Simple Cubic Unit Cell Practice Problems

Which of the following is the type of packing depicted in the illustration below?

Assume that at 298 K and 789 mmHg pressure, 8.4634 g of an alkali metal completely reacts with gaseous halogen in a 0.750 L container. 12.9 kJ are released during the reaction (ΔH = −12.9 kJ). The end product, a binary ionic compound, crystallizes in a unit cell with cations aligned along each edge between anions and anions in a face-centered cubic arrangement. The edge length of the unit cell is 696 pm. Additionally, the cube's center contains a cation. Draw a detailed illustration of the unit cell from above, labeling the ions. Are the anions in contact with each other?

The Cr³⁺ ion can have a coordination number that ranges from 4- to 6-fold coordination. Predict the coordination number of Cr³⁺ in CrCl₃ assuming the chloride ions are two coordinate.

The Cr³⁺ ion can have a coordination number that ranges from 4- to 6-fold coordination. Predict the coordination number of Cr³⁺ in CrP assuming the phosphide ions are four coordinate.

Identify which unit cell below has the least dense packing of atoms: 

Consider the unit cell of a compound containing potassium, nitrogen and oxygen.: 

Identify the type of lattice structure.

Consider the unit cell of titanium(IV) oxide.

Identify the empirical formula.

Consider a primitive cubic lattice. If you pull the top straight up keeping all the angles at 90°, determine the primitive lattice that formed.

Identify the three-dimensional primitive lattice that satisfies the property below: 

Has an internal angle of 120°C and is equal on two dimensions. 

(i) tetragonal

(ii) rhombohedral 

(iii)  triclinic

(iv) orthorhombic

(v) hexagonal

(vi) monoclinic

Consider the transformation of the primitive cubic lattice below: 

The transformation consists of extending the length on one dimension and compressing it on another. What type of primitive lattice was formed? 

 Consider the the pack of golf balls in the image below

Identify the coordination number of this packing 

Determine the formula of a solid that crystallizes with the following arrangement (A = red; B = blue). 

For the following structure, determine the number of atoms per unit cell.

A hypothetical element has a radius of 156 pm, a molar mass of 196 g/mol, and a density of 10.7 g/cm³. Based on the information given, estimate the value of the Avogadro's number.

The diameter of a K atom is 235 pm Shown below are 2 different ways to pack the atoms.  

Identify which arrangement would lead to a greater density for K if the packing is extended to three dimensions.

The diameter of a K atom is 235 pm Shown below are 2 different ways to pack the atoms.  

How much has the number of atoms on the surface increased in going to arrangement 1 from arrangement 2?

For the simple cubic unit cell, identify each of the following: 

i. the number of atoms

ii. fraction of each atom in the cube

iii. Total number of atoms inside the cube