Question

The atomic masses of two elements P and Q are 20 and 40 respectively . If ${}^{\prime }{a}^{\prime }g$ of P contains ${}^{\prime }{b}^{\prime }$ atoms , how many atoms are present in ${}^{\prime }2a^{\prime }g$ of Q .
A.a
B.b
C.2a
D.2b

Answer 1

Hint:According to Avogadro's hypothesis equal volumes of all gases under similar conditions of temperature and pressure contain equal numbers of atoms or molecules.

Complete step by step answer:
The given masses of P and Q are 20 and 40 respectively.
Let us first take out the number of moles in ${}^{\prime }{a}^{\prime }g$ of P
Number of moles = ${\displaystyle \frac{w}{M}}$ where w = given mass and M = molecular mass
Number of atoms = $N_{\circ }\times moles$ where $N_{\circ }=$ Avogadro's number

In case of P number of atoms = ${\displaystyle \frac{a}{20}}\times N_{\circ }=b$ (equation 1)
Now , number of atoms in Q = ${\displaystyle \frac{2a}{40}}\times N_{\circ }={\displaystyle \frac{a}{20}}\times N_{\circ }$ (equation 2)

On substituting the value of ${\displaystyle \frac{a}{20}}\times N_{\circ }$ from equation 1, we get
therefore , Number of atoms in ${}^{\prime }2a^{\prime }g$ of Q = b

Therefore option B is correct.

Additional information :
Avogadro's number and mole concept help in the chemical calculation in a number of ways are as follows:-
In the calculation of the actual mass of a single atom of an element or a single molecule of a substance.
In the calculation of the number of atoms or molecules in a given mass of the element or compound.
In the calculation of the number of molecules present in a given volume of gas under given conditions.
In the calculation of size of the individual atoms molecules assuming them to be spherical.


Note: When we look at the question we would think that Q contains double the number of atoms of what P contains but we should be careful and first find out the number of moles in both elements and then find the number of atoms .