Question

How would you determine the empirical formula of a compound found to contain 63.50% silver, 8.25% nitrogen and the remainder oxygen?

Answer 1

We know that a chemical formula is the brief representation of the molecule of substance (compound or element) in terms of the symbols of various elements present in it. Chemical formula is of two types, empirical formula and molecular formula.

Complete step by step answer:
Let’s understand the empirical formula in detail. This formula gives the simplest whole number ratio of atoms of various elements present in one molecule of the compound. For example, the empirical formula of ${{\text{H}}_{\text{2}}}{{\text{O}}_{\text{2}}}$ is HO.
Given that,
% of silver=63.50
% of Nitrogen=8.25
% of oxygen=$100 - \left( {63.50 + 8.25} \right) = 100 - 71.75 = 28.25$
Then, we have to calculate the gram atoms. Gram atoms can be calculated by dividing the percentage of each element by atomic mass of the element.
Gram atoms or moles of silver=$\dfrac{{63.50}}{{107.87}} = 0.589$
Gram atoms or moles of nitrogen=$\dfrac{{8.25}}{{14}} = 0.589$
Gram atoms or moles of oxygen=$\dfrac{{28.25}}{{16}} = 1.77$
Then, we have to divide the gram atoms or moles of different elements by the smallest among them to find the atomic ratio or molar ration.
Molar ratio of silver (Ag)= $\dfrac{{0.589}}{{0.589}} = 1$
Molar ratio of nitrogen (N)=$\dfrac{{0.589}}{{0.589}} = 1$
Molar ratio of oxygen (O)=$\dfrac{{1.77}}{{0.589}} = 3$

So, the empirical formula of the compound is ${\text{AgN}}{{\text{O}}_{\text{3}}}$.

Additional Information:
Let’s discuss molecular formulas in detail. Molecular formula of a compound gives the actual ratio of the atoms of various elements present in one molecule of the compound. In writing the molecular formula, no common factor is removed and the actual ratio of the atoms is considered. For example, the molecular formula of hydrogen peroxide is ${{\text{H}}_{\text{2}}}{{\text{O}}_2}$. It is to be noted that the compounds are known by their molecular formula and not by empirical formulae. The empirical formulae have only theoretical importance.

Note: The relation between empirical formula and molecular formula is,
Molecular formula=n$\times$ empirical formula
Here, n is the common factor or multiplying factor. The value of n may be 1,2,3,4…. etc. In the case of n=1 , then the molecular formula is the same as the empirical formula.