Question

Asbestosis is a lung disease caused by inhaling asbestos fibers. The US Department of Health and Human Services considers a particular form of asbestos to be a carcinogen. The composition of this form of asbestos is 26.31% Mg, 20.20% Is, 1.45% H and the rest of the mass is due to oxygen. The molar mass of the compound is 277 g/mol. What is the molecular formula for the carcinogenic form of asbestos

Answer 1

Answer: The molecular formula for the carcinogenic form of asbestos
`Mg_3Si_2H_4O_9`

Step-by-step explanation:

a) If percentage are given then we are taking total mass is 100 grams.

So, the mass of each element is equal to the percentage given.

Mass of Mg = 26.31 g

Mass of Si= 20.20 g

Mass of H= 1.45 g

Mass of O= (100-(26.31+ 20.20+ 1.45)) = 52.04 g

Step 1 : convert given masses into moles

Moles of Mg=
`\frac{\text{ given mass of Mg}}{\text{ molar mass of Mg}}= (26.31g)/(24g/mole)=1.10moles`

Moles of Si=
`\frac{\text{ given mass of Si}}{\text{ molar mass of Si}}= (20.20g)/(28g/mole)=0.72moles`

Moles of H=
`\frac{\text{ given mass of H}}{\text{ molar mass of H}}= (1.45g)/(1g/mole)=1.45moles`

Moles of O=
`\frac{\text{ given mass of O}}{\text{ molar mass of O}}= (52.04g)/(16g/mole)=3.25moles`

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

For Mg =
`(1.10)/(0.72)=1.5`

For Si =
`(0.72)/(0.72)=1`

For H=
`(1.45)/(0.72)=2`

For O =
`(3.25)/(0.72)=4.5`

The ratio of Mg : Si: H: O = 1.5 : 1 : 2 : 4.5

Converting them into whole numbers :

The ratio of Mg : Si: H: O = 3 : 2 : 4 : 9

Hence the empirical formula is
`Mg_3Si_2H_4O_9`

Empirical mass =
`3* 24+2* 28+4* 1+9* 16=276g`

Molecular mass = 277 g

`n= \frac{\text {Molecular mass}}{\text {Empirical mass}}=(277)/(276)=1`

Thus molecular formula =
`1* Mg_3Si_2H_4O_9=Mg_3Si_2H_4O_9`