VerifiedHint: Let's convert the volume of a hydrogen atom from angstroms to meters using the given conversion factor, and then multiply that volume by the number of atoms in a mole. Then use the formula for the volume of a sphere $V = \dfrac{4}{3}\pi r^3$ to calculate the volume of a hydrogen atom.
Solution:
Equation
$V = \dfrac{4}{3}\pi r^3$
where:
V is the volume of the hydrogen atom
r is the radius of the hydrogen atom
To calculate the total atomic volume of a mole of hydrogen atoms, we first need to determine the volume of a single hydrogen atom and then multiply it by Avogadro's number.
The volume of a single hydrogen atom can be calculated using the formula for the volume of a sphere:
$V = \dfrac{4}{3}\pi r^3$
Substituting the given value of
r (0.5 Å), we get:
$V = \dfrac{4}{3}\pi (0.5 \times 10^{-10} \text{ m})^3$
$V = 1.25 \times 10^{-23} \text{ m}^3$
To calculate the total atomic volume of a mole of hydrogen atoms, we multiply the volume of a single atom by Avogadro's number (6.022 × 10²³ atoms/mole):
$\text{Total Volume} = V \times N$
$\text{Total Volume} = 1.25 \times 10^{-23} \text{ m}^3/\text{atom} \times 6.022 \times 10^{23} \text{ atoms}/\text{mole}$
$\text{Total Volume} = 3.157 \times 10^{-7} \text{ m}^3/\text{mole}$
Answer
The total atomic volume of a mole of hydrogen atoms is approximately 3.157 × 10⁻⁷ m³. Rounding off the value of 3.157 × 10⁻⁷ m³ to two decimal places gives us 3.16 × 10⁻⁷ m³.
Note
This is just a simplified solution to the problem. In reality, the calculation of atomic volume is more complex, as it takes into account the packing arrangement of atoms in a solid.
