All calculatorsAvogadro’s Number Calculator
Convert between particles (atoms/molecules/ions/formula units), moles, and mass (g). Uses Avogadro’s constant (6.022×1023) and supports auto molar mass from a chemical formula. Includes step-by-step working and an optional mini chart linking mass ↔ moles ↔ particles.
Background
Avogadro’s number \(N_A = 6.02214076\times 10^{23}\) particles per mole connects microscopic counts to lab-scale amounts. With molar mass \(M\) (g/mol), the bridge is \(n=\frac{m}{M}\) and \(N=n\cdot N_A\).
How to use this calculator
- Choose particle type (molecules, atoms, ions, formula units) — for labeling only.
- Provide one known: moles n, particles N, or mass m. If using mass, provide molar mass M (or a formula to auto-calc).
- Output: We compute all three: moles, particles, and mass; plus a step-by-step derivation.
Formula & Equation Used
Core relations: \(N = n\,N_A\), \(n = \frac{m}{M}\), \(N = \frac{m}{M}N_A\)
Where: \(N\) = particles (atoms/molecules/ions), \(n\) = moles, \(N_A = 6.022\times 10^{23}\,\text{mol}^{-1}\), \(m\) = mass (g), \(M\) = molar mass (g·mol⁻¹).
Molar mass from formula: Sum of atomic weights multiplied by subscripts (handles parentheses, e.g., Ca(OH)₂).
Examples
How many molecules are in 18 g of H₂O?
M(H₂O)=18.015 g/mol → \(n=\frac{18}{18.015}\approx 0.999\) mol → \(N \approx 0.999\times 6.022\times10^{23}\approx 6.01\times10^{23}\) molecules.
How many moles is 3.01×10²³ CO₂ molecules?
\(n = \frac{N}{N_A} = \frac{3.01\times10^{23}}{6.022\times10^{23}} \approx 0.500\) mol.
What mass is 1.5×10²⁴ SO₄²⁻ ions?
\(n=\frac{N}{N_A}\approx 2.49\) mol; with M(SO₄)=96.06 g/mol → \(m\approx 239\) g.
Frequently Asked Questions
Q: Does Avogadro’s number apply to ions and formula units?
Yes. It’s a count-per-mole constant regardless of particle identity.
Q: How precise are results?
Atomic masses and \(N_A\) are treated as exact to displayed digits. Enable “significant figures” for rounded outputs.
