{C}, 1\text{ atm}\) → \(24\text{ dm}^3\text{ mol}^{-1}\).

Molar volume applies only to gases, not to solids or liquids. \(1\text{ dm}^3 = 1\,000\text{ cm}^3\).

\[\text{Number of moles, } n = \frac{\text{Volume of gas}}{\text{Molar volume}}\]

\(\text{Volume of gas} = \text{Number of moles } (n) \times \text{Molar volume}\)

4. The Mole Bridge

The number of moles (\(n\)) acts as the central conversion hub. To convert from one measurable property to another, the quantity must first be converted into moles.

\[\text{Number of particles} \underset{\times N_A}{\overset{\div N_A}{\rightleftharpoons}} \text{Number of moles } (n) \underset{\div \text{Molar mass}}{\overset{\times \text{Molar mass}}{\rightleftharpoons}} \text{Mass (g)}\]

\[\text{Number of moles } (n) \underset{\div \text{Molar volume}}{\overset{\times \text{Molar volume}}{\rightleftharpoons}} \text{Volume of gas}\]

Quantity Relationship formula Key condition
Number of particles \(n = \dfrac{\text{Number of particles}}{N_A}\) \(N_A = 6.02 \times 10^{23}\text{ mol}^{-1}\)
Mass \(n = \dfrac{\text{Mass (g)}}{\text{Molar mass (g mol}^{-1}\text{)}}\) Molar mass = RAM, RMM or RFM in \(\text{g mol}^{-1}\)
Volume of gas \(n = \dfrac{\text{Volume of gas}}{\text{Molar volume}}\) Gases only; \(22.4\text{ dm}^3\text{ mol}^{-1}\) at STP or \(24\text{ dm}^3\text{ mol}^{-1}\) at room conditions

Try These Questions First

Answer mentally, then check the explanation.

1

Calculate the number of molecules found in \(1.2\text{ mol}\) of hydrogen gas, \(\text{H}_2\).

Answer: \(\text{Number of molecules} = \text{Number of moles} \times N_A = 1.2\text{ mol} \times 6.02 \times 10^{23}\text{ mol}^{-1} = 7.224 \times 10^{23}\text{ molecules}\)
2

What is the mass in grams of \(0.5\text{ mol}\) of ammonia, \(\text{NH}_3\)? (Given RAM: H = 1, N = 14)

Answer: \(\text{Molar mass of }\text{NH}_3 = 14 + 3(1) = 17\text{ g mol}^{-1}\)
\(\text{Mass} = \text{Number of moles} \times \text{Molar mass} = 0.5\text{ mol} \times 17\text{ g mol}^{-1} = 8.5\text{ g}\)
3

Calculate the volume of \(16\text{ g}\) of oxygen gas, \(\text{O}_2\), at STP. (Given RAM: O = 16, molar volume at STP = \(22.4\text{ dm}^3\text{ mol}^{-1}\))

Answer: \(\text{Molar mass of }\text{O}_2 = 2 \times 16 = 32\text{ g mol}^{-1}\)
\(\text{Number of moles of }\text{O}_2 = \dfrac{16\text{ g}}{32\text{ g mol}^{-1}} = 0.5\text{ mol}\)
\(\text{Volume of }\text{O}_2 = 0.5\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 11.2\text{ dm}^3\)

Common Mistakes

Avoid these errors when solving mole calculations.

!
Confusing molecules with total atoms. Diatomic gases such as \(\text{O}_2\), \(\text{N}_2\) and \(\text{Cl}_2\) contain 2 atoms per molecule. When asked for total atoms, multiply the number of molecules by the number of atoms per molecule.
!
Volume unit errors. Forgetting to convert \(\text{cm}^3\) to \(\text{dm}^3\) by dividing by \(1\,000\) before dividing by molar volume, leading to answers that are off by a factor of \(1\,000\).
!
Molar volume condition mix-up. Using \(22.4\text{ dm}^3\text{ mol}^{-1}\) when the question specifies room conditions (\(24\text{ dm}^3\text{ mol}^{-1}\)), or vice versa.
!
Applying molar volume to non-gases. Molar volume applies strictly to gases, not to solids or liquids such as liquid water.

Common Misconceptions

Compare each misconception with the correct fact.

Misconception

One mole of different substances has the same mass.

Correct Fact

Just as a dozen feathers and a dozen bowling balls have different masses, \(1\text{ mol}\) of different substances has different masses because their atoms or molecules have different relative masses.

Misconception

Molar mass and relative molecular mass have the same unit.

Correct Fact

Relative molecular mass (RMM) is a ratio and is dimensionless (no unit), whereas molar mass has the unit \(\text{g mol}^{-1}\).

Misconception

Avogadro's constant changes depending on temperature and pressure.

Correct Fact

The Avogadro constant (\(6.02 \times 10^{23}\text{ mol}^{-1}\)) is a fixed constant representing the number of entities in \(1\text{ mol}\). Only molar volume of gas changes with temperature and pressure.

Summary

Key facts to remember.

  • \(1\text{ mol}\) of any substance contains \(6.02 \times 10^{23}\) particles (atoms, molecules, or formula units).
  • Molar mass is the mass of \(1\text{ mol}\) of substance (\(\text{g mol}^{-1}\)), equal in numerical value to RAM, RMM, or RFM.
  • Molar volume is the volume occupied by \(1\text{ mol}\) of gas: \(22.4\text{ dm}^3\text{ mol}^{-1}\) at STP (\(0^\circ\text{C}, 1\text{ atm}\)) and \(24\text{ dm}^3\text{ mol}^{-1}\) at room conditions (\(25^\circ\text{C}, 1\text{ atm}\)).
  • In all quantitative calculations, always convert the given quantity (mass, volume, or particles) to number of moles first before finding the target quantity.

Quick Activity

Complete all parts before checking your score.

A. Objective Quiz

1

What is the volume occupied by \(0.2\text{ mol}\) of methane gas, \(\text{CH}_4\), at room conditions? (Molar volume of gas at room conditions \(= 24\text{ dm}^3\text{ mol}^{-1}\))

2

A sample contains \(3.01 \times 10^{24}\) formula units of zinc chloride, \(\text{ZnCl}_2\). How many moles of zinc chloride are present in the sample? (Take \(N_A = 6.02 \times 10^{23}\text{ mol}^{-1}\))

B. Fill in the Blanks

3

The volume occupied by one mole of any gas at standard temperature and pressure (STP) is ______ \(\text{dm}^3\text{ mol}^{-1}\).

4

The mass of one mole of a substance is known as its ______.

C. Match Each Chemical Term with Its Definition or Value

Drag each term on desktop. On mobile, tap a term and then tap the matching box.

Chemical Term

Avogadro constant (\(N_A\)) Molar mass Molar volume at room conditions Molar volume at STP

Definition or Value

1 Number of particles contained in one mole of substance (\(6.02 \times 10^{23}\text{ mol}^{-1}\))
2 Mass of one mole of substance with the unit \(\text{g mol}^{-1}\)
3 \(24\text{ dm}^3\text{ mol}^{-1}\) at \(25^\circ\text{C}\) and \(1\text{ atm}\)
4 \(22.4\text{ dm}^3\text{ mol}^{-1}\) at \(0^\circ\text{C}\) and \(1\text{ atm}\)
Complete every answer before checking.
 

Keywords

Tap or hover over a term to read its meaning.

Mole (mol) Avogadro constant (\(N_A\)) Molar mass Molar volume STP Room conditions
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

Mole Concepts

3.2 Mole Concept - Chemistry Form 4
CHEMISTRY • Form 4 • Chapter 3: The Mole Concept, Chemical Formula and Equation

3.2Mole Concept

In everyday life, counting large numbers of items is simplified using grouping units such as a pair (2 items) or a dozen (12 items). In chemistry, because atoms, molecules, and ions are unimaginably tiny and exist in immense quantities, chemists use the unit mole (symbol: mol) to measure the amount of substance. A mole acts as a counting bridge that connects microscopic particles to measurable laboratory quantities like mass in grams and gas volume in cubic decimetres.

Learning Objectives

  • Define mole.
  • Interrelate the Avogadro constant, \(N_A\), the number of particles, and the number of moles.
  • State the meaning of molar mass.
  • Interrelate the molar mass, mass, and the number of moles.
  • State the meaning of molar volume.
  • Interrelate the molar volume, volume of gas, and the number of moles.
  • Solve numerical problems involving the number of particles, number of moles, mass of substances, and volume of gases.

The Mole Conversion Map

The number of moles is the central medium connecting mass, volume of gas, and number of particles.

Brief Explanation

Understand the mole, Avogadro constant, molar mass and molar volume.

Mole (mol) is the SI unit of amount of substance. One mole of substance contains \(6.02214076 \times 10^{23}\) elementary entities of the substance. This number is a fixed value known as the Avogadro constant, \(N_A\), expressed in \(\text{mol}^{-1}\). For calculations at this level, \(N_A\) is taken as \(6.02 \times 10^{23}\text{ mol}^{-1}\).

1. Definition of Mole and Avogadro Constant

One mole of any substance contains \(6.02 \times 10^{23}\) representative particles.

  • Atomic substance: \(1\text{ mol}\) of copper, \(\text{Cu} = 6.02 \times 10^{23}\text{ Cu}\) atoms.
  • Molecular substance: \(1\text{ mol}\) of water, \(\text{H}_2\text{O} = 6.02 \times 10^{23}\text{ H}_2\text{O}\) molecules.
  • Ionic substance: \(1\text{ mol}\) of sodium chloride, \(\text{NaCl} = 6.02 \times 10^{23}\text{ NaCl}\) formula units.

\[\text{Number of moles, } n = \frac{\text{Number of particles}}{N_A}\]

\(\text{Number of particles} = \text{Number of moles } (n) \times N_A\)

2. Number of Moles and Mass of Substances

Molar mass is the mass of one mole of substance, with the unit \(\text{g mol}^{-1}\). Its numerical value is identical to the relative atomic mass (RAM), relative molecular mass (RMM), or relative formula mass (RFM).

  • Copper, \(\text{Cu}\) (RAM = 64) → Molar mass \(= 64\text{ g mol}^{-1}\).
  • Water, \(\text{H}_2\text{O}\) (RMM = 18) → Molar mass \(= 18\text{ g mol}^{-1}\).
  • Sodium chloride, \(\text{NaCl}\) (RFM = 58.5) → Molar mass \(= 58.5\text{ g mol}^{-1}\).

\[\text{Number of moles, } n = \frac{\text{Mass (g)}}{\text{Molar mass (g mol}^{-1}\text{)}}\]

\(\text{Mass (g)} = \text{Number of moles } (n) \times \text{Molar mass (g mol}^{-1}\text{)}\)

3. Number of Moles and Volume of Gases

Molar volume is the volume occupied by \(1\text{ mol}\) of any gas under specific temperature and pressure conditions.

  • STP: \(0^\circ\text{C}, 1\text{ atm}\) → \(22.4\text{ dm}^3\text{ mol}^{-1}\).
  • Room conditions: \(25^\circ\text{C}, 1\text{ atm}\) → \(24\text{ dm}^3\text{ mol}^{-1}\).

Molar volume applies only to gases, not to solids or liquids. \(1\text{ dm}^3 = 1\,000\text{ cm}^3\).

\[\text{Number of moles, } n = \frac{\text{Volume of gas}}{\text{Molar volume}}\]

\(\text{Volume of gas} = \text{Number of moles } (n) \times \text{Molar volume}\)

4. The Mole Bridge

The number of moles (\(n\)) acts as the central conversion hub. To convert from one measurable property to another, the quantity must first be converted into moles.

\[\text{Number of particles} \underset{\times N_A}{\overset{\div N_A}{\rightleftharpoons}} \text{Number of moles } (n) \underset{\div \text{Molar mass}}{\overset{\times \text{Molar mass}}{\rightleftharpoons}} \text{Mass (g)}\]

\[\text{Number of moles } (n) \underset{\div \text{Molar volume}}{\overset{\times \text{Molar volume}}{\rightleftharpoons}} \text{Volume of gas}\]

Quantity Relationship formula Key condition
Number of particles \(n = \dfrac{\text{Number of particles}}{N_A}\) \(N_A = 6.02 \times 10^{23}\text{ mol}^{-1}\)
Mass \(n = \dfrac{\text{Mass (g)}}{\text{Molar mass (g mol}^{-1}\text{)}}\) Molar mass = RAM, RMM or RFM in \(\text{g mol}^{-1}\)
Volume of gas \(n = \dfrac{\text{Volume of gas}}{\text{Molar volume}}\) Gases only; \(22.4\text{ dm}^3\text{ mol}^{-1}\) at STP or \(24\text{ dm}^3\text{ mol}^{-1}\) at room conditions

Try These Questions First

Answer mentally, then check the explanation.

1

Calculate the number of molecules found in \(1.2\text{ mol}\) of hydrogen gas, \(\text{H}_2\).

Answer: \(\text{Number of molecules} = \text{Number of moles} \times N_A = 1.2\text{ mol} \times 6.02 \times 10^{23}\text{ mol}^{-1} = 7.224 \times 10^{23}\text{ molecules}\)
2

What is the mass in grams of \(0.5\text{ mol}\) of ammonia, \(\text{NH}_3\)? (Given RAM: H = 1, N = 14)

Answer: \(\text{Molar mass of }\text{NH}_3 = 14 + 3(1) = 17\text{ g mol}^{-1}\)
\(\text{Mass} = \text{Number of moles} \times \text{Molar mass} = 0.5\text{ mol} \times 17\text{ g mol}^{-1} = 8.5\text{ g}\)
3

Calculate the volume of \(16\text{ g}\) of oxygen gas, \(\text{O}_2\), at STP. (Given RAM: O = 16, molar volume at STP = \(22.4\text{ dm}^3\text{ mol}^{-1}\))

Answer: \(\text{Molar mass of }\text{O}_2 = 2 \times 16 = 32\text{ g mol}^{-1}\)
\(\text{Number of moles of }\text{O}_2 = \dfrac{16\text{ g}}{32\text{ g mol}^{-1}} = 0.5\text{ mol}\)
\(\text{Volume of }\text{O}_2 = 0.5\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 11.2\text{ dm}^3\)

Common Mistakes

Avoid these errors when solving mole calculations.

!
Confusing molecules with total atoms. Diatomic gases such as \(\text{O}_2\), \(\text{N}_2\) and \(\text{Cl}_2\) contain 2 atoms per molecule. When asked for total atoms, multiply the number of molecules by the number of atoms per molecule.
!
Volume unit errors. Forgetting to convert \(\text{cm}^3\) to \(\text{dm}^3\) by dividing by \(1\,000\) before dividing by molar volume, leading to answers that are off by a factor of \(1\,000\).
!
Molar volume condition mix-up. Using \(22.4\text{ dm}^3\text{ mol}^{-1}\) when the question specifies room conditions (\(24\text{ dm}^3\text{ mol}^{-1}\)), or vice versa.
!
Applying molar volume to non-gases. Molar volume applies strictly to gases, not to solids or liquids such as liquid water.

Common Misconceptions

Compare each misconception with the correct fact.

Misconception

One mole of different substances has the same mass.

Correct Fact

Just as a dozen feathers and a dozen bowling balls have different masses, \(1\text{ mol}\) of different substances has different masses because their atoms or molecules have different relative masses.

Misconception

Molar mass and relative molecular mass have the same unit.

Correct Fact

Relative molecular mass (RMM) is a ratio and is dimensionless (no unit), whereas molar mass has the unit \(\text{g mol}^{-1}\).

Misconception

Avogadro's constant changes depending on temperature and pressure.

Correct Fact

The Avogadro constant (\(6.02 \times 10^{23}\text{ mol}^{-1}\)) is a fixed constant representing the number of entities in \(1\text{ mol}\). Only molar volume of gas changes with temperature and pressure.

Summary

Key facts to remember.

  • \(1\text{ mol}\) of any substance contains \(6.02 \times 10^{23}\) particles (atoms, molecules, or formula units).
  • Molar mass is the mass of \(1\text{ mol}\) of substance (\(\text{g mol}^{-1}\)), equal in numerical value to RAM, RMM, or RFM.
  • Molar volume is the volume occupied by \(1\text{ mol}\) of gas: \(22.4\text{ dm}^3\text{ mol}^{-1}\) at STP (\(0^\circ\text{C}, 1\text{ atm}\)) and \(24\text{ dm}^3\text{ mol}^{-1}\) at room conditions (\(25^\circ\text{C}, 1\text{ atm}\)).
  • In all quantitative calculations, always convert the given quantity (mass, volume, or particles) to number of moles first before finding the target quantity.

Quick Activity

Complete all parts before checking your score.

A. Objective Quiz

1

What is the volume occupied by \(0.2\text{ mol}\) of methane gas, \(\text{CH}_4\), at room conditions? (Molar volume of gas at room conditions \(= 24\text{ dm}^3\text{ mol}^{-1}\))

2

A sample contains \(3.01 \times 10^{24}\) formula units of zinc chloride, \(\text{ZnCl}_2\). How many moles of zinc chloride are present in the sample? (Take \(N_A = 6.02 \times 10^{23}\text{ mol}^{-1}\))

B. Fill in the Blanks

3

The volume occupied by one mole of any gas at standard temperature and pressure (STP) is ______ \(\text{dm}^3\text{ mol}^{-1}\).

4

The mass of one mole of a substance is known as its ______.

C. Match Each Chemical Term with Its Definition or Value

Drag each term on desktop. On mobile, tap a term and then tap the matching box.

Chemical Term

Avogadro constant (\(N_A\)) Molar mass Molar volume at room conditions Molar volume at STP

Definition or Value

1 Number of particles contained in one mole of substance (\(6.02 \times 10^{23}\text{ mol}^{-1}\))
2 Mass of one mole of substance with the unit \(\text{g mol}^{-1}\)
3 \(24\text{ dm}^3\text{ mol}^{-1}\) at \(25^\circ\text{C}\) and \(1\text{ atm}\)
4 \(22.4\text{ dm}^3\text{ mol}^{-1}\) at \(0^\circ\text{C}\) and \(1\text{ atm}\)
Complete every answer before checking.
 

Keywords

Tap or hover over a term to read its meaning.

Mole (mol) Avogadro constant (\(N_A\)) Molar mass Molar volume STP Room conditions
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Mole Concept, Chemical Formulae and Equations
Topic : Mole Concept
Form 4 Chemistry
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