Question

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

Answer 1

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 $'a'g$ of P
Number of moles = $\dfrac{w}{M}$ 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 = $\dfrac{a}{{20}} \times {N_ \circ } = b$ (equation 1)
Now , number of atoms in Q = $\dfrac{{2a}}{{40}} \times {N_ \circ } = \dfrac{a}{{20}} \times {N_ \circ }$ (equation 2)

On substituting the value of $\dfrac{a}{{20}} \times {N_ \circ }$ from equation 1, we get
therefore , Number of atoms in $'2a'g$ 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 .