Q. A dibasic acid containing $C , H$ and $O$ was found to contain $C =26.7 \%$ and $H =2.2 \%$. The vapour density of diethyl ester was found to be $73 .$ What is the molecular formula of acid?
Organic Chemistry – Some Basic Principles and Techniques
Solution:
Element
C
H
O
Percentage
26.7
2.2
71.1
Atomic mass
12
1
16
Atomic ratio
$\frac{26.7}{12}=2.225$
$\frac{2.2}{1}=2.2$
$\frac{4.44}{2.2} \approx 2$
Simplest ratio
$\frac{2.225}{2.2} \approx 1$
$=\frac{2.2}{2.2}=1$
$\frac{71.1}{16}=4.44$
Simple whole no. ratio
1
1
2
Hence, empirical formula is $CHO _{2}$
Empirical Formula Mass $=12+1+2 \times 16=45$
Molecular mass of diethyl ester $=73 \times 2=146$
Molecular mass of acid = Molecular mass of ester
$-\left(2 \times\right.$ molecular mass of $\left. C _{2} H _{5}\right)+(2 \times$ atomic mass of $H )$
$=146-(2 \times 29)+2=90$
$n=\frac{\text { Molecular mass }}{\text { Empirical formula mass }}=\frac{90}{45}=2$
Molecular formula $=(\text { Empirical Formula })_{n}=\left( CHO _{2}\right)_{2}= C _{2} H _{2} O _{4}$
| Element | C | H | O |
|---|---|---|---|
| Percentage | 26.7 | 2.2 | 71.1 |
| Atomic mass | 12 | 1 | 16 |
| Atomic ratio | $\frac{26.7}{12}=2.225$ | $\frac{2.2}{1}=2.2$ | $\frac{4.44}{2.2} \approx 2$ |
| Simplest ratio | $\frac{2.225}{2.2} \approx 1$ | $=\frac{2.2}{2.2}=1$ | $\frac{71.1}{16}=4.44$ |
| Simple whole no. ratio | 1 | 1 | 2 |