Question

Two bulbs A and B contain 16g of \[{{O}_{2}}\]and 16g of\[{{O}_{3}}\]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

Answer 1

Hint: The formula for calculating the number of moles of a gas is given by:
\[no.ofmoles=\dfrac{GivenMass}{MolarMass}\]. The number of moles gives us the amount of substance present in a vessel.
1 mole of a substance= molar mass of the substance= \[6.023\times {{10}^{23}}\]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 \[{{O}_{2}}\]
Given mass of \[{{O}_{2}}\]=16g
Molar mass of \[{{O}_{2}}\]=32g
Using the formula for number of moles:
\[no.ofmoles=\dfrac{GivenMass}{MolarMass}\]
\[no.ofmole{{s}_{{{O}_{2}}}}=\dfrac{16}{32}=\dfrac{1}{2}\]
Now, will calculate the number of molecules of \[{{O}_{2}}\] in terms of Avogadro number
1 mole of \[{{O}_{2}}\]..= \[{{N}_{a}}\]number of molecules of \[{{O}_{2}}\]
Therefore, \[\dfrac{1}{2}\]moles of \[{{O}_{2}}\]= \[\dfrac{1}{2}\]\[{{N}_{a}}\] number of molecules of \[{{O}_{2}}\]
-Now, we will do the calculations for \[{{O}_{3}}\] molecules
\[\to \]First we will calculate the number of moles of \[{{O}_{3}}\]
Given mass of \[{{O}_{3}}\]=16g
Molar mass of \[{{O}_{3}}\]=48g
Using the formula for number of moles:
\[no.ofmoles=\dfrac{GivenMass}{MolarMass}\]
\[no.ofmole{{s}_{{{O}_{3}}}}=\dfrac{16}{48}=\dfrac{1}{3}\]
\[\to \]Now, will calculate the number of molecules of \[{{O}_{3}}\].in terms of Avogadro number
1 mole of \[{{O}_{3}}\]= \[{{N}_{a}}\].number of molecules of \[{{O}_{3}}\]
Therefore, \[\dfrac{1}{3}\] moles of \[{{O}_{3}}\]= \[\dfrac{1}{3}\]\[{{N}_{a}}\] number of molecules of \[{{O}_{3}}\]
Hence, from the above calculations we find that both bulbs contain different numbers of atoms.
Also, Bulb A contains\[\dfrac{1}{2}\].\[{{N}_{a}}\] 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.