An internationally accepted procedure is as follows: We start with a “perfect” sphere of pure 28Si i — Physical Chemistry — Kinetics Chemistry Question
Avogadro’s Number
An internationally accepted procedure is as follows:
We start with a “perfect” sphere of pure 28Si isotope. The mass of this sphere is W g. The volume V of the sphere is found from the accurate measurement of the diameter of the sphere. The unit cell of a crystal of silicon is a “diamond cubic lattice”, i.e. a face-centered unit cell but with 4 Si atoms inside the cube. The length of the unit cell can be determined precisely from X-ray crystallographic measurements of a single crystal of 28Si isotope.
The experimental data are as follow:
Mass of the sphere, W: 1000.064 543(15) g
Volume of the sphere: 431.049 110(10) cm3
Length of the unit cell, α: 543.099 619(20) pm
Atomic mass of 28Si, M(Si) = 27.976 970 029(23) g mol-1
Number of Si atoms in the unit cell, N.
Write down the equation for calculating Avogadro’s number NA in terms of the parameters.
Model Answer
Let the volume of the unit cell v = α3,
The number of unit cell in volume V of the silicon sphere = (V/v)
If N is the number of silicon atoms in the unit cell, the number of silicon atoms in silicon sphere = N(V/v)
The amount of substance of Si in the sphere: n(Si) = (W/A) (W is mass of the sphere)
The number of silicon atoms in sphere = n(Si) × NA.
i. e. (W/A) NA = n (V/v)
NA = n(V/v) × (A/W)
How many silicon atoms are in the unit cell?
Model Answer
For a face-centered unit cell, the number of atoms at the 8 corners of cell = 8; the number at the 6 faces = 6. Each corner has (1/8) of atom in unit cell and each face has (1/2) of atom. Thus total number of Si atoms in the unit cell = [8 × (1/8)] + [6 × (1/2)] + 4 = 1 + 3 + 4 = 8.
n = 8
Calculate Avogadro’s number using the above data. Give answer to 7 significant figures.
Model Answer
The volume v of the unit cell must be given in cm3.
1 pm = 10-12 m = 10-10 cm
NA = 6.022 141×1023