D. Quantities in Chemical Reactions · Quantities in Chemical ReactionsMolar Mass: Linking Moles to Grams
D3.2 D2.1 D2.3 A1.12About 70 minutes
Learning goals- I can explain the link between atomic mass and molar mass.
- I can calculate the molar mass of elements, compounds with brackets, and hydrates.
- I can convert between mass and amount in moles with n = m ÷ M.
- I can use correct units (g, mol, g/mol) and significant figures.
Words to know
atomic mass
The average mass of one atom of an element, in atomic mass units (u), taking all its natural isotopes into account. It is the decimal number on the periodic table.
molar mass (M)
The mass of one mole of a substance, in grams per mole (g/mol).
formula mass / molecular mass
The sum of the atomic masses in a formula, in u. It has the same number as the molar mass.
hydrate
An ionic compound with water molecules built into its crystals, written with a raised dot, such as CuSO₄·5H₂O.
mass (m)
How much matter a sample has, usually measured in grams (g) on a balance.
A mole of what, weighing how much?
In the last lesson you met the mole, 6.02 × 10²³ particles. That number is useless in the lab unless you can measure it. Nobody can count 6.02 × 10²³ atoms, but everyone can use a balance. Molar mass is the bridge: it tells you how many grams one mole of a substance weighs. Once you know it, a balance becomes a particle counter.
From atomic mass to molar mass
Every box on the periodic table shows an atomic mass, such as 12.01 for carbon. That number is the average mass of one atom, in atomic mass units (u). It is an average because most elements are a natural mixture of isotopes; you work out such averages in the unit Matter, Chemical Trends, and Chemical Bonding.
Here is the beautiful part. The mole was chosen so that the same number, in grams, is the mass of one mole of atoms:
- one carbon atom: 12.01 u
- one mole of carbon atoms: 12.01 g
So the molar mass of carbon is M = 12.01 g/mol. The units g/mol mean "grams per mole".
| Element | Molar mass (g/mol) | Element | Molar mass (g/mol) |
|---|
| H | 1.01 | S | 32.07 |
| C | 12.01 | Cl | 35.45 |
| N | 14.01 | K | 39.10 |
| O | 16.00 | Ca | 40.08 |
| Na | 22.99 | Fe | 55.85 |
| Mg | 24.31 | Cu | 63.55 |
| Al | 26.98 | Zn | 65.38 |
| P | 30.97 | Ag | 107.87 |
Molar mass of a compound
A formula tells you how many moles of each kind of atom are in one mole of the compound. So the molar mass of a compound is the sum of the molar masses of all the atoms in its formula:
M(compound) = Σ (number of atoms of each element × molar mass of that element)
For water, H₂O: M = 2(1.01) + 1(16.00) = 18.02 g/mol.
Three rules keep you out of trouble:
- A subscript applies only to the element right before it (in CO₂ the 2 belongs to O).
- A subscript after brackets multiplies everything inside them: Ca(OH)₂ has 1 Ca, 2 O and 2 H.
- In a hydrate, the number in front of H₂O multiplies the whole water molecule, and you add the water to the rest: CuSO₄·5H₂O means CuSO₄ plus 5 H₂O.
Worked exampleExample 1: A compound with brackets
Find the molar mass of aluminium sulfate, Al₂(SO₄)₃.
- Count atoms. The 3 after the bracket multiplies S and O: Al: 2; S: 1 × 3 = 3; O: 4 × 3 = 12.
- Al: 2 × 26.98 = 53.96
- S: 3 × 32.07 = 96.21
- O: 12 × 16.00 = 192.00
- Add: 53.96 + 96.21 + 192.00 = 342.17
M(Al₂(SO₄)₃) = 342.17 g/mol
Worked exampleExample 2: A hydrate
Copper(II) sulfate pentahydrate, CuSO₄·5H₂O, forms bright blue crystals. Find its molar mass.
- First the CuSO₄ part: 63.55 + 32.07 + 4(16.00) = 159.62
- Then the water part: 5 × M(H₂O) = 5 × 18.02 = 90.10
- The dot means add, not multiply: 159.62 + 90.10 = 249.72
M(CuSO₄·5H₂O) = 249.72 g/mol. More than a third of the mass of the blue crystals is water!
Converting between mass and moles
Molar mass is a conversion factor, just like Avogadro's constant:
n = m ÷ M and m = n × M
where n is in mol, m in g and M in g/mol. A handy memory aid: mass is moles times molar mass. Always write the units; if they cancel to the unit you want, the setup is right:
g ÷ (g/mol) = g × (mol/g) = mol
Worked exampleExample 3: Grams to moles
A student measures 25.0 g of water. What amount of water is this?
- M(H₂O) = 18.02 g/mol
- n = m ÷ M = 25.0 g ÷ 18.02 g/mol = 1.3873… mol
- 25.0 has 3 significant figures, so round to 3.
Worked exampleExample 4: Moles to grams
A recipe for a lab solution calls for 0.150 mol of sodium chloride. What mass should you weigh out?
- M(NaCl) = 22.99 + 35.45 = 58.44 g/mol
- m = n × M = 0.150 mol × 58.44 g/mol = 8.766 g
- Round to 3 significant figures.
Weigh out 8.77 g of NaCl.
Each pile is one mole, so each holds the same number of particles, but the masses differ because the particles have different masses (sizes are only suggestive).Just for funWhy was the chemistry student so calm before the molar mass quiz?
She knew every question was just a matter of adding things up.
Hands-on activityOne mole in the kitchen
You need: a kitchen scale, table salt (sodium chloride, NaCl), baking soda (sodium hydrogen carbonate, NaHCO₃), white sugar (sucrose, C₁₂H₂₂O₁₁), water, a measuring cup and four small bowls.
- Calculate the molar mass of each substance (use the table above). Check: NaCl 58.44 g/mol, NaHCO₃ 84.01 g/mol, C₁₂H₂₂O₁₁ 342.34 g/mol, H₂O 18.02 g/mol.
- Weigh out one mole of each solid into its own bowl (remember to zero the scale with the empty bowl first). Measure one mole of water: about 18 g, which is about 18 mL, a little more than one tablespoon (15 mL).
- Line up the four bowls. Each holds 6.02 × 10²³ particles. Which pile is biggest? Why?
- Put the ingredients back or use them in cooking afterwards (do not taste the baking soda on its own).
What to look for: the sugar pile is by far the largest (342 g, more than 1½ cups), because each sucrose molecule has 45 atoms. The water is the smallest. Your explanation should say that the piles have equal numbers of particles but the particles have different masses.
Your turn
1Find the molar mass of carbon dioxide, CO₂.
12.01 + 2(16.00) = 44.01 g/mol
2Find the molar mass of ammonia, NH₃.
14.01 + 3(1.01) = 17.04 g/mol
3Find the molar mass of magnesium nitrate, Mg(NO₃)₂.
Mg 24.31 + N 2(14.01) = 28.02 + O 6(16.00) = 96.00. Total 148.33 g/mol.
4Find the molar mass of ammonium phosphate, (NH₄)₃PO₄.
N 3(14.01) = 42.03; H 12(1.01) = 12.12; P 30.97; O 4(16.00) = 64.00. Total 149.12 g/mol.
5What amount of calcium carbonate is in 10.0 g of chalk (pure CaCO₃, M = 100.09 g/mol)?
n = 10.0 ÷ 100.09 = 0.0999 mol
6What is the mass of 2.50 mol of oxygen gas, O₂?
M = 32.00 g/mol; m = 2.50 × 32.00 = 80.0 g
7Find the molar mass of Epsom salt, MgSO₄·7H₂O.
MgSO₄: 24.31 + 32.07 + 64.00 = 120.38. Water: 7 × 18.02 = 126.14. Total 246.52 g/mol.
More practice: warm-up
1What is the molar mass of sodium, Na?
2What are the units of molar mass?
3Find the molar mass of oxygen gas, O₂.
4Find the molar mass of nitrogen gas, N₂.
5Find the molar mass of hydrogen chloride, HCl.
1.01 + 35.45 = 36.46 g/mol
More practice: on your own
1A sugar cube has a mass of 5.00 g. What amount of sucrose, C₁₂H₂₂O₁₁ (M = 342.34 g/mol), is this?
n = 5.00 ÷ 342.34 = 0.0146 mol (1.46 × 10⁻² mol).
2What is the mass of 0.0250 mol of iron(III) oxide, Fe₂O₃ (rust)?
M = 2(55.85) + 3(16.00) = 159.70 g/mol. m = 0.0250 × 159.70 = 3.9925 g ≈ 3.99 g.
3Which has the larger mass: 1.00 mol of water or 0.500 mol of carbon dioxide? Show your work.
Water: 1.00 × 18.02 = 18.0 g. CO₂: 0.500 × 44.01 = 22.0 g. The carbon dioxide has the larger mass, even though it is fewer moles.
4A barbecue tank holds 1.00 kg of propane, C₃H₈. What amount of propane is this?
M = 3(12.01) + 8(1.01) = 44.11 g/mol. Convert to grams first: 1.00 kg = 1000 g. n = 1000 ÷ 44.11 = 22.7 mol.
5Explain why one mole of oxygen atoms has a mass of 16.00 g but one mole of oxygen gas has a mass of 32.00 g.
Oxygen gas is made of O₂ molecules. One mole of O₂ molecules contains two moles of O atoms, so its mass is 2 × 16.00 = 32.00 g.
Challenge
1A metal chloride has the formula XCl₂ and a molar mass of 110.98 g/mol. Identify X.
Chlorine part: 2 × 35.45 = 70.90. M(X) = 110.98 − 70.90 = 40.08 g/mol, which is calcium. The compound is CaCl₂.
2A gas sample of 0.250 mol has a mass of 11.0 g. Find its molar mass. Then decide whether it could be CO₂, N₂O or C₃H₈, and whether molar mass alone can identify it.
M = m ÷ n = 11.0 ÷ 0.250 = 44.0 g/mol. CO₂ is 44.01, N₂O is 44.02 and C₃H₈ is 44.11 g/mol, so all three fit to three significant figures. Molar mass alone cannot identify this gas; you would need another test (for example, propane burns, carbon dioxide turns limewater milky).
3Washing soda is a hydrate, Na₂CO₃·xH₂O, with a molar mass of 286.19 g/mol. Find x.
M(Na₂CO₃) = 2(22.99) + 12.01 + 3(16.00) = 105.99. Water part = 286.19 − 105.99 = 180.20 g/mol. x = 180.20 ÷ 18.02 = 10, so the formula is Na₂CO₃·10H₂O.
Quiz
1. What is the molar mass of sulfuric acid, H₂SO₄?
2. The atomic mass of carbon is 12.01 u. What is the mass of one mole of carbon atoms?
3. How many oxygen atoms are counted when you find the molar mass of Ca(OH)₂?
4. What amount is 36.0 g of water?
5. What is the mass of 0.200 mol of sodium hydroxide, NaOH (M = 40.00 g/mol)?
6. In CuSO₄·5H₂O, what does the raised dot mean when calculating molar mass?
Big idea: Molar mass (g/mol) turns a balance into a particle counter. It is the sum of the atomic masses in a formula, and it converts mass to moles (n = m ÷ M) and back (m = n × M). This completes expectation D3.2 (Avogadro's constant, the mole and molar mass) and gives practice for D2.3.
How to help: Ask your teen to read a few formulas aloud and say how many of each atom they contain, especially ones with brackets such as Ca(OH)₂ and Al₂(SO₄)₃. Doing the kitchen activity together makes "one mole" something they can see and hold.
Common difficulties:
- Applying a subscript to the wrong atoms. Only a subscript after a bracket multiplies more than one element.
- Multiplying instead of adding for hydrates (the dot means "plus this much water").
- Using 16.00 for oxygen gas instead of 32.00. Diatomic elements (H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂) have double the atomic molar mass.
- Dividing the wrong way. Writing units and cancelling them shows whether n = m ÷ M was set up correctly.
- Forgetting to change kilograms to grams before dividing by g/mol.