Question

A metal M of atomic mass 54.94 has a density of 7.42 g/cc. Calculate the apparent volume occupied by one atom of the metal.

Answer 1

Hint: The volume of one mole of the metal is calculated by the mass of the metal to the density of the metal. For calculating the volume of one atom, divide the volume of one mole of the metal to the Avogadro’s number.

Complete answer:
The volume of the compound or a substance is calculated by dividing the mass of the compound or substance to the density of the compound or substance.
In the question, the mass of the metal M is 54.94
And the density of the metal is given \[7.42\text{ }g/cc\]
So, we have to calculate the apparent volume occupied by one atom.
The volume of one mole of the metal can be calculated by dividing the given mass to the given volume.
$\text{Volume = }\dfrac{\text{mass}}{\text{density}}\text{ = }\dfrac{\text{54}\text{.94}}{7.42}\text{ = 7}\text{.40c}{{\text{m}}^{3}}$
So, the volume of one mole of the metal is $7.40\text{ c}{{\text{m}}^{3}}$
For calculating the volume occupied by one atom of the metal we have to divide the volume of one mole of the metal to the avogadro’s number.
$\text{Volume of one atom = }\dfrac{\text{Volume of one mole}}{\text{Avogadro }\!\!'\!\!\text{ s number}}$
Avogadro’s number may be defined as the number of atoms present in one gram atom or one mole of the element, or the number of molecules present in one gram molecule or one mole molecule of the substance. The value of Avogadro’s number is $6.022\text{ x 1}{{\text{0}}^{23}}$
$Avogadro's\ number\text{ (}{{\text{N}}_{A}}\text{) = 6}\text{.022 x 1}{{\text{0}}^{23}}$
So, the value of volume of one atom is,
$\text{Volume of one atom = }\dfrac{\text{Volume of one mole}}{\text{Avogadro }\!\!'\!\!\text{ s number}}=\dfrac{7.40}{6.022\text{ x 1}{{\text{0}}^{23}}}=1.23\text{ x 1}{{\text{0}}^{-23}}c{{m}^{3}}$
So, the volume of one atom of the molecule is $1.23\text{ x 1}{{\text{0}}^{-23}}c{{m}^{3}}$.

Note:
You may get confused that $7.40\text{ c}{{\text{m}}^{3}}$is the volume of one atom, but it is the value of one mole. That's why it is divided with Avogadro's number. For example, one mole of hydrogen have $6.022\text{ x 1}{{\text{0}}^{23}}$ atoms of hydrogen whereas one mole of hydrogen molecule will have $\text{2 x }6.022\text{ x 1}{{\text{0}}^{23}}$ because each hydrogen molecule contains 2 atoms of hydrogen.