Question

A white oxide of tungsten is $\mathbf{79}\mathbf{.}\mathbf{2976}\mathbf{\%}$tungsten by mass. A blue tungsten oxide also contains exclusively tungsten and oxygen and but it is $\mathbf{80}\mathbf{.}\mathbf{8473}\mathbf{\%}$tungsten by mass. Determine the empirical formulas of white tungsten oxide and blue tungsten oxide.

Short answer

We are given with the mass of tungsten of both white oxide and blue oxide. To calculate the empirical formula of both white oxide and blue oxide tungsten involves

Step-by-step solution

Calculation of mass of element present in 100 gms

The two compounds formed by tungsten (w), Oxygen, (o) are white blue in colour. Their composition in mass percent is:

White Tungsten Oxide: W$\left(79.2976\%\right)$

Blue Tungsten Oxide: W $\left(80.8473\%\right)$

The mass of elements present in 100gm of each compound is white tungsten oxide:

$$\begin{gathered} W=79.2976g \\ O=\left(100.0g--79.2976g\right) \\ =20.7024g \end{gathered}$$

Blue tungsten Oxide:

$$\begin{gathered} W=80.8473g \\ O=\left(100.0g--80.8473g\right) \\ =19.1527g \end{gathered}$$

Calculation of the number of moles of each element present in the samples

The number of moles of each element present in the sample is determined using their molar masses.

White Tungsten Oxide:

Moles of W = $79.2976g\times \frac{1molW}{183.84}=0.431340mol$

Moles of O = $20.7024g\times \frac{1molofO}{16.00g}=1.29390mol$

Blue Tungsten Oxide:

Moles of W:$80.8473g\times \frac{1molW}{183.84}=0.439770mol$

Moles of O:$19.1527g\times \frac{1molO}{16.00g}=1.19704mol$

Calculation of ratio of the amount of elements present in each compound

In each compound, the ratio of the amount of elements is obtained and then it is divided by the smallest amount as follows:

White Tungsten Oxide:

W: O$=0.4313401:1.29390$

W: O$=\frac{0.431340}{0.431340}:\frac{1.29390}{0.431340}$

$=1:3$

Blue Tungsten Oxide:

W: O$=0.439770:1.19704$

W: O$=\frac{0.439770}{0.439770}:\frac{1.19704}{0.439770}$

$=1:2.7$

Formation of the empirical formula of the two compounds

When we multiple each of the terms in blue tungsten Oxide by 3, the ratio becomes . Therefore, the empirical formula of the two compound is:

White Tungsten Oxide:$W{O}_3$

Blue Tungsten Oxide:$W_3{O}_8$