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Question: Which of the following has a maximum number of atoms? A)\(24\,g\,C\left( {12} \right)\) B)\(56\,...

Which of the following has a maximum number of atoms?
A)24gC(12)24\,g\,C\left( {12} \right)
B)56gFe(56)56\,g\,Fe\left( {56} \right)
C)27gAl(27)27\,g\,Al\left( {27} \right)
D)108gAg(108)108\,g\,Ag\left( {108} \right)

Explanation

Solution

We know that Avogadro’s number is the number of atoms in one mole of any substance. The units of Avogadro’s number are electrons, atoms, ions, or molecules depending on the nature of the substance.
1mole = 6.022 \times1023unit{\text{1}}\,{\text{mole = 6}}{\text{.022 \times 1}}{{\text{0}}^{{\text{23}}}}\,{\text{unit}}

Complete step by step answer:
We know that Avogadro’s number is the number of atoms in one mole of any substance. The units of Avogadro’s number are electrons, atoms, ions, or molecules depending on the nature of the substance.
1mole = 6.022 \times1023unit{\text{1}}\,{\text{mole = 6}}{\text{.022 \times 1}}{{\text{0}}^{{\text{23}}}}\,{\text{unit}}
Complete step by step answer:
We know that,
The atomic mass of the substance is the sum of protons or electrons in an atom. For example, the atomic mass of carbon is 6 which means the number of electrons is six.
The number of atoms in carbon can be calculated as,
The molar mass of carbon is 12g/mol.12\,g/mol.
The mass of carbon is 24g.24\,g.
The Avogadro’s number is 6.022×1023atoms.6.022 \times {10^{23}}\,atoms.
Now we can be calculate the number of atoms in 24g24\,g of carbon as,
24g×(6.022×1023atoms12g)=12.04×1023atoms24\,g \times \left( {\dfrac{{6.022 \times {{10}^{23}}\,atoms}}{{12\,g}}} \right) = 12.04 \times {10^{23}}\,atoms
The number of atoms in 24g24\,g of carbon is 12.04×1023 atoms.12.04 \times {10^{23}}{\text{ }}atoms.
Let us calculate the number of atoms in iron.
The molar mass of Iron is 56g/mol.56\,g/mol.
The mass of Iron is 56g.56\,g.
The Avogadro’s number is 6.022×1023atoms.6.022 \times {10^{23}}\,atoms.
The number of atoms in 56g56\,g of Iron can be calculated as,
56g×(6.022×1023atoms56g)=6.022×1023atoms56\,g \times \left( {\dfrac{{6.022 \times {{10}^{23}}\,atoms}}{{56\,g}}} \right) = 6.022 \times {10^{23}}\,atoms
The number of atoms in 56g56\,g of Iron is 6.022×1023atoms6.022 \times {10^{23}}\,atoms
Let us calculate the number of atoms in Aluminium.
The molar mass of Aluminium is 27g/mol.27\,g/mol.
The mass of Aluminium is 27g.27\,g.
The Avogadro’s number is 6.022×1023atoms.6.022 \times {10^{23}}\,atoms.
The number of atoms in 27g27\,g of Aluminium can be calculated as,
27g×(6.022×1023atoms27g)=6.022×1023atoms27\,g\, \times \left( {\dfrac{{6.022 \times {{10}^{23}}\,atoms}}{{27\,g}}} \right) = 6.022 \times {10^{23}}\,atoms
The number of atoms in 27g27\,g of Aluminium is 6.022×1023atoms6.022 \times {10^{23}}\,atoms
Let us calculate the number of atoms in Silver.
The molar mass of Silver is 108g/mol.108\,g/mol.
The mass of Silver is 108g.108\,g.
The Avogadro’s number is 6.022×1023atoms.6.022 \times {10^{23}}\,atoms.
The number of atoms in 108g108\,g of Silver can be calculated as,
108g×(6.022×1023atoms108g)=6.022×1023atoms108\,g\, \times \left( {\dfrac{{6.022 \times {{10}^{23}}\,atoms}}{{108\,g}}} \right) = 6.022 \times {10^{23}}\,atoms
The number of atoms in 108g108\,g of Silver is 6.022×1023atoms6.022 \times {10^{23}}\,atoms
Thus, carbon has a maximum number of atoms.

So, the correct answer is Option A .

Note:
We can find the elements with the maximum number of atoms can also be found by calculating the number of moles. We know that, number of moles of an element and the number of atoms are directly proportional.
The number of moles can be calculated using the formula,
Moles=MassMolecularMassMoles = \dfrac{{Mass}}{{Molecular\,Mass}}