Question

Two elements ‘P’ and ‘Q’ combine to form a compound. The atomic mass of ‘P’ is 12 and ‘Q’ is 16. The percentage of ‘P’ in the compound is 27.3. What will be the empirical formula of the compound?
(A) \[\text{ }{{\text{P}}_{\text{2}}}{{\text{Q}}_{\text{2}}}\text{ }\]
(B) $\text{ PQ }$
(C) $\text{ }{{\text{P}}_{\text{2}}}\text{Q }$
(D) $\text{ P}{{\text{Q}}_{\text{2}}}\text{ }$

Answer 1

Hint: An empirical formula establishes the relation between the numbers of moles of an atom present in the compound. It tells us the relative ratios of the different atoms in the compound. This ratio is true for molar masses too. The general empirical formula of a compound can be depicted as $\text{A}x\text{B}y$, where the x is the number of atoms of A and y is the number of atoms of B and $x:y$ is the relative ratio of the moles of atoms.

Complete step by step solution:
As we know, the empirical formula gives us the simple whole-number ratio between the atoms present in a compound. The empirical formula may be the same for different compounds. They do not give any idea about the arrangement or the number of atoms present in a compound.
Follow the following step to determine the empirical formula of the compound.
Step 1) Assume a 100 gram of the compound. It would be easy to convert the percentage that can be easily converted into the grams.
Step 2) Use molar mass and Convert the elements into its moles.
 Step 3) we know that the atoms combine in the whole-number ratio. In this step find out the whole number ratio or relative ratio of moles by dividing the moles of each element by the smallest number of moles. Here we will get a ratio of moles of elements.
Step 4) we will get the formula as $x:y:z$ and we will get the empirical formula as ${{\text{P}}_{x}}{{\text{Q}}_{y}}{{\text{R}}_{y}}$ .
Here, we have given the element ‘P’ and ‘Q’.
Let us take the element ‘P’, the mass percent of ‘P’ is equal to 27.3%. The mass percentage of compounds is always $100{\scriptstyle{}^{0}/{}_{0}}$ . Therefore, the mass percentage of ‘Q’ is equal to the,
$\text{mass }{\scriptstyle{}^{0}/{}_{0}}\text{ of Q = (100 }-\text{ 27}\text{.3)}{\scriptstyle{}^{0}/{}_{0}}\text{ = 72}\text{.7}{\scriptstyle{}^{0}/{}_{0}}$
So, the mass percent of ‘Q’ is equal to 72.7%.
If we consider an $100\text{ g}$ of the compound, then
$\begin{align}
& \text{mass}\,\text{of P = 27}\text{.3 g} \\
& \text{mass}\,\text{of Q = 72}\text{.7 g} \\
\end{align}$
We know the atomic mass of ‘P’ is 12 g. Therefore, the moles of ‘P’ is,
$\text{moles of P = }\dfrac{27.3}{12}\text{ = 2}\text{.275 }\simeq \text{ 2}$
Similarly, we know the molar mass of ‘Q’ is 16.therefore, the number of moles of ‘Q’ are:
$\text{moles of Q = }\dfrac{72.7}{16}\text{ = 4}\text{.54 }\simeq \text{ 4}$
Let us find out the relative ratio of the number of moles of ‘P’ and ‘Q’.
$\text{P:Q }\Rightarrow \text{ 2 : 4 }\Rightarrow \text{ }\dfrac{2}{2}:\dfrac{4}{2}=\text{ 1:2}$
Therefore, the empirical formula for the compound is $\text{P}{{\text{Q}}_{\text{2}}}$

Hence, (D) is the correct option.

Note: Students should not be confused with molecular formula and empirical formula. The empirical formula will give the simple whole-number ratio of the atoms present in one molecule of the compound while the molecular formula gives the actual number of atoms present in a molecule. The empirical formula is a theoretical concept and the molecular formula is an experimental value.