Question

g a compound containing only carbon and hydrogen produces 1.80 gCO2 and 0.738 gH2O. Find the empirical formula of the compound. Express your answer as an empirical formula.

Answer 1

Answer: The empirical formula for the given compound is
`CH_2`

Step-by-step explanation:

The chemical equation for the combustion of hydrocarbon having carbon, hydrogen and oxygen follows:

`C_xH_y+O_2\rightarrow CO_2+H_2O`

where, 'x' and 'y' are the subscripts of Carbon and hydrogen respectively.

We are given:

Mass of
`CO_2=1.80g`

Mass of
`H_2O=0.738g`

We know that:

Molar mass of carbon dioxide = 44 g/mol

Molar mass of water = 18 g/mol

For calculating the mass of carbon:

In 44 g of carbon dioxide, 12 g of carbon is contained.

So, in
`1.80g` of carbon dioxide,
`(12)/(44)* 1.80=0.491g` of carbon will be contained.

For calculating the mass of hydrogen:

In 18 g of water, 2 g of hydrogen is contained.

So, in
`0.738g` of water,
`(2)/(18)* 0.738=0.082g` of hydrogen will be contained.

To formulate the empirical formula, we need to follow some steps:

Step 1: Converting the given masses into moles.

Moles of Carbon =
`\frac{\text{Given mass of Carbon}}{\text{Molar mass of Carbon}}=(0.491g)/(12g/mole)=0.0409moles`

Moles of Hydrogen =
`\frac{\text{Given mass of Hydrogen}}{\text{Molar mass of Hydrogen}}=(0.082g)/(1g/mole)=0.082moles`

Step 2: Calculating the mole ratio of the given elements.

For the mole ratio, we divide each value of the moles by the smallest number of moles calculated which is
`0.0409` moles.

For Carbon =
`(0.0409)/(0.0409)=1`

For Hydrogen =
`(0.082)/(0.0409)=2.00\approx 2`

Step 3: Taking the mole ratio as their subscripts.

The ratio of C : H = 1 : 2

Hence, the empirical formula for the given compound is
`C_1H_2=CH_2`