Crystal Density Calculator
Calculate the theoretical density of a crystalline material based on its unit cell volume, molar mass, and formula units (Z).
Calculation Parameters
Specify your stoichiometry inputs.
Calculated Result
Expert Tip
The constant NA is Avogadro's number, approximately 6.022 × 10²³ mol⁻¹.
How this Calculator Works
This calculator computes the theoretical density of a crystalline solid based on unit cell parameters. Adjust the inputs below:
- Formula Units per Cell (Z): Total number of formula units (or atoms) in one unit cell (Default: 4 for NaCl)
- Molar Mass (M): Gram molecular weight of the substance in g/mol (Default: 58.44 g/mol)
- Unit Cell Volume (Vc): The volume of the unit cell in cubic Ångströms (Default: 179.4 ų)
The results are computed instantly and updated in the results panel on the right.
Formula & Methodology
Where:
- ρ: Theoretical density (g/cm³).
- Z: Number of formula units per cell.
- M: Molar mass (g/mol).
- Vc: Unit cell volume (ų).
- NA: Avogadro's constant (6.02214076 × 10²³).
Step-by-Step Calculation Example
To calculate the theoretical density of NaCl manually, follow these steps:
- Identify the input parameters. For example:
- Z = 4 formula units per cell
- Molar Mass (M) = 58.44 g/mol
- Unit Cell Volume (Vc) = 179.4 ų
- Apply the formula:
1. Apply Avogadro's constant NA = 6.022e23 2. Convert Vc from ų to cm³: Vc * 10⁻²⁴ = 1.794e-22 cm³ 3. Calculate ρ = (4 * 58.44) / (1.794e-22 * 6.022e23) = 233.76 / 108.0 = 2.165 g/cm³
- Verify the calculated value which is updated instantly in the results panel on the right.
Frequently Asked Questions
What is the formula for theoretical crystal density? ▼
Density (ρ) = (Z × Molar Mass) / (N_A × V_cell), where Z is formula units per cell and V_cell is unit cell volume.
What is Z in crystal density calculations? ▼
Z is the total integer number of formula units contained within a single unit cell (e.g. Z = 4 for NaCl FCC cell).
How does ionic radius substitution affect crystal density? ▼
Substituting larger or heavier ions into a crystal lattice increases unit cell volume and modifies overall mass density.