Master AP Chemistry Topic 1.1 with this free practice quiz. Test your skills on moles, molar mass conversions, and dimensional analysis to prepare for your AP exam.
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The Pre-Quiz Review
Mole conversions are a fundamental part of chemistry because chemists regularly need to move between the microscopic world of atoms, molecules, and formula units and the measurable world of grams. The mole provides the connection between these two worlds.
For this review, you should understand five closely related ideas:
- Moles
- Molar Mass
- Avogadro’s Number
- Dimensional Analysis
- Gram-to-Mole Conversions
These concepts work together. In particular, Avogadro’s number connects moles to particles, while molar mass connects moles to grams.
1. Moles
What Is a Mole?
A mole (mol) is the SI unit used to measure an amount of a substance.
A mole is similar to other counting units. For example:
- 1 dozen = 12 objects
- 1 pair = 2 objects
- 1 mole = 6.022 × 10²³ particles
The particles being counted can be:
- Atoms
- Molecules
- Formula units
- Ions
- Electrons
- Other specified particles
The word particle is therefore a general term. You must determine what is being counted from the substance and the wording of the problem.
Examples of What a Mole Can Represent
1 mol of carbon atoms contains:
6.022 × 10²³ carbon atoms
1 mol of H₂O molecules contains:
6.022 × 10²³ H₂O molecules
1 mol of NaCl formula units contains:
6.022 × 10²³ NaCl formula units
Notice that the type of particle changes, but the number of particles in one mole remains the same.
Why Chemists Use Moles
Individual atoms and molecules are extremely small, so counting them individually is impractical.
For example, a small sample of water contains an enormous number of H₂O molecules. Instead of saying:
6,022,000,000,000,000,000,000 molecules
chemists can simply say:
1 mol of H₂O
The mole allows chemists to work with enormous numbers of particles using a practical laboratory quantity.
Amount of Substance vs. Mass
A mole measures amount of substance, not mass.
This distinction is important.
For example:
- 1 mol of H₂ contains 6.022 × 10²³ H₂ molecules.
- 1 mol of O₂ contains 6.022 × 10²³ O₂ molecules.
- 1 mol of CO₂ contains 6.022 × 10²³ CO₂ molecules.
They all contain the same number of molecules, but they do not have the same mass because their molecules have different masses.
Therefore:
Moles tell you how many particles you have, while grams tell you how much those particles weigh.
Mole as a Counting Unit
The mole always represents the same number of specified particles:
1 mol = 6.022 × 10²³ particles
However, the word “particles” must be interpreted correctly.
For example:
- 1 mol Na atoms = 6.022 × 10²³ Na atoms
- 1 mol Cl⁻ ions = 6.022 × 10²³ Cl⁻ ions
- 1 mol O₂ molecules = 6.022 × 10²³ O₂ molecules
- 1 mol NaCl formula units = 6.022 × 10²³ NaCl formula units
For ionic compounds such as NaCl, the appropriate term is generally formula units, not molecules.
2. Molar Mass
What Is Molar Mass?
Molar mass is the mass of exactly 1 mole of a substance.
The standard unit for molar mass is:
g/mol
Molar mass tells you how many grams correspond to one mole.
For example, if a substance has a molar mass of 18.02 g/mol, then:
1 mol of the substance = 18.02 g
Likewise:
18.02 g of the substance = 1 mol
This relationship allows you to convert between grams and moles.
Molar Mass and the Periodic Table
The molar mass of an element is numerically equal to its average atomic mass on the periodic table, but the units are different.
For example:
- H ≈ 1.008 g/mol
- C ≈ 12.01 g/mol
- O ≈ 16.00 g/mol
- Na ≈ 22.99 g/mol
- Cl ≈ 35.45 g/mol
If the periodic table gives oxygen an atomic mass of approximately 16.00, then:
1 mol O atoms = 16.00 g O
The numerical value is the same, but the concept and units differ.
3. Calculating Molar Mass of Compounds
For a compound, you must add the masses of all atoms present in one formula unit or molecule.
General Procedure
To calculate molar mass:
- Write the chemical formula.
- Identify the number of atoms of each element.
- Find the atomic mass of each element on the periodic table.
- Multiply each atomic mass by the number of atoms of that element.
- Add all the contributions together.
- Express the final answer in g/mol.
Example: H₂O
Water has the formula:
H₂O
This means one H₂O molecule contains:
- 2 H atoms
- 1 O atom
Using approximate atomic masses:
- H = 1.008 g/mol
- O = 16.00 g/mol
Calculate each contribution:
2 × 1.008 = 2.016 g/mol
1 × 16.00 = 16.00 g/mol
Add them:
2.016 + 16.00 = 18.016 g/mol
Therefore:
Molar mass of H₂O ≈ 18.02 g/mol
Example: CO₂
CO₂ contains:
- 1 C atom
- 2 O atoms
Using:
- C = 12.01 g/mol
- O = 16.00 g/mol
Calculate:
1 × 12.01 = 12.01
2 × 16.00 = 32.00
Total:
12.01 + 32.00 = 44.01 g/mol
Therefore:
Molar mass of CO₂ = 44.01 g/mol
Example: NaCl
NaCl contains:
- 1 Na atom
- 1 Cl atom
Using:
- Na = 22.99 g/mol
- Cl = 35.45 g/mol
Therefore:
22.99 + 35.45 = 58.44 g/mol
So:
Molar mass of NaCl = 58.44 g/mol
4. Subscripts and Coefficients
Understanding chemical formulas is essential when calculating molar mass.
Subscripts
A subscript tells you how many atoms of an element are present in one formula unit or molecule.
For example:
H₂O
The subscript ₂ means there are two hydrogen atoms.
There is no subscript written after O, so its subscript is understood to be 1.
Therefore:
H₂O contains:
- 2 H
- 1 O
Coefficients
A coefficient tells you how many molecules, formula units, or moles are present.
For example:
3H₂O
means:
- 3 H₂O molecules, if counting molecules
- 3 mol H₂O, if referring to moles
It does not change the molar mass of H₂O itself.
The molar mass of H₂O remains approximately:
18.02 g/mol
A coefficient changes the amount of substance, not the molar mass of the substance.
Parentheses in Chemical Formulas
Parentheses indicate that the entire group inside the parentheses is multiplied by the subscript outside.
For example:
Ca(OH)₂
The subscript ₂ applies to both O and H.
Therefore, Ca(OH)₂ contains:
- 1 Ca
- 2 O
- 2 H
Its molar mass is calculated as:
Ca + 2(O) + 2(H)
Using approximate atomic masses:
40.08 + 2(16.00) + 2(1.008)
= 40.08 + 32.00 + 2.016
= 74.096 g/mol
So:
Molar mass of Ca(OH)₂ ≈ 74.10 g/mol
5. Avogadro’s Number
What Is Avogadro’s Number?
Avogadro’s number is the number of particles in exactly one mole.
It is:
6.022 × 10²³ particles/mol
More precisely, the mole is defined using the exact value:
6.02214076 × 10²³ particles/mol
For most introductory chemistry calculations, 6.022 × 10²³ is the expected value.
Avogadro’s number is represented by:
Nₐ
where the subscript “a” stands for Avogadro.
What Does 6.022 × 10²³ Mean?
The number:
6.022 × 10²³
is an extremely large number.
Written out, it is:
602,200,000,000,000,000,000,000
Therefore:
1 mol = 6.022 × 10²³ particles
This is why the mole is useful for counting microscopic particles.
Moles to Particles
To convert from moles to particles, multiply by Avogadro’s number.
The conversion factor is:
6.022 × 10²³ particles / 1 mol
or equivalently:
1 mol / 6.022 × 10²³ particles
Which form you use depends on which unit you need to cancel.
Example: Moles to Molecules
How many molecules are present in 2.00 mol H₂O?
Start with:
2.00 mol H₂O
Multiply by:
6.022 × 10²³ molecules H₂O / 1 mol H₂O
The mol units cancel:
2.00 mol H₂O × (6.022 × 10²³ molecules H₂O / 1 mol H₂O)
= 1.2044 × 10²⁴ molecules H₂O
With appropriate significant figures:
1.20 × 10²⁴ molecules H₂O
Particles to Moles
To convert from particles to moles, divide by Avogadro’s number.
The conversion factor is:
1 mol / 6.022 × 10²³ particles
Example
How many moles are in 3.011 × 10²³ atoms of carbon?
Set up:
3.011 × 10²³ atoms C × (1 mol C / 6.022 × 10²³ atoms C)
The atom units cancel.
The result is:
0.5000 mol C
6. Important Relationships to Memorize
There are two especially important conversion relationships in this topic.
Moles and Particles
1 mol = 6.022 × 10²³ particles
Therefore:
moles → particles: multiply by 6.022 × 10²³
particles → moles: divide by 6.022 × 10²³
Moles and Grams
Molar mass provides the conversion:
1 mol = molar mass in grams
For example, for H₂O:
1 mol H₂O = 18.02 g H₂O
Therefore:
moles → grams: multiply by molar mass
grams → moles: divide by molar mass
7. Dimensional Analysis
What Is Dimensional Analysis?
Dimensional analysis is a problem-solving method that uses units to guide calculations.
Instead of simply memorizing whether to multiply or divide, you arrange conversion factors so that unwanted units cancel and the desired unit remains.
This makes dimensional analysis especially useful for mole conversions.
The basic principle is:
Start with the given quantity → multiply by conversion factors → cancel units → arrive at the desired unit.
Conversion Factors
A conversion factor is a ratio containing two equivalent quantities.
For example:
1 mol / 18.02 g
and
18.02 g / 1 mol
represent the same relationship but are used for opposite conversion directions.
Because:
1 mol H₂O = 18.02 g H₂O
both of the following are valid conversion factors:
1 mol H₂O / 18.02 g H₂O
18.02 g H₂O / 1 mol H₂O
Why Units Matter
Suppose you have:
36.04 g H₂O
and want moles.
You need grams to cancel.
Therefore, use:
1 mol H₂O / 18.02 g H₂O
Set up:
36.04 g H₂O × (1 mol H₂O / 18.02 g H₂O)
The grams cancel:
g H₂O × mol H₂O / g H₂O
leaving:
mol H₂O
The numerical answer is:
2.00 mol H₂O
The Cancellation Rule
When using dimensional analysis, a unit in the numerator can cancel the same unit in the denominator.
For example:
g × mol/g = mol
The g units cancel.
Similarly:
mol × particles/mol = particles
The mol units cancel.
This is one of the most important habits to develop when solving conversion problems.
8. Gram-to-Mole Conversions
What Is a Gram-to-Mole Conversion?
A gram-to-mole conversion determines how many moles of a substance are represented by a given mass in grams.
The basic relationship is:
moles = grams ÷ molar mass
In symbolic form:
mol = g / (g/mol)
Because:
g ÷ (g/mol) = mol
Why Do You Need Molar Mass?
Grams and moles measure different things.
- Grams measure mass.
- Moles measure amount of substance.
Molar mass provides the bridge between them.
For example:
18.02 g H₂O = 1 mol H₂O
Therefore, if you know the mass of H₂O, you can determine how many moles it represents.
9. Step-by-Step Gram-to-Mole Method
Use the following procedure for essentially every gram-to-mole problem.
Step 1: Identify the Given Mass
Look for the mass provided in the problem.
For example:
36.0 g H₂O
The given quantity is:
36.0 g H₂O
Step 2: Determine the Molar Mass
Calculate the molar mass of the substance from its chemical formula.
For H₂O:
Molar mass = 18.02 g/mol
Step 3: Set Up the Conversion Factor
Because you want grams to cancel, put grams in the denominator:
1 mol H₂O / 18.02 g H₂O
Step 4: Multiply
Set up:
36.0 g H₂O × (1 mol H₂O / 18.02 g H₂O)
Step 5: Cancel Units
The g H₂O units cancel:
36.0 g H₂O × (1 mol H₂O / 18.02 g H₂O)
You are left with:
mol H₂O
Step 6: Calculate and Report the Answer
36.0 ÷ 18.02 ≈ 2.00
Therefore:
36.0 g H₂O ≈ 2.00 mol H₂O
The exact number of significant figures depends on the values provided in the problem.
10. Worked Gram-to-Mole Examples
Example 1: Water
Problem: How many moles are in 45.0 g of H₂O?
Step 1: Find molar mass
H₂O:
2(1.008) + 16.00 = 18.016 g/mol
≈ 18.02 g/mol
Step 2: Set up dimensional analysis
45.0 g H₂O × (1 mol H₂O / 18.02 g H₂O)
Step 3: Cancel units
g H₂O cancels.
Step 4: Calculate
45.0 ÷ 18.02 ≈ 2.50
Answer
2.50 mol H₂O
Example 2: Carbon Dioxide
Problem: How many moles are in 88.02 g of CO₂?
Molar mass of CO₂:
12.01 + 2(16.00)
= 44.01 g/mol
Set up:
88.02 g CO₂ × (1 mol CO₂ / 44.01 g CO₂)
Calculate:
88.02 ÷ 44.01 = 2.00
Answer:
2.00 mol CO₂
Example 3: Sodium Chloride
Problem: How many moles are in 117 g of NaCl?
Molar mass:
Na + Cl
= 22.99 + 35.45
= 58.44 g/mol
Conversion:
117 g NaCl × (1 mol NaCl / 58.44 g NaCl)
≈ 2.00 mol NaCl
Example 4: Calcium Hydroxide
Problem: How many moles are in 148.2 g of Ca(OH)₂?
First calculate molar mass:
Ca = 40.08
O = 16.00 × 2 = 32.00
H = 1.008 × 2 = 2.016
Total:
40.08 + 32.00 + 2.016
= 74.096 g/mol
Now convert:
148.2 g Ca(OH)₂ × (1 mol Ca(OH)₂ / 74.096 g Ca(OH)₂)
≈ 2.000 mol Ca(OH)₂
11. The Reverse Conversion: Moles to Grams
Although this section focuses on gram-to-mole conversions, it is important to recognize the reverse process.
To convert moles → grams, multiply by molar mass.
Formula
grams = moles × molar mass
Example
How many grams are in 3.00 mol CO₂?
Molar mass of CO₂:
44.01 g/mol
Set up:
3.00 mol CO₂ × (44.01 g CO₂ / 1 mol CO₂)
The mol units cancel.
Answer:
132 g CO₂
The key distinction is:
grams → moles: divide by molar mass
moles → grams: multiply by molar mass
12. The Mole Map
A useful way to organize these relationships is to think of moles as the central unit.
Grams ↔ Moles ↔ Particles
grams ⇄ moles ⇄ particles
The conversion between grams and moles uses molar mass.
The conversion between moles and particles uses Avogadro’s number.
Therefore:
grams → moles: divide by molar mass
moles → grams: multiply by molar mass
moles → particles: multiply by 6.022 × 10²³
particles → moles: divide by 6.022 × 10²³
13. Converting Directly Between Grams and Particles
Sometimes a problem may require more than one conversion.
For example, you might be asked to convert:
grams → molecules
There is no single conversion factor that directly converts grams into molecules. You must go through moles.
The pathway is:
grams → moles → particles
For example:
g → mol → molecules
First use molar mass.
Then use Avogadro’s number.
Example: Grams to Molecules
Suppose you have a sample of H₂O and want to determine the number of molecules.
The pathway is:
grams H₂O → moles H₂O → molecules H₂O
The first conversion uses:
1 mol H₂O / 18.02 g H₂O
The second conversion uses:
6.022 × 10²³ molecules H₂O / 1 mol H₂O
The intermediate unit, mol H₂O, cancels.
This leaves:
molecules H₂O
This same principle applies to longer dimensional-analysis problems.
14. Reading Chemical Formulas Correctly
Before performing a mole conversion, make sure you understand the substance’s formula.
Example: H₂SO₄
H₂SO₄ contains:
- 2 H atoms
- 1 S atom
- 4 O atoms
Its molar mass is:
2(1.008) + 32.06 + 4(16.00)
= 98.08 g/mol
Therefore:
1 mol H₂SO₄ = 98.08 g H₂SO₄
Example: Al₂(SO₄)₃
The formula:
Al₂(SO₄)₃
contains:
- 2 Al atoms
- 3 S atoms
- 12 O atoms
Why 12 oxygen atoms?
The subscript ₃ outside the parentheses multiplies the entire SO₄ group:
3 × 4 O = 12 O
Its molar mass is calculated by adding:
2 Al + 3 S + 12 O
This is why correctly reading subscripts and parentheses is essential.
15. Units You Should Recognize
Different units indicate different quantities.
Mass
Common mass units include:
- g = grams
- kg = kilograms
- mg = milligrams
For basic mole conversions, grams are usually used.
If a problem gives kilograms or milligrams, you may first need to convert the mass to grams.
Useful relationships include:
1 kg = 1000 g
1 g = 1000 mg
Amount of Substance
mol = mole
This is the unit for amount of substance.
Number of Particles
Particle quantities may be expressed as:
- atoms
- molecules
- formula units
- ions
- particles
These are counts rather than physical mass units.
Molar Mass
The standard unit is:
g/mol
This means grams per mole.
For example:
18.02 g/mol
means that every 1 mol of H₂O has a mass of 18.02 g.
16. Significant Figures in Mole Calculations
Your final answer should generally follow the significant-figure rules associated with the measurements in the problem.
For multiplication and division:
The final answer should have the same number of significant figures as the measurement with the fewest significant figures.
For example:
12.0 g ÷ 18.02 g/mol
The measured value 12.0 has three significant figures.
Therefore, the final answer should generally contain three significant figures.
When possible, keep extra digits during intermediate calculations and round only at the end.
17. Scientific Notation and Avogadro’s Number
Avogadro’s number is normally written in scientific notation:
6.022 × 10²³
In scientific notation:
- 6.022 is the coefficient
- 10²³ indicates the power of ten
Because 10²³ is enormous, Avogadro’s number represents an extremely large number of particles.
When multiplying or dividing by Avogadro’s number, pay careful attention to the exponent.
For example:
2 × 6.022 × 10²³ = 1.2044 × 10²⁴
The result may need to be rewritten in proper scientific notation if the coefficient is 10 or greater.
18. Common Mistakes to Avoid
Mistake 1: Using the Wrong Molar Mass
Always calculate the molar mass from the entire chemical formula.
For example, the molar mass of O₂ is not 16.00 g/mol.
Oxygen atoms have a molar mass of approximately 16.00 g/mol, but O₂ contains two oxygen atoms:
2 × 16.00 = 32.00 g/mol
Therefore:
Molar mass of O₂ = 32.00 g/mol
Mistake 2: Ignoring Subscripts
For H₂O, do not calculate:
H + O
You must calculate:
2H + O
The subscript ₂ means there are two hydrogen atoms.
Mistake 3: Misreading Parentheses
For Ca(OH)₂, the ₂ applies to both O and H.
It does not mean there are only two hydrogen atoms without affecting oxygen; it means the entire OH group occurs twice.
Mistake 4: Multiplying When You Should Divide
For:
grams → moles
you normally divide by molar mass.
For:
moles → grams
you normally multiply by molar mass.
However, dimensional analysis is safer than simply memorizing these rules because the units tell you which conversion factor to use.
Mistake 5: Forgetting Units
Do not treat units as optional labels.
Write them throughout the calculation.
For example:
25.0 g × 1 mol / 18.02 g
is much safer than simply writing:
25.0 × 1 / 18.02
The units show whether the conversion is set up correctly.
Mistake 6: Using Avogadro’s Number for Gram-to-Mole Problems
Avogadro’s number is used to convert between:
moles ↔ particles
Molar mass is used to convert between:
grams ↔ moles
For a basic gram-to-mole conversion, Avogadro’s number is not needed.
Mistake 7: Confusing Atomic Mass and Molar Mass
The periodic table gives atomic masses, such as:
C ≈ 12.01
For mole calculations, this corresponds numerically to:
12.01 g/mol
Do not confuse the mass of one individual atom with the mass of one mole of atoms.
Mistake 8: Changing the Chemical Formula
When calculating molar mass, do not change subscripts in the formula.
For example, H₂O must remain H₂O.
Changing the subscript changes the substance itself.
Coefficients may indicate how many units of a substance are present, but they do not change the identity or molar mass of the substance.
19. A Reliable Strategy for Any Mole Conversion Problem
When you see a mole conversion problem, follow this sequence.
Step 1: Identify the Given Quantity
Determine whether the problem gives you:
- grams
- moles
- atoms
- molecules
- formula units
- another particle count
Step 2: Identify the Desired Quantity
Determine what the problem is asking for.
For example:
Given: grams
Wanted: moles
Therefore, this is a gram-to-mole conversion.
Step 3: Identify the Required Conversion Factor
Use:
Molar mass for grams ↔ moles.
Use:
Avogadro’s number for moles ↔ particles.
Step 4: Write the Conversion Factor So Units Cancel
Put the unwanted unit on the opposite side of the conversion factor from where it appears in the given quantity.
Step 5: Cancel Units
Make sure every unwanted unit cancels.
Step 6: Calculate
Perform the numerical calculation.
Step 7: Check the Answer
Ask:
- Did the units become the requested unit?
- Did I use the correct chemical formula?
- Did I calculate molar mass correctly?
- Did I use the correct conversion factor?
- Is the magnitude of the answer reasonable?
- Did I round appropriately?
20. Essential Formulas and Relationships
Moles From Grams
moles = grams ÷ molar mass
or:
mol = g / (g/mol)
Grams From Moles
grams = moles × molar mass
or:
g = mol × (g/mol)
Particles From Moles
particles = moles × 6.022 × 10²³ particles/mol
Moles From Particles
moles = particles ÷ 6.022 × 10²³ particles/mol
Avogadro’s Number
1 mol = 6.022 × 10²³ particles
Molar Mass
1 mol of a substance = its molar mass in grams
For example:
1 mol H₂O = 18.02 g H₂O
1 mol CO₂ = 44.01 g CO₂
1 mol NaCl = 58.44 g NaCl
21. Quick Reference: Which Conversion Factor Do I Use?
| Conversion | Conversion factor |
|---|---|
| Grams → Moles | 1 mol / molar mass in g |
| Moles → Grams | molar mass in g / 1 mol |
| Moles → Particles | 6.022 × 10²³ particles / 1 mol |
| Particles → Moles | 1 mol / 6.022 × 10²³ particles |
| Grams → Particles | Grams → moles → particles |
| Particles → Grams | Particles → moles → grams |
22. Key Concepts to Know Before the Quiz
Before starting the quiz, you should be able to explain each of the following without relying on memorization alone:
Moles
A mole is a unit for measuring the amount of a substance.
1 mol = 6.022 × 10²³ specified particles
Molar Mass
Molar mass is the mass of one mole of a substance.
Its unit is:
g/mol
For compounds, calculate it by adding the atomic masses of all atoms represented by the chemical formula.
Avogadro’s Number
Avogadro’s number tells you how many particles are present in one mole:
6.022 × 10²³ particles/mol
Dimensional Analysis
Dimensional analysis uses conversion factors and unit cancellation to convert from one unit to another.
The units should guide the setup of the calculation.
Gram-to-Mole Conversion
To convert grams into moles:
grams → divide by molar mass → moles
or, using dimensional analysis:
grams × (1 mol / molar mass in grams)
23. Final Checklist
You are ready to begin a mole conversion quiz when you can confidently do all of the following:
- Define a mole.
- Explain what 6.022 × 10²³ represents.
- Distinguish between atoms, molecules, formula units, and ions.
- Explain what molar mass means.
- Identify molar mass in g/mol.
- Use a periodic table to obtain atomic masses.
- Calculate the molar mass of an element.
- Calculate the molar mass of a compound.
- Correctly interpret subscripts.
- Correctly interpret parentheses and subscripts.
- Distinguish coefficients from subscripts.
- Convert grams → moles.
- Convert moles → grams.
- Convert moles → particles.
- Convert particles → moles.
- Recognize when a problem requires more than one conversion.
- Set up conversion factors so that units cancel.
- Use dimensional analysis rather than guessing whether to multiply or divide.
- Keep units throughout a calculation.
- Use appropriate significant figures.
- Recognize and correct common setup and calculation errors.
The Most Important Idea
For this entire topic, remember the central relationship:
grams ⇄ moles ⇄ particles
grams ⇄ moles: use molar mass
moles ⇄ particles: use Avogadro’s number
Once you identify the starting unit and the desired unit, the correct conversion path and conversion factor can be determined from the units themselves.