Question

Gallium oxide, Ga.Oy, forms when gallium is combined with oxygen. A 1.25 g of Ga is allowed to react with excess oxygen and 1.68 g of the gallium oxide formed. What is the chemical formula of the gallium oxide if the molar mass is 187.44 g/mol?

Answer 1

Answer : The chemical formula of a compound is,
`Ga_2O_3`

Solution : Given,

Mass of gallium = 1.25 g

Mass of gallium oxide = 1.68 g

Mass of oxygen = Mass of gallium oxide - Mass of gallium

Mass of oxygen = 1.68 - 1.25 = 0.43 g

Molar mass of Ga = 69.72 g/mole

Molar mass of O = 16 g/mole

Step 1 : convert given masses into moles.

Moles of Ga =
`\frac{\text{ given mass of Ga}}{\text{ molar mass of Ga}}= (1.25g)/(69.72g/mole)=0.0179moles`

Moles of O =
`\frac{\text{ given mass of O}}{\text{ molar mass of O}}= (0.43g)/(16g/mole)=0.027moles`

Step 2 : For the mole ratio, divide each value of moles by the smallest number of moles calculated.

For Ga =
`(0.0179)/(0.0179)=1`

For O =
`(0.027)/(0.0179)=1.5`

The ratio of Ga : O = 1 : 1.5

To make in whole number we multiple ratio by 2, we get:

The ratio of Ga : O = 2 : 3

The mole ratio of the element is represented by subscripts in empirical formula.

The Empirical formula =
`Ga_2O_3`

The empirical formula weight = 2(69.72) + 3(16) = 187.44 gram/eq

Now we have to calculate the molecular formula of the compound.

Formula used :

`n=\frac{\text{Molecular formula}}{\text{Empirical formula weight}}`

`n=(187.44)/(187.44)=1`

Molecular formula =
`(Ga_2O_3)_n=(Ga_2O_3)_1=Ga_2O_3`

Therefore, the chemical of the compound is,
`Ga_2O_3`