Question

Suppose two elements $ X $ and $ Y $ combine to form two compounds $ X{Y_2} $ and $ {X_2}{Y_3} $ when $ 0.05 $ mole of $ X{Y_2} $ weights $ 5g $ while $ 3.011 \times {10^{23}} $ molecules of $ {X_2}{Y_3} $ weights $ 85g $ . The atomic masses of $ X $ and $ Y $ are respectively:
(A) $ 20,30 $
(B) $ 30,40 $
(C) $ 40,30 $
(D) $ 80,60 $

Answer 1

Hint: Here we calculate the atomic mass of $ X $ and $ Y $ by using mole formula so, the mole formula divides the mass of the material by its molar mass. The molar mass of a substance is the mass in grams of one mole of that substance. This mass is given by the atomic weight of the chemical unit that makes up that substance in atomic mass units.

Complete answer:
The mole is the base unit of amount of substance in the International System of Units. It is defined as exactly $ 6.023 \times {10^{23}} $ particles, which may be atoms, molecules, ions, or electrons.
 $ \Rightarrow $ mole = $ \dfrac{{mass}}{{molar\;mass}} $
Here, we are calculating the molecular weight by putting the value of mass and mole.
Let the atomic weight of $ X $ is $ x $ and $ Y $ is $ y $
For, $ X{Y_2} $
By putting the values in the mole formula
 $ \Rightarrow 0.1 = \dfrac{{10}}{{x + 2y}} $
 $ \Rightarrow x + 2y = \dfrac{{10}}{{0.1}} $
 $ \Rightarrow 100 $
For, $ {X_3}{Y_2} $
By putting the values in the formula
 $ \Rightarrow 0.05 = \dfrac{9}{{3x + 2y}} $
 $ \Rightarrow 3x + 2y = \dfrac{9}{{0.05}} $
 $ \Rightarrow 180 $
On, solving equation $ 1 $ and $ 2 $ , we get $ y = 30 $
 $ \Rightarrow x + 2(30) = 100 $
 $ \Rightarrow x = 100 - 60 $ $ \Rightarrow 40 $
So, the correct answer is (C) $ 40,30 $ .

Additional Information:
The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. The mole may also be used to measure the amount of atoms, ions, electrons, or other entities. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance in mole per unit volume of solution, for which the unit typically used is moles per litre.

Note:
We can also calculate the atomic masses of $ X $ and $ Y $ by calculating the $ Y $ first. But this rearrangement will give us complicated equations. Do not forget to multiply the number of atoms of a particular element present in the compound, while calculating the molecular weight of the compound.