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

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.