Question

Suppose the elements X and Y combine to form two compounds $X{{Y}_{2}}$ and ${{X}_{3}}{{Y}_{2}}$. When 0.1 mole of $X{{Y}_{2}}$ weighs 10gm and 0.05 mole of ${{X}_{3}}{{Y}_{2}}$ weighs 9gm. Calculate the atomic weight of X and Y.

Answer 1

. Mole is generally represented by mol which is used to measure the amount of any substance. A mole of any substance or a mole of particles is defined to be exactly equal to $6.02214076\times {{10}^{23}}$ particles and particles may be ions, atoms, electrons or molecules.

Complete step by step answer:
Atomic weight can also be known by relative atomic mass which means ratio of the average mass of a chemical element atoms to some standard value. The standard unit of atomic mass is given by one-twelfth the mass of an atom of the isotope carbon-12. It is measured in terms of atomic mass units denoted by amu which is also called daltons.
Now, let atomic weight of X = AX
Atomic weight of Y = AY
Now we know that = mole is given by $\dfrac{weight}{atomic weight}$
Mole of $X{{Y}_{2}}$ = 0.1 (given)
$\therefore 0.1=\dfrac{10}{AX+2AY}$
$AX + 2AY = 100g$ (1)
Mole of ${{X}_{3}}{{Y}_{2}}$= 0.05
$0.05 =\dfrac{9}{3AX+2AY}$
$3AX+2AY = 180g$ (2)

By solving equations 1 and 2
$2AX = 80$
$AX = 40$; $AY = 30gmo{{l}^{-1}}$
Hence the atomic weights of X and Y is 40, $30gmo{{l}^{-1}}$ respectively.

Note: Atomic weight is measured in the term of isotopes where isotopes are those compounds which have the same chemical element but different atomic mass numbers. Atomic mass number is given by total number of protons and neutrons.