Mole Calculator
Convert between moles, grams, and particles instantly. Enter a value and molar mass to calculate the number of moles, the mass in grams, or the total count of atoms and molecules using Avogadro's number (6.022 × 10²³).
Mole Calculator
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Understanding the Mole
The mole (symbol: mol) is one of the seven SI base units and serves as the cornerstone of quantitative chemistry. One mole of any substance contains exactly 6.02214076 × 10²³ elementary entities. This defining constant is known as Avogadro's number (Nₐ), named after the Italian scientist Amedeo Avogadro.
To put Avogadro's number in perspective, if you could count one atom every second, it would take more than 19 quadrillion years to finish counting a single mole of atoms. That is roughly 1.4 million times the current age of the universe. Chemists need such an enormous number because individual atoms and molecules are extraordinarily small: a single water molecule is only about 2.75 angstroms wide.
The Mole Concept and n = m / M
The fundamental relationship that connects mass, moles, and molar mass is:
- n = number of moles (mol)
- m = mass of the substance (grams)
- M = molar mass (g/mol), which equals the sum of atomic masses from the periodic table
This formula can be rearranged to solve for any variable. To find mass: m = n × M. To find molar mass: M = m / n. These three rearrangements form the foundation of nearly every stoichiometry problem in general chemistry.
Moles in Chemical Reactions
Balanced chemical equations express the ratios of reactants and products in moles rather than grams. For example, in the reaction 2H₂ + O₂ → 2H₂O, the coefficients tell us that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. These molar ratios allow chemists to predict exactly how much of each reactant is needed and how much product will form, which is critical for industrial manufacturing, pharmaceutical synthesis, and laboratory research.
Molarity: Moles in Solution
When a substance is dissolved in a solvent, its concentration is often expressed as molarity (M), defined as the number of moles of solute per liter of solution: Molarity = n / V. A 1.0 M solution of hydrochloric acid (HCl) contains 1 mole of HCl (36.46 g) dissolved in enough water to make exactly 1 liter of solution. Molarity is the standard unit of concentration used in titrations, dilution problems, and equilibrium calculations throughout chemistry.
Reference Table: One Mole of Common Substances
The table below shows the mass and particle count for one mole of several commonly encountered substances. Every row contains exactly 6.022 × 10²³ formula units, yet the masses vary widely because each substance has a different molar mass.
| Substance | Formula | Molar Mass (g/mol) | Mass of 1 mol | Particles in 1 mol |
|---|---|---|---|---|
| Water | H₂O | 18.015 | 18.015 g | 6.022 × 10²³ molecules |
| Sodium Chloride | NaCl | 58.44 | 58.44 g | 6.022 × 10²³ formula units |
| Carbon Dioxide | CO₂ | 44.01 | 44.01 g | 6.022 × 10²³ molecules |
| Glucose | C₆H₁₂O₆ | 180.16 | 180.16 g | 6.022 × 10²³ molecules |
| Iron | Fe | 55.845 | 55.845 g | 6.022 × 10²³ atoms |
| Sulfuric Acid | H₂SO₄ | 98.079 | 98.079 g | 6.022 × 10²³ molecules |
| Calcium Carbonate | CaCO₃ | 100.09 | 100.09 g | 6.022 × 10²³ formula units |
How to Convert Between Moles, Mass, and Particles
The following three worked examples demonstrate the most common mole conversions you will encounter in general chemistry courses and laboratory work.
Example 1: Grams to Moles (NaCl)
A student weighs out 14.61 grams of sodium chloride (NaCl) for a lab experiment. How many moles of NaCl is this?
Step 1 — Find the molar mass: Na (22.99) + Cl (35.45) = 58.44 g/mol
Step 2 — Apply n = m / M: n = 14.61 g ÷ 58.44 g/mol
n = 0.2500 mol NaCl
Example 2: Moles to Grams (H₂O)
A recipe for a buffer solution calls for 3.50 moles of water. What mass of water should be measured?
Step 1 — Find the molar mass: H₂O = 2(1.008) + 15.999 = 18.015 g/mol
Step 2 — Apply m = n × M: m = 3.50 mol × 18.015 g/mol
m = 63.05 g of water
Example 3: Moles to Particles (CO₂)
A sealed flask contains 0.75 moles of carbon dioxide gas. How many individual CO₂ molecules are present?
Step 1 — Apply N = n × Nₐ: N = 0.75 mol × 6.022 × 10²³ mol⁻¹
Step 2 — Calculate: N = 4.517 × 10²³
N = 4.517 × 10²³ molecules of CO₂
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