Question

NaBr heated in Na vapor produced nonstoichiometric compounds; i.e., the atomic ratios are not whole numbers. The additional uptake of Na atoms occurs by the reaction: Na -> Na⁺ + e^-, where the Na⁺ ions sit on vacant Na⁺ sites and the e^- sits on vacant Br^- sites. If a maximum amount of Na is taken up by the material in question 1 (NaBr with a= 5.94Å and observed density= 3.203g/cc), what would be the formula of the material that is formed?  

Answer 1

1. Calculate the volume (V) of the unit cell using the cell-edge length (a)

                V = a³ = (5.94 angstrom)³ = 209.58 angstrom³

2. convert to cm³
         (209.58 angstrom³)(1cm/1x10⁸ angstrom)³ = 2.096x10^-22 cm³

3. Calculate the mass of the NaBr unit cell from the molar mass and using Avogadro's number

          (102.89 g/mol)(1mol/6.02x10²³) = 1.709x10^-22 g/unit cell

4. calculate the density (it should match the observed density=3.203 g/cc) to determine the structure.

       if a simple cubic structure (1 atom/unit cell): (1.709x10^-22 g/unit cell)/(2.096x10^-22 cm³/unit cell) = 0.815 g/cm³(so not a simple cubic structure)

      if a face-centered cubic structure (4atoms/unit cell): (4) (1.709x10^-22 g/unit cell)/(2.096x10^-22 cm³/unit cell) = 3.26 g/cm³(thus the structure of NaBr is face-centered cubic structure)