One mole of germanium has a volume of 13.6 cm3.Using X-ray diffraction,each germanium atom is found to have a cubic volume 0.284 nm on a side.Calculate the experimental value for Avogadro's number (N).

Question

Quizplus · Accepted Answer

- First, we need to convert the volume of one mole of germanium from cm3 to nm3. 
- 1 cm = 10-7 nm, so 1 cm3 = (10-7 nm)3 = 10-21 nm3. 
- Therefore, 13.6 cm3 = 13.6 x 10-21 nm3. 
- Now we can calculate the number of cubic volumes (0.284 nm on a side) in one mole of germanium:

Number of cubic volumes = (13.6 x 10-21 nm3) / (0.284 nm)3 
= 1.204 x 1023

- Each cubic volume corresponds to one germanium atom, so the number of atoms in one mole of germanium is also 1.204 x 1023. 
- Finally, we can calculate Avogadro's number by dividing the number of atoms in one mole by the definition of a mole (6.022 x 1023 atoms/mol):

N = (1.204 x 1023) / 6.022 x 1023 = 1.999 ≈ 2.09 x 1023.

The best choice is D because it is closest to the calculated value of 2.09 x 1023.

One Mole of Germanium Has a Volume of 13