Question

A compound has the following $\% $composition. \[{\text{Zn = 22}}{\text{.65 % }}\],\[{\text{S}} = 11.15{\text{ }}\% \] ,\[{\text{O}} = 61.32{\text{ }}\% \]and \[{\text{H}} = 4.88\% .\]Its relative molecular mass is\[287g\]. Its molecular formula assuming that all the hydrogen in the compound is present in combination with oxygen as water of crystallization is:
 ${\text{Zn}} = 65$, ${\text{S}} = 32$, ${\text{O}} = 16$, ${\text{H}} = 1$
A.\[{\text{ZnS}}{{\text{O}}_{\text{4}}}{\text{.7}}{{\text{H}}_{\text{2}}}{\text{O}}\]
B.\[{\text{ZnS}}{{\text{O}}_{\text{4}}}{\text{.5}}{{\text{H}}_{\text{2}}}{\text{O}}\]
C.\[{\text{ZnS}}{{\text{O}}_{\text{4}}}{\text{.3}}{{\text{H}}_{\text{2}}}{\text{O}}\]
D.\[{\text{ZnS}}{{\text{O}}_{\text{4}}}{\text{.}}{{\text{H}}_{\text{2}}}{\text{O}}\]

Answer 1

Hint: International Union of Pure and Applied Chemistry is an international federation of chemists all around the world which has set the conventional naming system for chemical compounds. The moles of the elements present in their simplest ratio will be used to find out the molecular formula of the compound.

Complete step by step answer:
To solve this question firstly we calculate its molecular formula.
For finding the molecular formula of the compound we have to follow the following rules:
 • Firstly, write down the mass percentage of the constituent elements.
• Then, write the atomic masses of those elements.
• Now, divide the percentage of each element with its atomic mass.
• Then, finally divide all the values by the smallest value obtained.
 • This will give you the simplest molecular formula of the compound.
The table for calculating the molecular formula of the compound is given below:

Element	percentage	Atomic Mass	Ratio=$\dfrac{{{\text{percentage}}}}{{{\text{AtomicMass}}}}$	Simplest Ratio
Zn	22.65	65	$\dfrac{{22.65}}{{65}}$=$0.34$	$\dfrac{{0.34}}{{0.34}} = 1$
S	11.15	32	$\dfrac{{11.15}}{{32}}$=$0.34$	$\dfrac{{0.34}}{{0.34}} = 1$
O	61.32	16	$\dfrac{{61.32}}{{16}}$=$3.83$	$\dfrac{{3.83}}{{0.34}} = 11$
H	4.88	1	$\dfrac{{4.88}}{1}$=$4.88$	$\dfrac{{4.83}}{{0.34}} = 14$

As it is given in the question that all the atoms of hydrogen are present as water of crystallization. So, $7$atoms of oxygen are in combination with hydrogen as water of crystallization and the remaining $4$ atoms are in combination with sulfur as sulfate.
So, molecular formula of the compound will be\[{\text{ZnS}}{{\text{O}}_{\text{4}}}{\text{.7}}{{\text{H}}_{\text{2}}}{\text{O}}\] . This formula can be verified by calculating its molecular mass: \[65{\text{ }} + {\text{ }}32{\text{ }} + {\text{ }}4\left( {16} \right){\text{ }} + {\text{ }}7(18){\text{ }} = {\text{ }}287{\text{ u}}{\text{.}}\]
As, this mass is equal to relative molecular mass.

Therefore, the correct option is A.

Note:
 Without determining the molecular formula of a compound, nomenclature is not possible for that compound. So, the molecular formula of a compound plays a vital role in the naming convention of any compound.