Question

Number of oxygen atoms in 8g of ozone is:
(A) $6.022 \times {10^{23}}$
(B) $6.022 \times \dfrac{{{{10}^{23}}}}{2}$
(C) $6.022 \times \dfrac{{{{10}^{23}}}}{3}$
(D) $6.022 \times \dfrac{{{{10}^{23}}}}{6}$

Answer 1

Hint: Ozone is made up of ordinary oxygen. The only difference is that ozone is made up of three oxygen atoms, while the stuff we breathe is made up of only two oxygen atoms. Solar rays high in the atmosphere convert oxygen into ozone. In the upper atmosphere, UV rays from the Sun break a normal oxygen molecule into two separate oxygen atoms. Another oxygen molecule then picks up one of these atoms and forms an ozone molecule.

Complete step by step solution:
The total number of atoms in any element is defined in terms of Avogadro’s number. You might be thinking that what is Avogadro number so let’s check it out first.
Avogadro’s number is defined as the number of units in one mole of any substance (defined as its molecular weight in grams)is equal to $6.022 \times {10^{23}}$. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound (in grams) is numerically equal to the average mass of one molecule of the compound, in Daltons.
Now, you might be thinking about what Daltons are. Let’s check it out.
Daltons is a universal atomic mass unit. One Dalton being twelfth of the mass of one carbon-12 (an isotope of carbon which contains 12 protons or neutrons) atom, which is approximately the mass of one nucleon (proton or neutron). Twelve grams of carbon-12 contains one mole of carbon atoms.
Let’s check an example then you will be clearer about it.
The average mass of one molecule of water is approximately 18 Daltons, and one mole of water (N molecules) is approximately 18 grams. Thus, the Avogadro constant is the proportionality factor that relates the molar mass of a substance to the average mass of one molecule of the same substance.
Now, since the concept of Avogadro’s number is clear. Let’s get back to our question.
Molar mass of ozone = 3 x molar mass of 1 oxygen atom = 48 grams
Number of moles in 48 grams of ozone = 1
Number of moles in 8 grams of ozone =$\dfrac{8}{{48}} = \dfrac{1}{6}$
So, the number of moles of oxygen atom is 3 times the number of moles of ozone because each ozone molecule contains 3 oxygen atoms. Therefore, the number of moles in 8g of ozone can be calculated as follows:
$N = 3 \times \dfrac{1}{6} = \dfrac{1}{2}$
So, number of atoms (n) can be calculated by multiplying number of moles by Avogadro’s number as:
$n = 6.022 \times {10^{23}} \times \dfrac{1}{2}$

So, the correct answer is (B).

Note: Remember that if two different compounds have the same Avogadro’s number, it only means that only their number of molecules are same nothing else and it will contain the same number of atoms from which that compound is made of in the same molecular ratio.