Question

The number of molecules present in $ 8 $ grams of oxygen are
(A) $ 6.022 \times {10^{23}} $
(B) $ 3.011 \times {10^{23}} $
(C) $ 12.044 \times {10^{23}} $
(D) $ 1.55 \times {10^{23}} $

Answer 1

Hint: One mole of any compound contains approximately $ 6.022 \times {10^{23}} $ particles. This number is called the Avogadro number expressed by $ {N_A} $ and was discovered by the famous scientist Amedeo Avogadro.

Complete step by step solution:
As in the question we are given the mass.
Mass of oxygen = $ 8g $
Molecular mass of oxygen ( $ {O_2} $ ) = $ 2 \times 16 $ $ \dfrac{g}{{gmol}} $ = $ 32\dfrac{g}{{gmol}} $
Therefore, number of moles = $ \dfrac{{8g}}{{16g}} \times gmol = 0.5gmol $
Now we found the number of moles of oxygen. As one mole of any compound contains $ 6.022 \times {10^{23}} $ particles or molecules so in order to find the total number of molecules present in $ 0.5g mol $ of oxygen, we need to multiply the number of moles calculated by Avogadro number ( $ {N_A} $ ).
Number of molecules = number of moles × Avogadro number ( $ {N_A} $ )
= $ 0.5gmol \times \dfrac{{6.022 \times {{10}^{23}}}}{{gmol}} = 3.011 \times {10^{23}} $
So according to the above explanation, the correct answer of the question is option (B): $ 3.011 \times {10^{23}} $ .

Note:
The mole is the unit of measurement for the amount of substance in the international system of units. A mole of a substance or a mole of particles is defined as containing approximately $ 6.022 \times {10^{23}} $ particles which may be atoms, molecules, ions, or electrons. The reason why this is called a basic unit is because once we find the total number of moles of any substance, we can find the number of molecules, no of atoms, volume occupied by that substance at STP (standard conditions of temperature and pressure) etc.

Note:
If we are asked to find the total number of molecules in any compound, we can simply proceed by finding the total number of moles in the given compound and then multiplying it by the Avogadro number whose value is $ 6.022 \times {10^{23}} $ . Always be careful regarding the units and avoid calculation mistakes.