Question

$10.00$ mg of the substance yields $11.53$ mg ${H_2}O$ and $28.16$ mg $C{O_2}.$ What is the empirical formula of menthol?

Answer 1

Menthol is a compound which can be made synthetically or it can be obtained from the oils, peppermint or other mints. It is an organic compound and its formula can be written as ${C_x}{H_y}{O_z}$ . In the solution we will first know the combustion reaction of Menthol and then find the millimoles of reactants as well as products. Then we will compare the millimoles of Carbon, hydrogen and oxygen to find the empirical formula of Menthol (values of x, y and z in the empirical formula).

Complete answer:
Empirical formula is the simplest formula of any organic compound. Let the empirical formula of Menthol be ${C_X}{H_Y}{O_Z}.$
Combustion reaction for menthol is given as follows:
$CxHyOz + {O_2} \to C{O_2} + {H_2}O$
Mass of Carbon dioxide $(C{O_2})$ formed is $28.16$ mg.
Number of moles of any compound is calculated by dividing the given mass of that compound with its molecular mass.
Molecular Mass of Carbon dioxide $(C{O_2})$ is $44{\text{g}}mo{l^{ - 1}}.$
Therefore number of moles of carbon dioxide formed are:
$\dfrac{{28.16}}{{44}} = 0.64mmol$
Mass of water $({H_2}O)$ formed is $11.53$ mg.
Hence, the number of moles of water formed are:
$\dfrac{{11.53}}{{18}} = 0.64mmol$
From CO₂, we get $1$ mole of Carbon (C) and $2$ moles of oxygen (O).
Hence, the number of millimoles of C are $0.64$ mmol and the number of millimoles of O are $1.28$ mmol.
From H₂O, we get $2$ moles of H and $1$ mole of O.
Hence, the number of millimoles of H are $1.28$ mmol and the number of millimoles of O are $0.64$ mmol.
Initially the mass of menthol is $10mg.$
In chemical reactions, the masses of products are always equal to that of reactants. Products have excess mass because the combustion reaction took place in presence of oxygen $({O_2})$ .
Total mass of water and carbon dioxide is:
$11.53mg + 28.16mg = 39.69mg$
Difference in masses of reactants and products is:
$39.69 - 10 = 29.69mg$
This difference is due to the oxygen from air present during oxygen and the millimoles of oxygen are:
$\dfrac{{29.69}}{{16}} = 1.8556mmol$
Then the millimoles of oxygen coming from menthol are:
$(1.28 + 0.64) - 1.8556 = 0.064{\text{ }}mmol$
Therefore, in menthol, the number of millimoles of C,H and O are found to be:
$C{\text{ = }}0.64mmol$
$H = 1.28mmol$
$O = 0.064mmol$
Now, we will divide each of these by $0.064$ , to get the simplest whole number.
$C{\text{ = 10}}mmol$
$H = 20mmol$
$O = 1mmol$
Therefore, the empirical formula of Menthol is found to be ${C_{10}}{H_{20}}O.$

Note:
We should know that menthol is an organic compound. It is a waxy and crystalline compound. It is clear or white in colour. It exists in solid state at room temperature and when the temperature is slightly raised, it melts. Menthol is used as an antipruritic which helps in reducing itching. It is also used as a topical analgesic.