Question

An oxide of niobium has a cubic unit cell in which there are oxide ions at the middle of each edge and niobum atoms at the center of each face. what is the empirical formula of this oxide?

Answer 1

The empirical formula for the niobium oxide with oxide ions at the middle of each edge and niobium atoms at the center of each face is Nb2O, obtained by counting the ions per unit cell and adjusting for their location in the structure.

Step-by-step explanation:

To determine the empirical formula of the niobium oxide, first, we need to consider how many ions are associated with each other in the cubic unit cell structure. A cubic unit cell with oxide ions at the middle of each edge and niobium atoms at the center of each face can be described as follows: each edge has 1/4 of an oxide ion since it is shared by 4 cubes, resulting in 1 oxide ion per unit cell (there are 12 edges, thus 12 x 1/4 = 3, but each oxygen is set twice, thus 3 / 2 = 1.5 but oxygen only gives 1 charge so we only take half). Each face-centered niobium contributes 1/2 of an atom to the unit cell since each face is shared between two unit cells, leading to 3 niobium atoms per unit cell (6 faces x 1/2 = 3). Therefore, for every 1 niobium atom, there is 0.5 of an oxide ion, and by multiplying both the niobium and oxide amounts by 2 to get whole numbers, we obtain the empirical formula Nb2O.

The coordination number of an ion in a crystalline structure is the number of counterions that surround it. In the niobium oxide unit cell described, the oxide ions are at the midpoint of each edge, and niobium atoms are at the center of each face. Without additional information, however, it is not possible to determine the exact coordination number, as this would depend on the 3D arrangement of the atoms within the cell.

Answer 2

Question 1:

1. One form of niobium oxide crystallizes in the unit cell shown above.

A. How many niobium atoms per unit cell? 3

B. How many oxygen atoms per unit cell? 3

C. What is the formula of niobium oxide? Nb2O5

Answer: A) 3 B) 3 C) Nb205

Question 2:

2. Quartz (left) and glass (right) are both forms of silicon dioxide. A piece of quartz breaks into a collection of smaller regular crystals with smooth faces. A piece of glass breaks into irregular shards. Use molecular structures to explain why the two solids break so differently. Select all that apply.

1. the bonding and geometry in quartz shows regular repeating patterns *

2. the bonding and geometry in quartz shows irregular repeating patterns

3. the bonding and geometry in glass shows irregular repeating patterns *

4. the atomic geometries of the two solids can explain why they break so differently *

5. the atomic geometries of the two solids cannot explain why they break so differently

6. the bonding and geometry in glass shows regular repeating patterns

Answer: 1,3,4

3. Solid silver adopts a face-centered cubic lattice. The metallic radius of a silver atom is 144 pm.

a. How many silver atoms occupy one unit cell of solid silver? 4

b. Calculate the length (in pm) of one side of the unit cell. 407

c. Calculate the volume (in m3) of one the unit cell. 6.74 x10^-29

d. What percentage (expressed to four significant figures) of the volume is empty? 25.95

Answer: a)4 b)407 c)6.74 x10^-29 d)25.95

4. Why hexane is insoluble in water? Select all that apply.

1. Water is polar solvent. *

2. Polar solvents dissolve both polar and non-polar compounds.

3. Polar solvents dissolve only polar compounds. *

4. Solubility does not depends on the polarity of the solvents and reagents.

5. Hexane is non-polar compound. *

Answer: 1,3,5

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