The mole and the Avogadro constant
Introduced| English | Meaning |
|---|---|
| mole/məʊl/ | The SI unit of amount of substance, containing exactly 6.02214076 times ten to the power 23 specified entities. |
| Avogadro constant/ˌævəˈɡædrəʊ ˈkɒnstənt/ | The number of specified elementary entities in one mole, exactly 6.02214076 times ten to the power 23 per mole. |
| molar mass/ˈməʊlə mæs/ | The mass of one mole of a substance. |
How can a balance help count invisible particles?
- A tiny sample contains far too many particles to count individually. Chemists measure an amount in moles 摩尔 and connect it to mass.
- This lesson is Supplement. First name the particles: atoms, molecules, ions or formula units are different things to count.
A mole is a unit of amount
- One mole, symbol mol, contains $6.02\times10^{23}$ specified particles at the precision used in this course. This is the course value for the Avogadro constant 阿伏伽德罗常数, $N_A$.
- One mole of oxygen molecules contains that many O₂ molecules, but twice as many oxygen atoms. Always say which entity the number describes.
The number of particles in one mole is called the ______ constant.
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It is about 6.02 × 10²³.
Convert between mass and amount
- Molar mass 摩尔质量, $M$, is the mass per mole, expressed in $\dfrac{\mathrm{g}}{\mathrm{mol}}$. Its numerical value matches $A_r$ for atoms or $M_r$ for a substance at this course's precision.
- Use $n=m/M$, $m=nM$ or $M=m/n$. Mass $m$ is in grams and amount $n$ is in moles; relative mass itself has no unit.
Water has $M_r=18$, so its molar mass is $18\ \dfrac{\mathrm{g}}{\mathrm{mol}}$. For 36 g of water, $n=m/M=36/18=2.0\ \mathrm{mol}$. For 3.0 mol of water, $m=nM=3.0\times18=54\ \mathrm{g}$. These are different samples.
How many moles are in 36 g of water (Mr = 18)?
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moles = 36 ÷ 18 = 2.
How many moles are in 88 g of CO₂ (Mr = 44)?
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moles = 88 ÷ 44 = 2.
What is the mass of 3 moles of water (Mr = 18)?
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mass = moles × Mr = 3 × 18 = 54 g.
The number of moles is calculated as:
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moles = mass ÷ Mr.
Match each quantity to its unit or description.
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The numerical molar mass matches Mr at this course precision, but they are different quantities.
Convert amount to a particle count
- Use $N=nN_A$ for a count and $n=N/N_A$ for an amount. The number $N$ is a count, not a mass or a volume.
- For 0.50 mol of CO₂, the molecule count is $0.50\times6.02\times10^{23}=3.01\times10^{23}$. Each molecule has two O atoms, so it contains $6.02\times10^{23}$ O atoms.
Do not multiply a mass in grams directly by the Avogadro constant. Convert to moles first. For ionic NaCl, name formula units or specified ions, not NaCl molecules.
How many CO₂ molecules are in 0.250 mol? Use NA = 6.02 × 10²³. Enter only the coefficient in N = ___ × 10²³.
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N=nNA=0.250×6.02×10²³=1.505×10²³ molecules.
What amount of oxygen ATOMS, in mol, is contained in 0.30 mol of O₂ molecules?
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Each O₂ molecule has 2 oxygen atoms, so atom amount = 2×0.30 = 0.60 mol.
Recover an unknown molar mass
- If a pure sample has mass 6.4 g and amount 0.20 mol, $M=m/n=6.4/0.20=32\ \dfrac{\mathrm{g}}{\mathrm{mol}}$.
- A matching molar mass does not by itself prove a substance's identity. Different substances can share the same numerical molar mass.
A pure sample has mass 2.8 g and amount 0.100 mol. Find its molar mass in $\dfrac{\mathrm{g}}{\mathrm{mol}}$.
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M=m/n=2.8/0.100=28 $\dfrac{\mathrm{g}}{\mathrm{mol}}$.
Choose a route before substituting
- Decide whether the answer is mass, amount, molar mass or number of specified particles. Write the equation and include the required unit.
- If atoms inside molecules are asked for, first count molecules and then use the formula's subscripts. Check that a smaller fraction of a mole gives fewer particles.
Mass → amount uses $n=m/M$. Amount → particle count uses $N=nN_A$. Name what you are counting and keep grams, moles and counts separate.
A sample of H₂SO₄ has mass 98 g and molar mass 98 $\dfrac{\mathrm{g}}{\mathrm{mol}}$. Find its amount and explain the distinction between grams and moles.
The numerical amount depends on both sample mass and the substance’s molar mass.
A 98 g H₂SO₄ sample has molar mass 98 $\dfrac{\mathrm{g}}{\mathrm{mol}}$. What is its amount?
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98 divided by 98 is 1. Other options — 2 moles (the lesson water and carbon dioxide samples); 54 g (the lesson mass of 3 moles of water).
CO₂ has molar mass 44 $\dfrac{\mathrm{g}}{\mathrm{mol}}$. Find the amount in 11.0 g, in mol.
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n=m/M=11.0/44=0.250 mol.
A sample contains 0.20 mol of CO₂. Find the amount of oxygen atoms and explain why its molecule count and oxygen-atom count differ.
Compare the reasoning and each criterion; equivalent wording is valid.