Question

What is the empirical formula of $C_{10}{H}_{22}$?

Answer 1

Hint: The shortest whole-number ratio of atoms is seen by the empirical formula. The mathematical formula is calculated by calculating the percentage composition of the constituent elements of a complex. There will be a series of laws to obey, which will be learned.

Complete step by step answer:
We need to know that the empirical formula is calculated using the following rules:
- The mass of each of the constituent elements is converted to moles using the respective atomic weights.
- Each mole value is divided by the smallest number of moles calculated.
- The mole ratio of the elements is represented as the subscripts as the empirical formula.
Let us consider an arbitrary compound $A_x{B}_y$. The empirical formula can be calculated by finding the values of x and y. Firstly the percentage composition of each of the constituent elements of the compound is calculated. This is followed by the number of moles of $x$ and $y$ calculated in the compound. Then each mole value is divided by the smallest number of moles calculated. If they are in decimal numbers, they are converted into whole numbers which replaces the values of $x$ and $y$ in the compound $A_x{B}_y$. This gives the empirical formula of the compound.
Decane is an alkane with the chemical formula $C_{10}{H}_{22}$. A substance's empirical formula has the smallest ratio of its constituent components. The carbon to hydrogen ratio in this case is $10:22$. As a result, we must determine which number has the largest common factor with the other.
$10=2\times 5$
$22=2\times 11$
The largest common factor between the two numbers is $2$, as you can see, so we divide all numbers by $2$.
${\displaystyle \frac{10}{2}}=5$
${\displaystyle \frac{22}{2}}=11$
Hence the empirical formula becomes $C_5{H}_{11}$.

Note: Calculating the percentage composition of each of a compound's constituent elements is the most important step in determining the analytical formula. The empirical and molecular formulas do not have to be the same. The simplest whole-number ratio of atoms in a compound is shown by an empirical formula, while the number of each kind of atom in a molecule is shown by a molecular formula.