Calculating the Number of Atoms in Potassium

How can we determine the number of atoms per nm3 in potassium?

Given the density of K as 0.89 and its atomic weight as 39.098 g/mol, what steps do we need to take to calculate the number of atoms per nm3?

Calculating the Number of Atoms in Potassium

Final answer: To calculate the number of atoms per nm3 in potassium, one must convert the given density to the correct units, find the number of moles based on density and atomic weight, and then use Avogadro's number to determine the number of atoms.

When determining the number of atoms per nm3 in potassium, it is essential to follow a specific set of steps to arrive at the correct answer. First, we need to convert the given density to the appropriate units, calculate the number of moles based on the density and atomic weight, and finally use Avogadro's number to find the number of atoms.

Given that the density of potassium is 0.89 g/cm3, the first step is to convert this value to g/nm3. Since there are 1e21 nm3 in 1 cm3, the density becomes 0.89 x 1e21 g/nm3. This conversion allows us to work with the correct units for the subsequent calculations.

Next, we utilize the atomic weight of potassium, which is 39.098 g/mol, to determine the number of moles in 1 nm3. To calculate the number of moles, we divide the mass (0.89 x 1e21 g/nm3) by the molar mass (39.098 g/mol). This step gives us the quantity of potassium in moles within 1 nm3.

Finally, to find the number of atoms per nm3, we multiply the number of moles by Avogadro's number, which is approximately 6.022 x 10^23 atoms/mol. This calculation yields the final result of the number of atoms in potassium within 1 nm3.