Answer:
The molecular formula of the compound is [tex]C_{7}H_{6}O_{2}[/tex].
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
[tex]m_{C} = \frac{68.84}{100}\times \left(122.12\,\frac{g}{mol} \right)[/tex]
[tex]m_{C} = 84.067\,g[/tex]
Hydrogen
[tex]m_{H} = \frac{4.96}{100}\times \left(122.12\,\frac{g}{mol} \right)[/tex]
[tex]m_{H} = 6.057\,g[/tex]
Oxygen
[tex]m_{O} = \frac{26.20}{100}\times \left(122.12\,\frac{g}{mol} \right)[/tex]
[tex]m_{O} = 31.995\,g[/tex]
Now, the number of moles ([tex]n[/tex]), measured in moles, of each element are calculated by the following expression:
[tex]n = \frac{m}{M}[/tex]
Where:
[tex]m[/tex] - Mass of the element, measured in grams.
[tex]M[/tex]- Molar mass of the element, measured in grams per mol.
Carbon ([tex]m_{C} = 84.067\,g[/tex], [tex]M_{C} = 12.011\,\frac{g}{mol}[/tex])
[tex]n = \frac{84.067\,g}{12.011\,\frac{g}{mol} }[/tex]
[tex]n = 7[/tex]
Hydrogen ([tex]m_{H} = 6.057\,g[/tex], [tex]M_{H} = 1.008\,\frac{g}{mol}[/tex])
[tex]n = \frac{6.057\,g}{1.008\,\frac{g}{mol} }[/tex]
[tex]n = 6[/tex]
Oxygen ([tex]m_{O} = 31.995\,g[/tex], [tex]M_{O} = 15.999\,\frac{g}{mol}[/tex])
[tex]n = \frac{31.995\,g}{15.999\,\frac{g}{mol} }[/tex]
[tex]n = 2[/tex]
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:
[tex]C_{7}H_{6}O_{2}[/tex]
