AP Chemistry 1.1: Moles and molar mass

• Khan Academy's first topic covers average atomic mass, the mole, Avogadro's number, molar mass, and mole/mass calculations.

• Atoms and molecules are extremely small.

  • For example, even a tiny amount of water contains an enormous number of H₂O molecules. Counting individual molecules would be impossible.

• Chemists solve this problem using the mole .

• A mole is simply a counting unit.

  • Think of:

  • 1 dozen = 12 objects

  • 1 pair = 2 objects

  • 1 mole = 6.022 × 10²³ objects

  • The number

  • 6.022 × 10²³

  • is called Avogadro's number .

• The objects being counted are usually called representative particles .

• Depending on the substance, these particles could be:

  • atoms

  • molecules

  • ions

  • formula units

Examples

• 1 mol He = 6.022 × 10²³ He atoms

  • 1 mol H₂O = 6.022 × 10²³ H₂O molecules

  • 1 mol NaCl = 6.022 × 10²³ NaCl formula units

  • Notice that ionic compounds such as NaCl are usually described in terms of formula units , not molecules.

Use:

• particles = moles × 6.022 × 10²³

Example

• How many molecules are present in 2.50 mol H₂O?

• 2.50 mol × (6.022 × 10²³ molecules / 1 mol)

  • = 1.51 × 10²⁴ molecules

• The unit "mol" cancels.

Important dimensional-analysis idea

• Set conversions up so unwanted units cancel.

  • For example:

  • 2.50 mol

• × 6.022 × 10²³ molecules / 1 mol

• The moles cancel, leaving molecules.

• Reverse the conversion:

  • moles = particles / Avogadro's number

Example

• A sample contains 3.011 × 10²³ atoms of carbon.

• 3.011 × 10²³ atoms × (1 mol / 6.022 × 10²³ atoms)

  • = 0.5000 mol C

• The periodic table lists an atomic mass for each element.

  • For example:

  • C ≈ 12.01

  • O ≈ 16.00

  • Cl ≈ 35.45

  • These values normally are not whole numbers because most naturally occurring elements contain multiple isotopes.

• Atomic mass for individual atoms can be expressed in atomic mass units , written:

  • amu

  • or

  • u

• An isotope is a version of an element that has:

  • the same number of protons

  • a different number of neutrons

• Since the number of protons determines the element, changing neutrons does not change the identity of the element.

  • For example:

• Carbon-12:

  • 6 protons 6 neutrons

• Carbon-13:

  • 6 protons 7 neutrons

• Both are carbon because both contain 6 protons .

• But their masses differ because they contain different numbers of neutrons.

• The atomic mass on the periodic table is a weighted average of the masses of an element's naturally occurring isotopes.

• "Weighted" means more common isotopes affect the average more.

Formula

• average atomic mass = Σ(isotope mass × fractional abundance)

• The symbol Σ means "add all of these together."

Example

• Suppose an imaginary element has:

  • isotope X-10: 80.0%

  • isotope X-11: 20.0%

• Convert percentages to decimals:

  • 80.0% = 0.800

  • 20.0% = 0.200

  • Then:

  • (10)(0.800) + (11)(0.200)

  • = 8.0 + 2.2

  • = 10.2 amu

  • Notice that 10.2 is much closer to 10 than 11 because isotope X-10 is much more abundant.

AP test shortcut

• If one isotope is overwhelmingly abundant, the average atomic mass should be closest to that isotope.

• If your answer is nowhere near the most abundant isotope, check your work.

• This mistake is extremely common.

  • If abundance = 25%

  • do not multiply by 25.

• Convert it to:

  • 0.25

  • Example:

  • (35 amu)(0.75) + (37 amu)(0.25)

  • not:

  • (35)(75) + (37)(25)

• Molar mass is the mass of exactly one mole of a substance.

• Units:

  • g/mol

• The periodic table gives you the numerical molar mass of an element.

  • Example:

  • Carbon atomic mass ≈ 12.01 amu

  • Carbon molar mass ≈ 12.01 g/mol

  • This means:

• 1 mol C has a mass of 12.01 g

• Similarly:

  • 1 mol O ≈ 16.00 g

  • 1 mol Na ≈ 22.99 g

• To find a compound's molar mass:

• Identify every element.

• Find its atomic mass.

• Multiply by the number of atoms.

• Add everything together.

  • Example: H₂O

• H₂O contains:

  • 2 H

  • 1 O

  • Using:

  • H = 1.008 g/mol

  • O = 16.00 g/mol

• Molar mass:

  • 2(1.008) + 16.00

  • = 18.016

  • ≈ 18.02 g/mol

  • Example: CaCl₂

  • Ca ≈ 40.08

  • Cl ≈ 35.45

• CaCl₂:

  • 40.08 + 2(35.45)

  • = 40.08 + 70.90

  • = 110.98 g/mol

• Do not forget the subscript 2.

  • Example: Al₂(SO₄)₃

  • This is harder because of parentheses.

• Count atoms first:

  • Al = 2

  • S = 3

  • O = 12

  • because:

  • 3 × O₄ = 12 oxygen atoms.

  • Then:

  • 2(26.98) + 3(32.06) + 12(16.00)

  • = 53.96 + 96.18 + 192.00

  • = 342.14 g/mol

Use:

• moles = mass / molar mass

  • or through dimensional analysis:

  • grams × (1 mol / molar mass in grams)

Example

• How many moles are in 36.0 g H₂O?

• 36.0 g H₂O × (1 mol H₂O / 18.02 g H₂O)

  • ≈ 2.00 mol H₂O

Use:

• mass = moles × molar mass

Example

• Find the mass of 3.00 mol CO₂.

• Molar mass CO₂:

  • 12.01 + 2(16.00)

  • = 44.01 g/mol

  • Then:

  • 3.00 mol × 44.01 g/mol

  • = 132 g CO₂

  • to three significant figures.

• Memorize this relationship:

  • particles ⇄ moles ⇄ grams

• Between particles and moles:

  • 6.022 × 10²³ particles = 1 mol

• Between moles and grams:

  • 1 mol = molar mass in grams

• You usually cannot directly convert particles to grams .

• Go through moles:

  • particles → moles → grams

  • or:

  • grams → moles → particles

• AP Chemistry calculations often require correct significant figures.

• For multiplication and division:

• Your final answer should generally have the same number of significant figures as the measurement with the fewest significant figures .

  • Example:

• 2.03 kg has 3 significant figures .

  • So a calculated answer based on that measurement would normally be reported using 3 significant figures.

• Khan Academy's current practice also asks students to calculate molar mass/moles and report answers with appropriate significant figures.

Memorize

• 1 mol = 6.022 × 10²³ particles

  • moles = mass / molar mass

  • mass = moles × molar mass

  • average atomic mass = Σ(mass × fractional abundance)

Understand

• Why atomic masses are decimals.

• Why the average atomic mass is closer to the most abundant isotope.

• Why molar mass connects microscopic particles to measurable mass.

Be able to do

• grams → moles

  • moles → grams

  • moles → particles

  • particles → moles

  • grams → particles

  • particles → grams

  • calculate molar mass

  • calculate average atomic mass