The Mole and Molar Mass

Why the Mole Exists

Atoms are far too small and too numerous to count one at a time. A single drop of water holds roughly 10^21 molecules. Chemists therefore use a counting unit called the mole (abbreviated mol), much as a grocer uses a dozen (12) or a ream (500). The mole lets you connect a number you can weigh on a balance to the number of particles actually reacting.

The mole is one of the most heavily tested ideas on the New York State Regents chemistry exam. It appears in Part A and Part B-1 multiple choice, and it is a favorite of Part B-2 and Part C constructed-response items, where you must show a numerical setup. Mastering it unlocks nearly every calculation in the Chemical Reactions blueprint band, which is 36-46% of the test.

Avogadro's Number

One mole always contains the same number of particles: 6.02 x 10^23, called Avogadro's number (named for Amedeo Avogadro). One mole of carbon atoms, one mole of water molecules, and one mole of sodium ions each contain 6.02 x 10^23 of that particle.

• 1 mol of any substance = 6.02 x 10^23 representative particles (atoms, molecules, ions, or formula units).
• To convert moles to particles, multiply by 6.02 x 10^23; to convert particles to moles, divide by it.
• Example: 2.0 mol of helium contains 2.0 x (6.02 x 10^23) = 1.2 x 10^24 atoms.

The Regents reference tables do not print Avogadro's number on a dedicated line, so memorize 6.02 x 10^23 as a value you must supply yourself.

Gram-Formula Mass (Molar Mass)

The gram-formula mass, also called the molar mass, is the mass in grams of one mole of a substance. You calculate it by adding the atomic masses of every atom shown in the chemical formula. Atomic masses come straight from the Periodic Table of the Elements on the NYS reference tables, where each value is already an isotope-weighted average, so you never average isotopes yourself.

Worked Procedure

1. Write the formula and list each element with its subscript.
2. Look up each atomic mass on the Periodic Table.
3. Multiply each atomic mass by its subscript.
4. Add all the products. Units are g/mol.

Notice the parentheses in calcium nitrate: the subscript 2 multiplies everything inside, giving 2 nitrogen and 6 oxygen. Distributing across parentheses is one of the most common trap questions on the exam.

The Mole Equation

The NYS reference tables print this relationship directly:

number of moles = given mass / gram-formula mass

This single equation, rearranged, handles most mole conversions:

• Solve for moles: moles = mass / molar mass.
• Solve for mass: mass = moles x molar mass.
• Solve for molar mass: molar mass = mass / moles.

Example

How many moles are in 24.0 g of carbon (C = 12.0 g/mol)? Setup: 24.0 g / 12.0 g/mol = 2.0 mol. Always write units; if your units divide out to mol, your setup is right.

Molar Volume of a Gas

For gases, the mole also connects to volume. At standard temperature and pressure (STP) -- defined in the Mathematical Relationships section of the 2025 reference tables as 273.15 K (0 degrees C) and 101.3 kPa (1 atm) -- one mole of any ideal gas occupies 22.4 liters, the molar volume. So 0.50 mol of oxygen gas at STP occupies 0.50 x 22.4 = 11.2 L, regardless of which gas it is.

Reading Molar Mass from the Reference Tables

A major Regents skill is finding values quickly on the supplied Reference Tables for Physical Science: Chemistry. For molar mass you use the Periodic Table of the Elements on those tables. Each box lists the element symbol, the atomic number (whole number, count of protons), and the atomic mass (the decimal value, an isotope-weighted average). You always use the decimal atomic mass for molar-mass calculations.

• The atomic number is the smaller whole number used to identify the element and its proton count.
• The atomic mass is the larger decimal value used for gram-formula mass.
• Selected atomic masses you will reuse often: H = 1.0, C = 12.0, N = 14.0, O = 16.0, Na = 23.0, S = 32.1, Cl = 35.5.

Knowing where these live saves time on a three-hour exam and prevents the error of mixing up atomic number with atomic mass.

Representative Particles

The phrase representative particle matters because a mole counts different things for different substances. For an element like neon, the particle is an atom. For a molecular compound like water, it is a molecule. For an ionic compound like NaCl, it is a formula unit (the smallest whole-number ratio of ions). All three still equal 6.02 x 10^23 particles per mole; only the name of the particle changes.

Common Mistakes and Exam Traps

• Forgetting to distribute a subscript across a polyatomic ion in parentheses.
• Confusing mass number (a single isotope) with atomic mass (the weighted average you use for molar mass).
• Mixing up atomic number (whole number, proton count) with atomic mass (decimal) on the Periodic Table.
• Inverting the mole equation -- dividing molar mass by mass instead of mass by molar mass; units catch this error.
• Using 22.4 L for a substance that is not a gas, or for a gas not at STP.
• Reporting an answer with the wrong number of significant figures; carry the precision of the data given.