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.
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.
Calculate the number of molecules found in \(1.2\text{ mol}\) of hydrogen gas, \(\text{H}_2\).
What is the mass in grams of \(0.5\text{ mol}\) of ammonia, \(\text{NH}_3\)? (Given RAM: H = 1, N = 14)
\(\text{Mass} = \text{Number of moles} \times \text{Molar mass} = 0.5\text{ mol} \times 17\text{ g mol}^{-1} = 8.5\text{ g}\)
Calculate the volume of \(16\text{ g}\) of oxygen gas, \(\text{O}_2\), at STP. (Given RAM: O = 16, molar volume at STP = \(22.4\text{ dm}^3\text{ mol}^{-1}\))
\(\text{Number of moles of }\text{O}_2 = \dfrac{16\text{ g}}{32\text{ g mol}^{-1}} = 0.5\text{ mol}\)
\(\text{Volume of }\text{O}_2 = 0.5\text{ mol} \times 22.4\text{ dm}^3\text{ mol}^{-1} = 11.2\text{ dm}^3\)
Common Mistakes
Avoid these errors when solving mole calculations.
Common Misconceptions
Compare each misconception with the correct fact.
One mole of different substances has the same mass.
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.
Molar mass and relative molecular mass have the same unit.
Relative molecular mass (RMM) is a ratio and is dimensionless (no unit), whereas molar mass has the unit \(\text{g mol}^{-1}\).
Avogadro's constant changes depending on temperature and pressure.
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
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 \(= 24\text{ dm}^3\text{ mol}^{-1}\))
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
The volume occupied by one mole of any gas at standard temperature and pressure (STP) is ______ \(\text{dm}^3\text{ mol}^{-1}\).
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 STPDefinition or Value
Keywords
Tap or hover over a term to read its meaning.
