Question

Calculate the number of iron atoms in a piece of iron weighing $\text{ 2}\text{.8 g }$.(Atomic mass of iron = 56)
A) $\text{ 30}\text{.11 }\times \text{1}{{\text{0}}^{\text{23}}}\text{ }$atoms
B) $\text{ 3}\text{.11 }\times \text{1}{{\text{0}}^{\text{23}}}\text{ }$atoms
C) $\text{ 3}\text{.0115 }\times \text{1}{{\text{0}}^{\text{22}}}\text{ }$atoms
D) $\text{ 301}\text{.1 }\times \text{1}{{\text{0}}^{\text{23}}}\text{ }$atoms

Answer 1

Avogadro's number is the total number of elementary particles like a molecule, atoms, ions, etc. in the 1 mole of a substance. Avogadro's number is equal to $\text{ 6}\text{.023 }\times \text{1}{{\text{0}}^{\text{23}}}\text{ }$ particles. The one mole of a substance is equal to the molecular weight of the substance. It is given as,
$\text{ mole of substance = }\dfrac{\text{weight }}{\text{molar mass}}\text{ = }\dfrac{\text{m}}{\text{M}}\text{ }$

Complete step by step answer:
We are given that, The weight of iron given is $\text{ 2}\text{.8 g }$
The atomic mass of iron is equal to 56. We are interested in determining the number of iron atoms in the given weight. To solve this question we should first know the concept of Avogadro's number. Avogadro's number relates the molar mass of a substance. It is defined as the total number of elementary particles like molecules, atoms, compounds, ions, etc. present per mole of the substance. According to which, the Avogadro's number is equal to the 1 mole of a substance. The relation is stated as follows,
$\text{ Avagadro }\\!\\!'\\!\\!\text{ s no}\text{. (}{{\text{N}}_{\text{A}}}\text{) = 1 mole of substance }$ (1)
The mole is the amount of the substance is defined as the ratio of the weight of a substance to the molar mass of the substance. Then the mole is written as,
$\text{ 1mole of substance = }\dfrac{\text{weight }}{\text{Molar mass}}\text{ = }\dfrac{\text{m}}{\text{M}}\text{ }$ (2)
Now from relation (1) and (2), Avogadro's number is equal to the ratio of the weight of a substance to the molar mass. $\text{ Avagadro }\\!\\!'\\!\\!\text{ s no}\text{. (}{{\text{N}}_{\text{A}}}\text{) = 1 mole of substance = }\dfrac{\text{m}}{\text{M}}\text{ }$
Thus, the number of moles of iron present in the $\text{ 2}\text{.8 g }$ sample is equal to,
$\text{ mole of substance = }\dfrac{\text{weight of iron }}{\text{Molar mass of iron}}\text{ = }\dfrac{2.8}{56}\text{ = 0}\text{.05 mole }$
Therefore, $\text{ 2}\text{.8 g }$ the iron sample contains $\text{ 0}\text{.05 }$ moles in it.
We know that one mole of a substance contains the $\text{ 6}\text{.023 }\times \text{1}{{\text{0}}^{\text{23}}}\text{ }$ particles .i.e.$\text{ 1 mole = 6}\text{.023 }\times \text{1}{{\text{0}}^{\text{23}}}\text{ atoms }$
Then the total number of atoms of iron in the $\text{ 0}\text{.05 }$moles is,
$\text{ No}\text{. of iron atoms = }\dfrac{5\times 6.023\times {{10}^{23}}}{1}\text{atoms = 3}\text{.0115}\times \text{1}{{\text{0}}^{\text{22}}}\text{ atoms }$
Thus, $\text{ 2}\text{.8 g }$of the iron sample contains the $\text{3}\text{.0115}\times \text{1}{{\text{0}}^{\text{22}}}$ atoms.

Hence, (C) is the correct option.

Note: remember a simple relation. if I want to convert the moles into the atom, multiply the molar mass the Avogadro's number and to convert the atoms to the moles then divide the amount by Avogadro's number or multiply by the reciprocal of Avogadro's number.