Consider the following unit cell for a binary ionic solid consisting of Zinc (la
ID: 1072277 • Letter: C
Question
Consider the following unit cell for a binary ionic solid consisting of Zinc (large black spheres marked with x) and Sulfur (small grey spheres) ions. Note that the zinc ions marked with x are fully inside the unit cell. What kind of unit cell is adopted by the Sulfide ions? Derive the net number of Zinc and Sulfide ions inside the unit cell. Hence state the expected empirical formula for Zinc (II) Sulfide. If the molecular mass of Zinc (II) Sulfide is 97.455 g mol^-1, derive the expected molecular formula. Zinc (II) Sulfate is an alternative salt of Zinc, which is widely used to supply Zinc in fertilizers and is known to exist in several hydrated forms with the general formula, ZnSO_4 xH_2O. If the molar mass of the unknown hydrate is 287.5546 g mol^-1, derive the expected number of water molecules x in the molecular formula of the hydrate.Explanation / Answer
1.1 As mentioned that the Zn ions are fully inside the cell so number of Zn ions = 4
the sulphide ions are 8 on eight corners so the total atom on corners = 8 X 1/8 = 1
Sulphide ions are six on each face so toal number of atoms on face = 6 X 1/2 = 3
total sulphur = 3+1= 4
The emprical formula will be ZnS
2) If molecular mass of ZnS = 97.455g / mole
expected molecular formula = ZnS [as emprical weight and molecular weight are equal]
3) Molar mass of unknown hydrate = 287.5543 g / mole
Molar mass of ZnSO4 = 161.47 g / mole
so mass of water = 287.5543 - 161.47 = 126.08 g
molar mass of water = 18.02
Number of water molecules = Mass of water / mol mass of water = 126.08 / 18.02 = 6.99 = 7(approx)