Question

1.60 g of an oxide of iron, on heating in a stream of hydrogen gas, completely to 1.12 g of iron. Find the empirical formula of the oxides.

Answer 1

The empirical formula of a chemical compound is expressed as the simplest positive integer ratio between the numbers of atoms of different elements present in a molecule of the compound.

Complete step by step answer:
Let's take an example that would make the concept of empirical formula clearer:
A simple example is that the empirical formula of sulfur monoxide would simply be SO, as is the formula of disulfur dioxide ${{S}_{2}}{{O}_{2}}$. Thus, sulfur monoxide and disulfur dioxide, are compounds of sulfur and oxygen and also have the same empirical formula. However, their molecular formulas, which express the number of atoms in each molecule of a compound, are not the same.
Now, let's have a look at the steps for determining an empirical formula:
- Start with the number of grams of each element of the compound given in the problem (If percentages are given, assume that the total mass is 100 grams so that the mass of each element will be equal to the percentage given)
- Convert the mass of each element into moles using the molar mass of the respective elements from the periodic table.
- Divide the value of each mole by the smallest number of moles calculated.
- Round to the nearest whole number. This is the mole ratio of the elements and is represented by subscripts in the empirical formula.
- If the number is too far to round up, then multiply each solution by the same factor to get the lowest possible whole number multiple.
- Now, let us assume the molecular formula of iron oxide be $F{{e}_{2}}{{O}_{x}}$
Let's check the chemical reaction occurring in order to proceed.
$F{{e}_{2}}{{O}_{x}}+{{H}_{2}}\to 2Fe+{{H}_{2}}O$
Since, 1.6g of $F{{e}_{2}}{{O}_{x}}$ contained 1.12g of Fe
Therefore, 1g of $F{{e}_{2}}{{O}_{x}}$ will contain =$\dfrac{1.12}{1.6}$
and, (112+16x) of $F{{e}_{2}}{{O}_{x}}$ will contain = $\dfrac{1.12}{1.6(112+16x)}$
We know that (112 + 16x) g of compound contains 112g of Fe
Therefore,

& \dfrac{1.12}{1.6(112 + 16x)} = 112 \\\ & 112 + 16x = 160 \\\ & x = 3 \\\ \end{aligned}$$ Therefore, Molecular formula will be $F{{e}_{2}}{{O}_{3}}$ Since, it is the simplest representation. So the empirical formula will also be $F{{e}_{2}}{{O}_{3}}$. **Note:** Don't get confused between molecular formula and empirical formula. Empirical formulas show the simplest whole-number ratio of atoms in a compound whereas molecular formulas show the number of each type of atom in a particular molecule.