We need to calculate the total volume of one mole of hydrogen atoms given their approximate atomic radius.
Concept: Sphere
The volume of an individual atom is calculated by modeling it as a sphere. To find the total volume of a mole of atoms, the volume of a single atom is multiplied by Avogadro's number (NA).
V=34πr3
Vtotal=NA⋅V
Given:
- Radius of a hydrogen atom: r=0.5A˚=0.5×10−10m
- Avogadro's number: NA=6.022×1023mol−1
Solving:
- First, determine the volume of a single hydrogen atom (Vatom) in cubic meters:
Vatom=34πr3=34⋅π⋅(0.5×10−10m)3=34⋅π⋅(0.125×10−30m3)≈5.23598×10−31m3
- Next, calculate the total atomic volume (Vtotal) for one mole of these atoms:
Vtotal=NA⋅Vatom=(6.022×1023mol−1)⋅(5.23598×10−31m3)=3.15311×10−7m3
Answer
3.15×10−7m3