Question

Gadolinium oxide, a colorless powder which absorbs carbon dioxide from the air, contains 86.76 mass % gd. determine its empirical formula.

Answer 1

The mass % of $Gd$ = 86.76 % (given)

The mass % of $O$ = 100 - 86.76 = 13.24 %

Considering the mass of Gadolinium oxide as 100 g.

Then 86.76 mass % $Gd$ means the compound contains 86.76 g of $Gd$ in 100 g of Gadolinium oxide.

So, 13.24 mass % $O$ means the compound contains 13.24 g of $O$ in 100 g of Gadolinium oxide.

Using formula of number of moles:

$Number of moles = \frac{mass}{Atomic mass}$

The atomic mass of $Gd = 157.25 u$

$Number of moles = \frac{86.76}{157.25} = 0.5517 mole$

The atomic mass of $O = 16 u$

$Number of moles = \frac{13.24}{16} = 0.8275 mole$

In order to get the empirical formula, the moles are divide by the lowest value that is 0.5517.

$Gd_{\frac{0.5517}{0.5517}} = Gd$

$O_{\frac{0.8275}{0.5517}} = O_{1.499}\simeq O_{1.5}$

So, the formula is $GdO_{1.5}$, will multiply by 2 to get the whole integer.

Hence, the empirical formula is $Gd_2O_{3}$.