Question

A compound on analysis gave the following percentage composition:
Na = 14.31\% ,{\text{ S = 9}}{\text{.97% , H = 6}}{\text{.22% , O = 69}}{\text{.5% }}
What would be the molecular formula of the compound assuming that all the hydrogen in the compound is reset in combination with oxygen as water of crystallization. Molecular weight of the compound is $322$ .
A. $N{a_2}S{O_4}$
B. $N{a_2}S{O_4}.10{H_2}O$
C. $N{a_2}S{H_{10}}{O_{12}}$
D. $N{a_2}S{O_4}.7{H_2}O$

Answer 1

In order to determine the chemical formula of a compound using the mass percentage of all the components we have to use quantitative analysis of the compound by using mass percentage and atomic weight ratio.

Complete step by step answer:
According to the question we have mass percentage of all components as:

Components	Mass percentage
Sodium	$14.31\%$
Sulphur	$9.97\%$
Hydrogen	$6.22\%$
Oxygen	$69.5\%$

For the determination of chemical formula we have to calculate integral ratio of mass percentage and atomic mass of components. That will be:

Components	Mass percentage	Atomic mass	{\text{mass% / atomic mass}}	Integral ratio
Sodium	$14.31\%$	$23$	$0.622$	$2$
Sulphur	$9.97\%$	$32$	$0.311$	$1$
Hydrogen	$6.22\%$	$1$	$6.22$	$20$
Oxygen	$69.5\%$	$16$	$4.34$	$14$

So, we can see there are two atoms of sodium,
One atom of sulphur,
Twenty atoms of hydrogen,
And fourteen atoms of oxygen.
So, the chemical formula will be: $N{a_2}S{O_{14}}{H_{20}}$
Empirical formula = $23 \times 2 + 32 \times 1 + 1 \times 20 + 16 \times 14 \Rightarrow 322$
By rearranging it we will get the molecular formula of given compound as:
$\Rightarrow N{a_2}S{O_4}.10{H_2}O$
Hence, option B is correct.

Note:
Empirical formula is defined as the formula that gives the simplest whole number ratio of atoms in a compound. There are some steps by which we can calculate empirical formulas. Firstly, we must know the number of grams of each element as given in the above problem. An empirical formula does not give any idea about the arrangement or number of atoms in the compound. It is standard for many ionic compounds, like calcium chloride $CaC{l_2}$ , and for macromolecules, such as silicon dioxide $Si{O_2}$ . On the other hand, the molecular formula shows the number of each type of atom in a molecule. The molecular formula shows the arrangement of the molecule. Different molecules could have the same empirical formula.