Question

How many atoms are present in $ 49\,g $ of $ {H_2}S{O_4} $ ?
A. $ 7 \times 6.023 \times {10^{23}} $
B. $ 5 \times 6.023 \times {10^{23}} $
C. $ 6 \times 6.023 \times {10^{23}} $
D. $ 7 \times 3.02 \times {10^{23}} $

Answer 1

Hint: In the given, we need to find the number of atoms in $ 49\,g $ of $ {H_2}S{O_4} $ . For this, we should know the molecular weight of $ {H_2}S{O_4} $ in order to calculate the number of moles of $ {H_2}S{O_4} $ . Then , after this we calculate the number of atoms by using the Avogadro number represented as $ {N_A} $ .

Complete Step By Step Answer:
Let us understand the answer in complete detail.
Here, we are given the weight of $ {H_2}S{O_4} $ i.e. $ 49\,g $
First, we will calculate the molecular weight or we can say molar mass of $ {H_2}S{O_4} $
Molar mass of $ {H_2}S{O_4} $ = $ (1 \times 2)\, + 32 + (16 \times 4) $
Molar mass of $ {H_2}S{O_4} $ = $ 2\, + 32 + 64 $
Molar mass of $ {H_2}S{O_4} $ = $ 98\,g/mol $
We know that,
Number of moles = $ \dfrac{{Given\,\,weight\,(g)}}{{Molar\,\,mass(g/mol)}} $
Number of moles of $ {H_2}S{O_4} $ = $ \dfrac{{49}}{{98}} $
Number of moles of $ {H_2}S{O_4} $ = $ 0.5\,mol $
After this,
We know that one mole is the amount of that of the substance which contains $ 6.023 \times {10^{23}} $ particles. These particles can be atoms, ions or molecules. This $ 6.023 \times {10^{23}} $ number is also called Avogadro number.
  $ 1 $ mol of $ {H_2}S{O_4} $ contains $ 6.023 \times {10^{23}} $ atoms.
 $ 0.5 $ mol of $ {H_2}S{O_4} $ contains $ 0.5 \times 6.023 \times {10^{23}} $
 $ 0.5 $ mol of $ {H_2}S{O_4} $ contains $ 3.01 \times {10^{23}} $
Also, the number of atoms in $ {H_2}S{O_4} $ is $ 7 $
The number of atoms in $ 49\,g $ or $ 0.5\,mol $ of $ {H_2}S{O_4} $ is $ 7 \times 3.01 \times {10^{23}} $
Therefore, the number of atoms in $ 49\,g $ of $ {H_2}S{O_4} $ is $ 7 \times 3.01 \times {10^{23}} $
Hence, the correct answer is option (D).

Note:
It must be remembered that the concept of Avogadro’s number is the same as dozens or gross to denote a particular amount or quantity. The number of entities present in one mole is equal to the Avogadro number i.e. $ 6.023 \times {10^{23}} $ . This can be atoms, particles, ions or molecules. The Avogadro number is useful in the calculation of substances which contain a large number of atoms and molecules.