Question

An organic compound containing C, H, Cl and O on analysis was found to contain $\mathrm{C}=43.98\%,\mathrm{H}=2.09\%$ and $\mathrm{Cl}=37.18\%$. What is the formula of the compound?

Answer 1

Step 1: Given information

• An organic compound contains Carbon, Hydrogen, Chlorine and Oxygen.
• The percentage of Carbon $\left(\mathrm{C}\right)=43.98\%$
• The percentage of Hydrogen $\left(\mathrm{H}\right)=2.09\%$
• The percentage of Chlorine $\left(\mathrm{Cl}\right)=37.18\%$

Step 2: Calculation of percentage of Oxygen in the compound

• The percentage of Oxygen is as follows:

$$\begin{gathered} \mathrm{Percentage}\mathrm{of}\mathrm{Oxygen}=\left(100-43.98-2.09-37.18\right)\% \\ =16.75\% \end{gathered}$$

Step 3: Formulas used to calculate the atomic ratio and simplest ratio

• The atomic ratio is calculated by dividing the percentage composition of each element by its atomic weight.

$\mathrm{Atomic}\mathrm{ratio}=\frac{\mathrm{Percentage}\mathrm{composition}\mathrm{of}\mathrm{an}\mathrm{element}}{\mathrm{Atomic}\mathrm{weight}\mathrm{of}\mathrm{an}\mathrm{element}}$

• The simplest ratio is calculated by dividing the atomic ratio of each element by the smallest atomic ratio.

$\mathrm{Simplest}\mathrm{ratio}=\frac{\mathrm{Atomic}\mathrm{ratio}\mathrm{of}\mathrm{an}\mathrm{element}}{\mathrm{Smallest}\mathrm{atomic}\mathrm{ratio}}$

Step 4: Determination of the empirical formula

Element	Percentage composition	Atomic weight	Atomic ratio	Simplest ratio
C	$43.98$	$12$	$\frac{43.98}{12}=3.7$	$\frac{3.7}{1.05}=3.5$
H	$2.09$	$1$	$\frac{2.09}{1}=2.09$	$\frac{2.09}{1.05}=2$
Cl	$37.18$	$35.5$	$\frac{37.18}{35.5}=1.05$	$\frac{1.05}{1.05}=1$
O	$16.75$	$16$	$\frac{16.75}{16}=1.05$	$\frac{1.05}{1.05}=1$

• The simplest ratio of $\mathrm{C}:\mathrm{H}:\mathrm{Cl}:\mathrm{O}=3.5:2:1:1$, which is not a whole number ratio.
• Thus, after multiplying by 2, the simplest ratio of $\mathrm{C}:\mathrm{H}:\mathrm{Cl}:\mathrm{O}=7:4:2:2$

Therefore, the empirical formula of the compound is ${\mathrm{C}}_7{\mathrm{H}}_4{\mathrm{Cl}}_2{\mathrm{O}}_2$.