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Question: Two bulbs A and B contain 16g of \[{{O}_{2}}\]and 16g of\[{{O}_{3}}\]respectively. Which of the foll...

Two bulbs A and B contain 16g of O2{{O}_{2}}and 16g ofO3{{O}_{3}}respectively. Which of the following statements are true?
(A)- Both bulbs contain same number of atoms
(B)- Both bulbs contain different number of atoms
(C)- Both bulbs contain same number of molecules
(D)- Bulb A contains\dfrac{1}{2}$$$${{N}_{a}} number of molecules while bulb B contains \dfrac{1}{3}$$$${{N}_{a}} number of molecules

Explanation

Solution

Hint: The formula for calculating the number of moles of a gas is given by:
no.ofmoles=GivenMassMolarMassno.ofmoles=\dfrac{GivenMass}{MolarMass}. The number of moles gives us the amount of substance present in a vessel.
1 mole of a substance= molar mass of the substance= 6.023×10236.023\times {{10}^{23}}number of atoms or molecules of the substance present.

Complete answer:
Let’s look at the solution:
First we will calculate the number of moles of O2{{O}_{2}}
Given mass of O2{{O}_{2}}=16g
Molar mass of O2{{O}_{2}}=32g
Using the formula for number of moles:
no.ofmoles=GivenMassMolarMassno.ofmoles=\dfrac{GivenMass}{MolarMass}
no.ofmolesO2=1632=12no.ofmole{{s}_{{{O}_{2}}}}=\dfrac{16}{32}=\dfrac{1}{2}
Now, will calculate the number of molecules of O2{{O}_{2}} in terms of Avogadro number
1 mole of O2{{O}_{2}}..= Na{{N}_{a}}number of molecules of O2{{O}_{2}}
Therefore, 12\dfrac{1}{2}moles of O2{{O}_{2}}= \dfrac{1}{2}$$$${{N}_{a}} number of molecules of O2{{O}_{2}}
-Now, we will do the calculations for O3{{O}_{3}} molecules
→\to First we will calculate the number of moles of O3{{O}_{3}}
Given mass of O3{{O}_{3}}=16g
Molar mass of O3{{O}_{3}}=48g
Using the formula for number of moles:
no.ofmoles=GivenMassMolarMassno.ofmoles=\dfrac{GivenMass}{MolarMass}
no.ofmolesO3=1648=13no.ofmole{{s}_{{{O}_{3}}}}=\dfrac{16}{48}=\dfrac{1}{3}
→\to Now, will calculate the number of molecules of O3{{O}_{3}}.in terms of Avogadro number
1 mole of O3{{O}_{3}}= Na{{N}_{a}}.number of molecules of O3{{O}_{3}}
Therefore, 13\dfrac{1}{3} moles of O3{{O}_{3}}= \dfrac{1}{3}$$$${{N}_{a}} number of molecules of O3{{O}_{3}}
Hence, from the above calculations we find that both bulbs contain different numbers of atoms.
Also, Bulb A contains12\dfrac{1}{2}.Na{{N}_{a}} number of molecules while bulb B contains \dfrac{1}{3}$$$${{N}_{a}} number of molecules.
So, option (B) and (D) are the correct answer for the above question.

Note:
Avogadro number is a constant and it relates the number of constituent particles in a sample to the amount of the sample present. Avogadro law states that at constant temperature and pressure, the volume of a gas is proportional to the amount of the gas.