Question

An organic compound on analysis gave $C\text{ = 54}\text{.5 }\!\!%\!\!\text{ and H = 9}\text{.1 }\!\!%\!\!\text{ }$ by mass. Its empirical formula is:
(a)- $CH{{O}_{2}}$
(b)- $C{{H}_{2}}O$
(c)- ${{C}_{2}}{{H}_{4}}O$
(d)- ${{C}_{3}}{{H}_{7}}O$

Answer 1

Hint: The empirical formula of a chemical compound is calculated with the help of two factors i.e., the percentage composition of elements and atomic mass of the element. Since the percentage of carbon and hydrogen is given, for calculation the percentage of oxygen, use the formula: % of O = 100 – (% of C + % of H)

Complete step by step answer:
The empirical formula is the chemical formula that tells the simplest whole-number ratio of the atoms of all elements present in one molecule.
It is deduced by- (a) percentage composition of elements (b)- atomic masses.
There are some steps for calculating the empirical formula:
i)- To convert the mass percent into grams. The given mass percentage represents the masses of the element in grams.

ii)- To calculate the number of moles. Divide the percentage of each element by its atomic mass.
\[\text{moles of the element= }\dfrac{\text{mass of the element}}{\text{At}\text{. mass of the element}}\]

iii)-To calculate the simplest molar ration. Divide the moles obtained in step (i) by the smallest quotient or the least value from amongst the values obtained for each element. This gives the simplest molar ratio.

iv)- To calculate the simplest whole number ratio. The simplest molar ratios, as calculated in step 2, are generally whole numbers. If not, then (a) raise the values to the nearest whole number, or (b) multiply the simplest atomic ratio by a suitable integer.

v)- To write the empirical formula. Insert the numerical value of the simplest whole number.
Given percentage of carbon = 54.5%
Percentage of hydrogen = 9.1 %
Percentage of oxygen = $100-(54.5+9.1)=36.4%$
According to the following steps, for iron and oxygen is solved in the table:

Element	Symbol	Percentage of elements	At. mass of elements	Moles of the element	Simplest molar ratio	Simplest whole number
Carbon	O	36.4	16	36.4/16 = 2.27	2.27/2.27 = 1	1
Oxygen	C	54.5	12	54.5/12 = 4.54	4.54/2.27 = 2	2
Hydrogen	H	9.1	1	9.1/1 = 9.1	9.1/2.27 = 4	4

So, the correct answer is “Option C”.

Note: The simplest molecular ratio should always be converted into the whole number. If not converted this would give the exact or true formula which gives the molecular formula. Don't get confused between molecular and empirical formulas.