Question

The empirical formula of a compound is ${{C}_ {2}} {{H}_ {4}} O$. 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

For calculating gram molecular mass as vapor density is given we can use the formula: Gram molecular mass= 2 (vapor density), gram molecular mass is the same as molar mass. The only difference is that the gram molecular mass specifies the mass unit to be used. Gram molecular mass may be reported in grams or grams per mole.

Complete step by step solution:
We have been provided with the empirical formula of a compound is ${{C}_ {2}} {{H}_ {4}} O$,
The empirical formula of a chemical compound is the simplest positive integer ratio of atoms present in a compound. A simple example of this concept is that the empirical formula of sulphur monoxide, would simply be $SO$, as is the empirical formula of sulphuric dioxide, ${{S}_ {2}} {{O}_ {2}}$.
Now, we will be finding empirical formula mass of ${{C}_ {2}} {{H}_ {4}} O$:
The empirical formula mass can be determined by multiplying each element's subscript by its atomic weight on the periodic table and adding them together.
So, the empirical formula mass of ${{C}_ {2}} {{H}_ {4}} O$ will be: $(12\times 2) +(1\times 4) +(1\times 16) =44g$
Now, according to the question we have been given that the empirical formula mass is equal to one half of its vapor density,
So, the vapor density will be: $2\times 44=88g$,
Now, as we need to find out the gram molecular mass of ${{C}_ {2}} {{H}_ {4}} O$:
Gram molecular mass is equal to the molecular weight of a substance or the sum of all the atomic masses in its molecular formula.
So, the gram molecular mass: molecular mass = $2\times$(vapor density)
So, the gram molecular mass of ${{C}_ {2}} {{H}_ {4}} O$ comes out to be: $2\times 88=176g$
So, we can say that the gram molecular mass of ${{C}_ {2}} {{H}_ {4}} O$ is 176g.

Therefore, we can conclude that option (A) is correct.

Note: Molar mass is also useful in analysing the results of experiments. If two equal amounts of moles of different substances take up different volumes, then it indicates that the molecules of the substance with the larger volume are larger than the molecules of the substance with the smaller volume.