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# Which of the following has the largest number of atoms?A.$4g{\text{ of }}{{\text{H}}_2}$B.$16g{\text{ of }}{{\text{O}}_2}$C.$28g{\text{ of }}{{\text{N}}_2}$D.$18g{\text{ of }}{{\text{H}}_2}O$

Last updated date: 13th Jun 2024
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Hint:
To solve this question, we must use the mole concept. First, we calculate the number of moles and then we can apply the mole concept. We must also know the concept of molecular mass to solve this question which is the sum of the atomic masses of all its constituent elements. Remember that the value of Avogadro number is given $6.02 \times {10^{23}}$ .

Complete step-by-step answer:We know, one mole of a substance contains $6.02 \times {10^{23}}$atoms.
We also know that, number of moles $= \dfrac{m}{\ MM \\ \\ \ }$ where, m is the given mass and MM represents molar mass.
Therefore, first we need to calculate the number of moles present in $4g{\text{ of }}{{\text{H}}_2}$.
Hence, the number of moles of ${H_2} = \dfrac{4}{2} = 2$moles of ${H_2}$. Since $1$ mole of ${H_2}$ $= 6.02 \times {10^{23}}$ ${H_2}$ atoms.
Therefore, $2$ moles of ${H_2}$ will contain $2 \times 6.02 \times {10^{23}} = 12.04 \times {10^{23}}$atoms.
Similarly, number of moles in $16g{\text{ }}of{\text{ }}{O_2}$ $= \dfrac{{16}}{{32}} = 0.5$moles.
$0.5$ moles of ${O_2}$ will contain = $0.5 \times 6.02 \times {10^{23}}$$= 3.01 \times {10^{23}}$atoms
Now, number of moles in $28{\text{ }}g{\text{ }}of{\text{ }}{N_2} =$ $\dfrac{{28}}{{28}} = 1$mole of N2. We know that $1$ mole of ${N_2}$ contains $6.02 \times {10^{23}}$atoms.
Lastly, number of moles in$18{\text{ }}g{\text{ }}of{\text{ }}{H_2}O{\text{ }} = {\text{ }}1$. Hence, the number of atoms in $18{\text{ }}g{\text{ }}of{\text{ }}{H_2}O{\text{ }}$ $= 6.02 \times {10^{23}}$atoms of H2O.
Therefore, we can conclude that the largest number of atoms is present in $4g{\text{ of }}{{\text{H}}_2}$ . It contains $12.04 \times {10^{^{23}}}$atoms. Rest all options contain less number of atoms.

Hence, option A is the correct option.

Note: You should be aware about the relationship between no. of moles, molar mass, and atoms of any given substance in order to solve this question. The relationship can be summarized as-
Molar mass of any substance is one mole of that substance which is the Avogadro constant $= 6.02 \times {10^{23}}$atoms or ions or molecules.