Question

A 0.2076 g sample of an oxide of cobalt on analysis was found to contain 0.1476 g cobalt. Calculate the empirical formula of the oxide. [Co = 59 amu]

Answer 1

Hint: The percentage composition of elements and the atomic mass of the element are the two factors that can be used to calculate the empirical formula of the compound. By converting the molecular formula into the simplest whole-number ratio we can obtain the empirical formula of the compound.

Complete Solution :
We can define the empirical formula of the compound as the simplest whole-number ratio of the atoms of all elements present in one molecule.
Some steps that are used to calculate the empirical formula of the compound are given below:
The percentage composition of elements and the atomic mass of the element are the two factors that can be used to calculate the empirical formula of the compound.
(i)- First, convert the mass percentage into grams.
(ii)- Now calculate the number of moles by dividing the given mass by its atomic mass.
(iii)- Then calculate the simplest molar ratio by dividing the smallest number of moles with other moles obtained.
(iv)- Now multiply the simplest molar ratio into a suitable integer to get the whole number.

So, the given amount of sample is 0.2076 g in which the mass of the cobalt is 0.1476 g. therefore, the mass of oxygen will be:
$0.2076 - 0.1476 = 0.06\text{ g}$
The number of moles of cobalt will be: $\dfrac{0.1476}{59} = 0.0025$
The number of moles of oxygen will be: $\dfrac{0.06}{16} = 0.00375$
The simplest ratio of cobalt will be: $\dfrac{0.0025}{0.0025} = 1$
The simplest ratio of cobalt will be: $\dfrac{0.00375}{0.0025} = 1.49$
Now, multiplying the simplest ratio with 2 to get the whole number.
The number of atoms of cobalt will be: $1\text{ x 2 = 2}$
The number of atoms of oxygen will be: $1.49\text{ x 2 = 3}$
So, the formula will be $C{{o}_{2}}{{O}_{3}}$.

Note: If you don’t convert the simplest number ratio to whole number ratio, the empirical formula will be wrong and you will get the molecular formula of the compound.