Question

The empirical formula of a compound is ${{\text{C}}_{\text{2}}}{{\text{H}}_{\text{4}}}{\text{O}}$. If the empirical formula mass is equal to one half of its vapor density, find the gram molecular mass of the compound.
A. \[176\]
B. \[66\]
C. \[44\]
D. \[88\]

Answer 1

Hint: To solve this question, first we need to understand the concept behind empirical formula. We can define the empirical formula of a chemical compound as the simplest positive integer ratio of the atoms present in a compound.

Complete step by step answer:
To calculate the empirical formula of a compound we first need to convert the mass of each element into moles with the help of the molar mass by referring to the periodic table. Then, we will divide each mole value with the smallest number of moles calculated in the reaction. After that we will round off the value to the nearest whole number. Therefore, we get a mole ratio of the elements and it is represented by subscripts in an empirical formula.
With reference to the compound given in the question that is, ${{\text{C}}_{\text{2}}}{{\text{H}}_{\text{4}}}{\text{O}}$ the empirical formula can be written as it contains carbon ${\text{C}}$, hydrogen ${\text{H}}$, and oxygen ${\text{O}}$, in a ratio of \[2:4:1\]. It can also be defined as one mole of this compound containing carbon, hydrogen, and oxygen in a \[2:4:1\] mole ratio.
There, to derive the empirical formula of ${{\text{C}}_{\text{2}}}{{\text{H}}_{\text{4}}}{\text{O}}$
Mass of ${{\text{C}}_{\text{2}}}{{\text{H}}_{\text{4}}}{\text{O}} = 44{\text{ }}g$
As we know that, vapor density V.D. \[ = 2\] (mass of compound) \[ = 2 \times 44 = 88{\text{ }}g\]
Therefore, molecular mass of the compound \[ = 2\] (vapor density)
So, molecular mass of the compound \[ = \;2 \times 88\; = 176{\text{ }}g\] (option A)

$\therefore $ Option A is the correct answer .

Note:
After solving this question, we need to understand the concept of the molecular formula of a compound. The actual numbers of atoms of each element occurring in the smallest freely existing unit or molecule of the compound is called the molecular formula of the compound.