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

Answer:

The molecular formula of the compound is $C_{7}H_{6}O_{2}$.

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

$m_{C} = \frac{68.84}{100}\times \left(122.12\,\frac{g}{mol} \right)$

$m_{C} = 84.067\,g$

Hydrogen

$m_{H} = \frac{4.96}{100}\times \left(122.12\,\frac{g}{mol} \right)$

$m_{H} = 6.057\,g$

Oxygen

$m_{O} = \frac{26.20}{100}\times \left(122.12\,\frac{g}{mol} \right)$

$m_{O} = 31.995\,g$

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

$n = \frac{m}{M}$

Where:

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

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

Carbon ($m_{C} = 84.067\,g$, $M_{C} = 12.011\,\frac{g}{mol}$)

$n = \frac{84.067\,g}{12.011\,\frac{g}{mol} }$

$n = 7$

Hydrogen ($m_{H} = 6.057\,g$, $M_{H} = 1.008\,\frac{g}{mol}$)

$n = \frac{6.057\,g}{1.008\,\frac{g}{mol} }$

$n = 6$

Oxygen ($m_{O} = 31.995\,g$, $M_{O} = 15.999\,\frac{g}{mol}$)

$n = \frac{31.995\,g}{15.999\,\frac{g}{mol} }$

$n = 2$

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:

$C_{7}H_{6}O_{2}$