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The Mole & Molar Mass

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Why chemists needed a new counting unit

Atoms are absurdly small — a single drop of water holds more atoms than there are stars in the observable universe. You cannot count them one by one, but reactions happen atom-by-atom in fixed ratios. Chemists solved this with the mole: a fixed-size bundle of particles, just like a "dozen" is a fixed bundle of 12.

Avogadro's number
1 mole = 6.022 × 10²³ particles
Particles can be atoms, molecules, ions, or electrons — always state what you are counting.

Molar mass: the bridge to the lab

You cannot weigh out "one mole" directly, but you can weigh grams on a balance. Molar mass (grams per mole, g·mol⁻¹) is the conversion factor between the mass you measure and the moles the reaction cares about. Conveniently, the molar mass of an element in g·mol⁻¹ is just its atomic mass from the periodic table.

Worked example

Find the molar mass of calcium nitrate, Ca(NO₃)₂.

  1. 1.Count every atom, distributing the subscript 2 across the parentheses: 1 Ca, 2 N, 6 O.
  2. 2.Look up atomic masses: Ca = 40.08, N = 14.01, O = 16.00 g·mol⁻¹.
  3. 3.Multiply and sum: (1 × 40.08) + (2 × 14.01) + (6 × 16.00).
  4. 4.= 40.08 + 28.02 + 96.00.
Answer: 164.10 g·mol⁻¹
Watch out

The most common mistake: forgetting the subscript outside the parentheses multiplies everything inside. In Ca(NO₃)₂ there are 6 oxygens, not 3.

Checkpoint

How many moles are in 36.0 g of water (H₂O, molar mass 18.0 g·mol⁻¹)?

Worked example

How many oxygen atoms are in 2.0 mol of CO₂?

  1. 1.Each CO₂ molecule contains 2 oxygen atoms.
  2. 2.Moles of O atoms = 2.0 mol CO₂ × 2 = 4.0 mol O atoms.
  3. 3.Convert moles to atoms with Avogadro: 4.0 × 6.022 × 10²³.
Answer: 2.4 × 10²⁴ oxygen atoms
Checkpoint

Which sample contains the greatest number of atoms?

On the exam

On the AP exam, moles are the hub of almost every quantitative problem. Train the reflex: grams → (÷ molar mass) → moles → (× ratio) → moles of target → (× molar mass or Avogadro) → answer.

Answer the 2 checkpoints as you read.

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