Calculating Density of NaCl Crystal

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SUMMARY

The density of crystalline NaCl can be calculated using its face-centered cubic (FCC) lattice structure, where the lattice parameter is given as a = 5.64 Å. The total number of atoms in the unit cell is determined by the contributions from corner and face-centered atoms, resulting in a total of 4 atoms per unit cell. To find the density, one must calculate the total mass of NaCl in the unit cell using Avogadro's number and the molar mass of NaCl, then divide this mass by the volume of the unit cell, which is derived from the lattice parameter.

PREREQUISITES
  • Understanding of face-centered cubic (FCC) lattice structures
  • Knowledge of atomic contributions in unit cells
  • Familiarity with Avogadro's number and molar mass calculations
  • Basic skills in calculating density from mass and volume
NEXT STEPS
  • Calculate the total atomic mass of NaCl in the unit cell using molar mass
  • Learn how to compute the volume of a cubic unit cell
  • Explore the concept of density and its formula in solid-state chemistry
  • Investigate other crystal structures and their density calculations
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Chemistry students, materials scientists, and anyone studying solid-state physics or crystallography will benefit from this discussion on calculating the density of NaCl crystals.

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Homework Statement



Calculate the density of crystalline NaCl, given that NaCl has a face-centred cubic lattice with a dimension a = 5.64A.

Homework Equations



1/8 Cl ion at each corner, 1/2 Cl ion on each face. 1 whole Na in the center, 1/4 Na ion along each edge.

The Attempt at a Solution



ok where do i begin
 
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For a FCC structure: corner atoms contribute only 1/8 and face-centered atoms contribute 1/6. So for a FCC system total number of atoms = 8(1/8) + 6(1/2) =4.
But which is corner atom and which is face-centered atom ?
Only idea comes to my mind is:
you should take 'a' as distance between two nearby Cl or Na atom. Then find the kg of NaCl single unit using 'mole' and 'Avogadro' stuff. Also you know volume. So you can compute density.
Hope this help
 
Last edited:
Given - "1/8 Cl ion at each corner, 1/2 Cl ion on each face. 1 whole Na in the center, 1/4 Na ion along each edge." - how would one determine the total atomic mass in the unit cell?

Then given the mass, how would one determined the density?
 

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