Avogadro's Number & Mole Calculator

Convert between moles, particles, and mass using Avogadro's number.

Select calculation type, enter your values, and instantly get results for atoms, molecules, ions, or electrons.

Examples

See how to use Avogadro's Number & Mole Calculator for different conversions.

Moles to Particles (Atoms)

Moles to Particles

Find the number of atoms in 2 mol of carbon.

Calculation Type: Moles to Particles

Moles (n): 2 mol

Particle Type: Atom

Particles to Moles (Molecules)

Particles to Moles

Find the number of moles in 1.204e24 molecules of water.

Calculation Type: Particles to Moles

Particles (N): 1.204e+24 particles

Particle Type: Molecule

Mass to Particles (Ions)

Mass to Particles

Find the number of ions in 9.5g of Na+ (molar mass 23g/mol).

Calculation Type: Mass to Particles

Mass (m): 9.5 g

Molar Mass (M): 23 g/mol

Particle Type: Ion

Particles to Mass (Electrons)

Particles to Mass

Find the mass of 3.011e23 electrons (molar mass 0.0005486g/mol).

Calculation Type: Particles to Mass

Particles (N): 3.011e+23 particles

Molar Mass (M): 0.0005486 g/mol

Particle Type: Electron

Other Titles
Understanding Avogadro's Number & Mole Calculator: A Comprehensive Guide
Master mole, mass, and particle conversions in chemistry.

What is Avogadro's Number?

  • Definition and Value
  • Historical Background
  • Importance in Chemistry
Avogadro's number (Nₐ) is the number of particles in one mole of a substance. Its value is 6.02214076 × 10²³ mol⁻¹.
Historical Background
Named after Amedeo Avogadro, this constant is fundamental in chemistry for relating macroscopic and microscopic quantities.
Importance in Chemistry
Avogadro's number allows chemists to count atoms, molecules, ions, or electrons by weighing samples and using molar mass.

Avogadro's Number in Practice

  • 1 mol of water contains 6.022e23 molecules.
  • 1 mol of sodium ions contains 6.022e23 ions.

Step-by-Step Guide to Using the Calculator

  • Choosing the Calculation Type
  • Entering Values
  • Interpreting Results
Choosing the Calculation Type
Select the type of conversion you need: moles ↔ particles, mass ↔ particles, or mass ↔ moles.
Entering Values
Enter the required values such as moles, particles, mass, or molar mass. Select the particle type for clarity.
Interpreting Results
The calculator provides the converted value and a summary of the calculation, including Avogadro's number.

Sample Calculations

  • Input: 2 mol carbon → 1.204e24 atoms.
  • Input: 1.204e24 molecules → 2 mol.

Real-World Applications of Avogadro's Number

  • Stoichiometry
  • Laboratory Analysis
  • Material Science
Stoichiometry
Avogadro's number is essential for balancing chemical equations and determining reactant/product quantities.
Laboratory Analysis
Used to calculate the number of particles in a given mass or volume of a substance.
Material Science
Helps in determining the number of atoms or molecules in crystals, polymers, and nanomaterials.

Practical Uses

  • Calculating atoms in a gold ring.
  • Finding molecules in a gas sample.

Common Misconceptions and Correct Methods

  • Avogadro's Number vs. Molar Mass
  • Unit Consistency
  • Particle Types
Avogadro's Number vs. Molar Mass
Avogadro's number is a count of particles per mole, while molar mass is the mass of one mole. They are related but not the same.
Unit Consistency
Always use consistent units (g, kg, mol) for accurate results.
Particle Types
Specify whether you are counting atoms, molecules, ions, or electrons for clarity in calculations.

Misconceptions

  • Confusing molar mass with Avogadro's number.
  • Using kg for mass and g/mol for molar mass gives wrong results.

Mathematical Derivation and Examples

  • Moles ↔ Particles Formula
  • Mass ↔ Moles Formula
  • Worked Examples
Moles ↔ Particles Formula
N = n × Nₐ; n = N / Nₐ, where N is particles, n is moles, Nₐ is Avogadro's number.
Mass ↔ Moles Formula
n = m / M; m = n × M, where m is mass, M is molar mass.
Worked Examples
Example: How many molecules in 18g of water (M=18g/mol)? n=1, N=6.022e23 molecules.

Mathematical Examples

  • N = 2 × 6.022e23 = 1.204e24 particles.
  • n = 1.204e24 / 6.022e23 = 2 mol.