The molar volume of a certain form of solid lead is 18 cm 3 /mol. Assuming cubic closest-packed structure, determine the following.
-The radius of a Pb atom
A) 1740 pm
B) 17.4 pm
C) 174 pm
D) 1.74 pm
E) none of these

Question

Quizplus · Accepted Answer

The molar volume of a substance is the volume occupied by one mole of it. For a cubic closest-packed (ccp) structure, the volume can be related to the atomic radius using the formula for the volume of a cube and considering the geometric arrangement of atoms. In a ccp structure, the atoms are arranged in such a way that the edge length of the unit cell is $2\sqrt{2}r$, where $r$ is the atomic radius. The volume of the unit cell can thus be expressed as $(2\sqrt{2}r)^3$. Given the molar volume (18 cm³/mol) and knowing that there are four atoms per unit cell in a ccp structure, we can solve for $r$. Rearranging the formula to solve for $r$ and converting units appropriately gives a radius in the ballpark of 174 pm.

The Molar Volume of a Certain Form of Solid Lead