Answer:
The empirical formula of the compound is
.
Explanation:
We need to determine the empirical formula in its simplest form, where hydrogen (
) is scaled up to a mole, since it has the molar mass, and both carbon (
) and oxygen (
) are also scaled up in the same magnitude. The empirical formula is of the form:
![C_{x}HO_{y}](https://tex.z-dn.net/?f=C_%7Bx%7DHO_%7By%7D)
Where
,
are the number of moles of the carbon and oxygen, respectively.
The scale factor (
), no unit, is calculated by the following formula:
(1)
Where:
- Mass of hydrogen, in grams.
- Molar mass of hydrogen, in grams per mole.
If we know that
and
, then the scale factor is:
![r = \frac{1.008}{0.2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B1.008%7D%7B0.2%7D)
![r = 5.04](https://tex.z-dn.net/?f=r%20%3D%205.04)
The molar masses of carbon (
) and oxygen (
) are
and
, then, the respective numbers of moles are: (
,
,
)
Carbon
(2)
![n_{C} = \frac{(5.04)\cdot (1.2\,g)}{12.011\,\frac{g}{mol} }](https://tex.z-dn.net/?f=n_%7BC%7D%20%3D%20%5Cfrac%7B%285.04%29%5Ccdot%20%281.2%5C%2Cg%29%7D%7B12.011%5C%2C%5Cfrac%7Bg%7D%7Bmol%7D%20%7D)
![n_{C} = 0.504\,moles](https://tex.z-dn.net/?f=n_%7BC%7D%20%3D%200.504%5C%2Cmoles)
Oxygen
(3)
![n_{O} = \frac{(5.04)\cdot (3.2\,g)}{15.999\,\frac{g}{mol} }](https://tex.z-dn.net/?f=n_%7BO%7D%20%3D%20%5Cfrac%7B%285.04%29%5Ccdot%20%283.2%5C%2Cg%29%7D%7B15.999%5C%2C%5Cfrac%7Bg%7D%7Bmol%7D%20%7D)
![n_{O} = 1.008\,moles](https://tex.z-dn.net/?f=n_%7BO%7D%20%3D%201.008%5C%2Cmoles)
Hence, the empirical formula of the compound is
.