Question

P and Q are $2$ elements which form ${{P}_{2}}{{Q}_{3}}$ and $P{{Q}_{2}}$.
If $0.15$ mole of ${{P}_{2}}{{Q}_{3}}$ weight $15.9gm$ and $0.15$ mole of $P{{Q}_{2}}$ weight $9.3gm$ .
What are atomic weights of P and Q?

Answer 1

We know that the atomic weight is the total weight of the atoms which is the weight of protons and neutrons added a bit by electrons. There is a slight difference between atomic weight and atomic mass and keep in mind while solving that. The formula here we are going to use is: Number of moles of any molecule can be found out by using the mathematical definition of moles that is ${{N}_{m}}=\dfrac{m}{M}$ where $N\text{ }=$ number of moles , $m\text{ }=~$ given mass, $M=\text{ }\dfrac{atomic}{molecular\text{ }mass}$

Complete answer: Let’s take the atomic mass of of $P$ be x and $Q$ be y than molecular mass of the given compounds will be
${{P}_{2}}{{Q}_{3}}=2\times x+3\times y$ and $P{{Q}_{2}}=x+2\times y$
As there are $2$ atoms of element P in and $3$ atoms of element Q in the ${{P}_{2}}{{Q}_{3}}$ molecule and one atom of element P and two atoms of element Q in $P{{Q}_{2}}.$ Given us to the value of N(number of moles) and m( given mass of the ${{P}_{2}}{{Q}_{3}}$ ) we can put the value of M( given mass of $P{{Q}_{2}}$ ) and get two equations having two variables and as we know when number of variables are equal to number of equation the variables can be easily obtained are:
$\dfrac{15.9}{(2x+3y)}=0.15$ and $\dfrac{9.3}{(x+2y)}=0.15$
On solving the equations we get $x=\left( \dfrac{13}{9} \right)y$
Putting the value of x in terms of y in the equation $1.2$ we get
$x=\dfrac{13}{5}=2.6gm$ and $y=\dfrac{9}{5}=1.8gm$
Therefore, the atomic mass of $P\left( x \right)~$ is $2.6gm$ and the atomic mass of $Q\left( y \right)~$ is $1.8gm.$

Note:
Remember that the mole is defined as $6.022\times {{10}^{23}}$ of anything for elements. It is $6.022\times {{10}^{23}}$ of atoms for molecules it $6.022\times {{10}^{23}}$ of elements of the molecule and the weight of these many atoms or elements is called the atomic weight or molecular weight.