Question

Polonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm^3 , a radius of 167 pm, and a molar mass of 209 g/mol .
Estimate Avogadro's number (the number of atoms in one mole).

Answer 1

1. Simple cubic structure means that there is 1 Polonium atom per cube. Given in the problem is the radius of the atom. We need to find the length of sides of the cube where the Po atom is contained. Imagine a square with a circle inside it. The circle given the radius can give us the dimension of the square.

Length of side = diameter of the radius = 2 x radius
Length of side = 2 x 167 pm = 334 pm (picometer) ===> convert to cm

Note: 1 picometer = 1 x 10^ (-12) m = 1 x 10^ (-10) cm

Length of side = 3.34 x 10^ (- 8) cm


2. Calculate for the mass inside the cell using the given density:

Density = mass / volume
mass inside the cell = density x volume; but volume is equal to (length of the side)^ 3
mass inside the cell = 9.3 g/cm^3 x [ 3.34 x 10^ (- 8) cm]^3
mass inside the cell = 3.4652 x 10^ (-22) g


3. Mass inside the cell can also be equated to:

Mass inside cell = molar mass of Po / Avogadro's number

Avogadro's number = molar mass of Po / mass inside cell

Avogadro's number = 209 g/mol / 3.4652 x 10^ (-22) g

Avogadro's number = 6.03 x 10^ 23 atoms / mole ===> answer