Question

Which has the maximum number of atoms?
A.\[24\] gram of \[C\]
B.56 grams of $Fe$ (56)
C.27 gram of $Al$ (27)
D.108 gram of $Ag$ (108)

Answer 1

Hint: We need to know and study the Avogadro’s number which defines the number of units in one mole of any substance. One mole of a substance is defined as the molecular weight of a substance in grams. It is a proportionality factor that is used to relate the number of constituent particles in a sample with the amount of substance in that sample. Its SI unit is the mole inverse and is equal to $6.02214076 \times {10^{23}}mo{l^{ - 1}}$ .

Complete step by step answer:
We know that one mole of a substance contains $6.02214076 \times {10^{23}}mo{l^{ - 1}}$ atoms. The number of moles of any substance is calculated by dividing the weight of the given substance with its atomic weight. Let us now calculate the number of moles of each of the given substances and calculate the number of atoms accordingly.
 \[24\] gram of \[C\] : The Atomic weight of $C$ is $12$ grams per mole. Therefore, the number of moles in 24 grams of $C$ is $\dfrac{{24}}{{12}} = 2moles$
Therefore, the number of atoms in 2 moles of C = $6.02214076 \times {10^{23}} \times 2$ number of atoms.
56 grams of $Fe$ (56): The atomic weight of $Fe$ is 56 grams per mole. Therefore, the number of moles in 56 grams of $Fe$ will be 1.
Therefore, the number of atoms in 1 mole of $Fe$= number of atoms.
27 gram of $Al$ (27): The atomic weight of $Al$ is 27 grams per mole. Therefore, the number of moles in 27 grams of $Al$ will be 1.
Therefore, the number of atoms in 1 mole of $Al$ = number of atoms.
108 gram of $Ag$ (108): The atomic weight of $Ag$ is 108 grams per mole. Therefore, the number of moles in 108 grams of $Ag$ will be 1.
Therefore, the number of atoms in 1 mole of $Ag$= number of atoms.
Hence, the maximum number of atoms is present in \[24\] gram of \[C\] .
Hence the correct option is option (A).

Note:
It must be noted that the Avogadro’s number is calculated based on the charge of electrons. The charge on an electron based on modern experiments is estimated to be \[1.60217653 \times {10^{ - 19}}coulombs\] per electron. Dividing the charge on a mole of electrons by the charge on a single electron the Avogadro's number of \[6.02214154 \times {10^{23}}\] particles per mole is obtained.