Molar Volume of Sodium
If you assume that an atom is a hard sphere, you can estimate the average volume of space it occupies using basic geometry.
Question
Estimate the volume, V , of a sodium atom ( Na ) using its metallic radius of 186
The molar mass of Na is 22.99g
The density of solid sodium is 0.97g/cm^3
(22.99g/mol) / (0.97g/cm^3) = _____________
What are the units of the above value?
To estimate the volume of a sodium atom (Na) using its metallic radius, we can assume that the atom is a sphere. The metallic radius is given as 186 pm (picometers), which is equal to 186 x 10^-12 meters.
The formula to calculate the volume of a sphere is:
V = (4/3) * π * r^3,
where V is the volume and r is the radius.
So, to estimate the volume of the sodium atom, we can substitute the metallic radius (r = 186 pm) into the formula:
V = (4/3) * π * (186 x 10^-12 meters)^3.
Now, let's calculate the volume:
V = (4/3) * 3.1415 * (186 x 10^-12 meters)^3
≈ 4.1907 x 10^-30 cubic meters.
Therefore, the estimated volume of a sodium atom is approximately 4.1907 x 10^-30 cubic meters.