Question

A metal oxide contains \[70\% \] metal with a molar mass of metal is \[56\] and the molar mass of the compound is \[160\] . what will be its empirical formula ?
(A) ${M_2}{O_5}$
(B) ${M_2}{O_3}$
(C) $MO$
(D) $M{O_3}$

Answer 1

Hint: The simplest whole number ratio of different atoms present in a compound is known as empirical formula. Whereas, molecular formula gives the exact number of different atoms present in a compound. Empirical formulas of a compound can be calculated if the mass percentage of different elements present in the compound is known.

Complete step by step answer:
The empirical formula of compound is calculated in a number of steps. The steps are as given below:
\[Step{\text{ }}1 - \] Conversion of mass percent of elements into grams.
\[Step{\text{ }}2 - \] Conversion into number of moles of each element.
\[Step{\text{ }}3 - \] Dividing the mole value obtained in the second step by the smallest number.
\[Step{\text{ }}4 - \] writing the empirical formula by mentioning the number after writing the symbol of respective elements.
Calculation of empirical formula of given compound:
Given, molar mass of metal \[ = {\text{ }}56g.\]
Molar mass of compound \[ = {\text{ }}160g.\]
Mass percent of metal \[ = {\text{ }}70\% .\]
Therefore, mass percent of oxygen \[ = {\text{ }}100 - 70{\text{ }} = {\text{ }}30\% .\]

Element	Percentage	Atomic Mass	Atomic Ratio	Simplest Ratio	Simplest Whole No.
Metal(M)	\[70\% \]	\[56\]	$\frac{{70}}{{56}} = 1.25$	$\frac{{1.25}}{{1.25}} = 1$	$2$
Oxygen(O)	\[30\% \]	\[16\]	$\frac{{30}}{{16}} = 1.87$	$\frac{{187}}{{1.25}} = 1.5$	$3$

Empirical formula of metal oxide is ${M_2}{O_3}$.
Hence, the correct option is (B) ${M_2}{O_3}$ .

Note:
Molecular formula of a compound can also be calculated by knowing its Empirical formula. For calculation of molecular formula, first we need to find the empirical formula mass by adding the atomic masses of various atoms present in the empirical formula. The formula used for this calculation is:
$\dfrac{\text{Molar mass}} {{\text{empirical formula mass}}}$ .