Question

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?

• A. $C{H}_2{O}_2$
• B. $C_2{H}_2{O}_4$
• C. $C_3{H}_3{O}_4$
• D. $C_4{H}_4{O}_4$

Answer 1

Answer: (B)

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 $CH{O}_2$

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

$-(2\times$ molecular mass of $C_2{H}_5)+(2\times$ 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 $=(\text{ Empirical Formula }{)}_n={\left(CH{O}_2\right)}_2=C_2{H}_2{O}_4$