Question

An organic acid is composed of carbon (68.84%), hydrogen (4.96%), and oxygen (26.20%). Its molar mass is 122.12 g/mol. Determine the molecular formula of the compound.

Answer 1

The molecular formula of the compound is
`C_(7)H_(6)O_(2)`.

Step-by-step explanation:

Let consider that given percentages are mass percentages, so that mass of each element are determined by multiplying molar massof the organic acid by respective proportion. That is:

Carbon

`m_(C) = (68.84)/(100)* \left(122.12\,(g)/(mol) \right)`

`m_(C) = 84.067\,g`

Hydrogen

`m_(H) = (4.96)/(100)* \left(122.12\,(g)/(mol) \right)`

`m_(H) = 6.057\,g`

Oxygen

`m_(O) = (26.20)/(100)* \left(122.12\,(g)/(mol) \right)`

`m_(O) = 31.995\,g`

Now, the number of moles (
`n`), measured in moles, of each element are calculated by the following expression:

`n = (m)/(M)`

Where:

`m` - Mass of the element, measured in grams.

`M`- Molar mass of the element, measured in grams per mol.

Carbon (
`m_(C) = 84.067\,g`,
`M_(C) = 12.011\,(g)/(mol)`)

`n = (84.067\,g)/(12.011\,(g)/(mol) )`

`n = 7`

Hydrogen (
`m_(H) = 6.057\,g`,
`M_(H) = 1.008\,(g)/(mol)`)

`n = (6.057\,g)/(1.008\,(g)/(mol) )`

`n = 6`

Oxygen (
`m_(O) = 31.995\,g`,
`M_(O) = 15.999\,(g)/(mol)`)

`n = (31.995\,g)/(15.999\,(g)/(mol) )`

`n = 2`

For each mole of organic acid, there are 7 moles of carbon, 6 moles of hydrogen and 2 moles of oxygen. Hence, the molecular formula of the compound is:

`C_(7)H_(6)O_(2)`