Question

What is the formula of the compound formed when two elements X (atomic mass=75) and Y (atomic mass=16) combine to give a compound having 75.8% of X.

Answer 1

Number of moles of the substance can be calculated by dividing the weight of the substance given with the molecular mass of the substance.
The equation is,$\text{No}\text{.}\,\text{of}\,\text{moles=}\dfrac{\text{Given}\,\text{weight}}{\text{Molecular}\,\text{mass}\,}$ $\text{No}\text{.}\,\text{of}\,\text{moles}\,\text{of}\,\text{the}\,\text{substance=}\dfrac{\text{Given}\,\text{weight}\,\text{of}\,\text{the}\,\text{substance}}{\text{Molecular}\,\text{mass}\,\text{of}\,\text{the}\,\text{substance}}$
Empirical equation is different from that of the molecular formulae.

Complete step-by-step answer: So in the question it is given the atomic mass of two elements and the composition of X in the given compound is given as 75.8% and we have to find the formulae of the compound.
Here with this information we can find the empirical formulae of the compound formed.
Empirical formulae is the formula which gives the simplest whole number ratio of the atoms in the formed compound.
So now let’s move to the solution part of the question, here we know that the compound is formed by combining two elements X and Y.
And we have found the number of atoms combined to form the compound given by finding its empirical formulae.
Let’s first write the given data and find the other data by calculating various parameters with the given data.
Given data:
The percentage composition of X in compound =75.8%
Atomic mass of $\text{X=75g/mol}$
Atomic mass of $\text{Y=16g/mol}$
If we take that the produced compound is of 100g, then the composition of X in the compound is and the composition of Y in the compound is, $100-75.8=24.2g$
The given molar mass for $\text{X=75g/mol}$ and molar mass of Y is $\text{Y=16g/mol}$
$\text{No}\text{.}\,\text{of}\,\text{moles=}\dfrac{\text{Given}\,\text{weight}}{\text{Molecular}\,\text{mass}\,}$
$\text{No}\text{.}\,\text{of}\,\text{moles of X=}\dfrac{75.8}{75}=1.010\simeq 1$
$\text{No}\text{.}\,\text{of}\,\text{moles of Y=}\dfrac{24.2}{16}=1.5125\simeq 1.5=\dfrac{3}{2}$
Now take the ratio of the number of moles of the elements,$1:\dfrac{3}{2}$
We can write as $X:Y=1:\dfrac{3}{2}$
Therefore, the empirical formulae of the compound formed is ${{X}_{2}}{{Y}_{3}}$

Note: The empirical formula is different from that of molecular formulae. The molecular formula gives the exact number of atoms that was involved in the chemical combination. From the empirical formulae obtained we could find the empirical mass of the compound, it is a theoretical value and may show difference from the exact value.
And by calculating the empirical mass we could calculate the value of n,
$\text{n=}\dfrac{\text{Molecular}\,\text{mass}}{\text{Empirical}\,\text{formula}\,\text{mass}}$
The molecular formulae of the compound is related empirical formulae by,
$\text{Molecular}\,\text{formula=n }\\!\\!\times\\!\\!\text{ Empirical}\,\text{formula}$