in an oxide of tungsten, the oxygen anions (o2-) are located halfway along all of the edges of the cubic unit cell, and the tungsten cations occupy positions at each corner of the unit cell. the density of the oxide is 6.013 g/cm3. the molar mass of w is 183.80 g/mol and the molar mass of o is 16.00 g/mol. (a) Provide the empirical formula of the oxide.
(b) Calculate the lattice parameter of the cubic unit cell.

Chemical element tungsten (W), often known as wolfram, is a Group 6 (VIb) refractory metal that is incredibly strong and is used to make lamp filaments and to boost the hardness and strength of steels.

What is cations ?

A positively charged cation is an atom or molecule with more protons than electrons. Eg: Na+ 3. An anion is an atom or molecule that is negatively charged, meaning it contains more electrons than protons.

O⁻²⇒ mid of all edges

no.of ion shared from 1 edge = 1/4

total edges = 12

total o⁻² ions = 12*1/4

total o⁻² ions = 3

tungsten caution ⇒ each corner

no.of ions shared from corner = 1/8

total corner = 8

total tungsten ion = 8*1/8

total tungsten ion = 1

empirical formula = wo₃

b) density = Z*M/Na * a³

Here, Z= 1( number of molecule in 1 Unit cell)

M= molar mass of WO₃= 231.84 gm / mole

Na = Avogadro number = 6.022*10²³

a= edge length

6.013= 1*231.84/ 6.022*10²³ *a³

a³= 231.84 * 10⁻²³ / 6.013 * 6.022

a³= 6.403 * 10⁻²³

a³= 6.403 * 10⁻²⁴

a= 4*10⁻⁸ cm

Therefore, the Edge length of unit cell is 4*10⁻⁸ cm.

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