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

Respuesta :

The mass % of [tex]Gd[/tex] = 86.76 % (given)

The mass % of [tex]O[/tex] = 100 - 86.76 = 13.24 %

Considering the mass of Gadolinium oxide as 100 g.

Then 86.76 mass % [tex]Gd[/tex] means the compound contains 86.76 g of [tex]Gd[/tex] in 100 g of Gadolinium oxide.

So, 13.24 mass % [tex]O[/tex] means the compound contains 13.24 g of [tex]O[/tex] in 100 g of Gadolinium oxide.

Using formula of number of moles:

[tex]Number of moles = \frac{mass}{Atomic mass}[/tex]

The atomic mass of [tex]Gd = 157.25 u[/tex]

[tex]Number of moles = \frac{86.76}{157.25} = 0.5517 mole[/tex]

The atomic mass of [tex]O = 16 u[/tex]

[tex]Number of moles = \frac{13.24}{16} = 0.8275 mole[/tex]

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

[tex]Gd_{\frac{0.5517}{0.5517}} = Gd[/tex]

[tex]O_{\frac{0.8275}{0.5517}} = O_{1.499}\simeq O_{1.5}[/tex]

So, the formula is [tex]GdO_{1.5}[/tex], will multiply by 2 to get the whole integer.

Hence, the empirical formula is [tex]Gd_2O_{3}[/tex].

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