A disbasic acid containing `C, H`, and `O` was found to contain `C = 26.7%` and `H=2.2%`. The vapor density of diethyl ester was found to be `73`. What is the molecular formula of the acid?

Options

A. `CH_(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

B

Explanation

`% O = (100%) - (% C + % H)`
`= (100%) - (26.7% + 2.2%) = 71.1%`
Considering `100 g` of the compound,
`n_(C ):n_(H):n_(O) = (26.7)/(12):(22)/(1):(71.1)/(16)`
`= 2.33:2.2:4.44`
`= (2.23)/(2.2):(2.2)/(2.2):(4.44)/(2.2)`
`= 1:1:2`
Therefore, empirical formula is `CHO_(2)` and empirical formula mass is `(12 + 1 + 2 xx 16) = 45`.
Molecular mass of acid
`=` Molecular mass of ester `(2 xx "Formula mass of" C_(2)H_(5)) + (2 xx At. "mass of" H)`
`= (146)-(2 xx 29) + (2 xx 1) = 90 u`
Molecular formula of acid
`= ((90 u)/(45 u)) (CHO_(2)) = (2)(CHO_(2))`
`= C_(2)H_(2)O_(4)`