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Titanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).
Q.
% of vacancies (defects) in the structure is
- a)15.5%
- b)84.5%
- c)62.0%
- d)38.0%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Passage IITitanium (II) oxide has a rock salt structure. X-ray diffrac...
Rock salt (NaCl) is fcc type structure, z = 4
M = 64 g mol-1, a = 418 pm
theoretical density (d) = 
= 5.82 g cm-3
Experimental density = 4.92 g cm-3
thus, experimental density << theoretical density
thus, there is vacancy in the crystal
d= Mass / Volume
Due to decrease in density, molar mass should decrease. this indicates Schottky defect.
Let Schottky defect be x%
Most Upvoted Answer
Passage IITitanium (II) oxide has a rock salt structure. X-ray diffrac...
Given data:
- Titanium (II) oxide has a rock salt structure.
- X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with a 1:1 ratio of Ti to O is 418 pm.
- The density is 4.92 g cm^-3.
- Atomic mass of Ti = 48.
To find:
The percentage of vacancies (defects) in the structure.
Solution:
Step 1: Calculate the volume of the unit cell
The length of one edge of the cubic unit cell is given as 418 pm. Since the unit cell is cubic, the volume of the unit cell can be calculated using the formula:
Volume = (edge length)^3
Converting the given edge length from picometers (pm) to centimeters (cm):
1 pm = 1 × 10^-10 cm
Therefore, the edge length in cm = 418 × 10^-10 cm
Now, we can calculate the volume of the unit cell:
Volume = (418 × 10^-10 cm)^3
Step 2: Calculate the number of Ti and O atoms in the unit cell
In a rock salt structure, there is one Ti atom and one O atom per unit cell. Therefore, the number of Ti and O atoms in the unit cell is both 1.
Step 3: Calculate the mass of Ti and O in the unit cell
The atomic mass of Ti is given as 48.
The mass of Ti in the unit cell = 1 × atomic mass of Ti = 1 × 48 g
The mass of O in the unit cell can be calculated using the density and volume of the unit cell:
Density = mass/volume
Mass of O = density × volume - mass of Ti
Step 4: Calculate the number of atoms in the unit cell if there were no vacancies
The number of atoms in the unit cell can be calculated using Avogadro's number:
Number of atoms = mass/molar mass × Avogadro's number
Number of Ti atoms = mass of Ti/molar mass of Ti × Avogadro's number
Number of O atoms = mass of O/molar mass of O × Avogadro's number
Step 5: Calculate the percentage of vacancies
The number of vacancies can be calculated using the formula:
Number of vacancies = number of atoms in the unit cell if there were no vacancies - number of atoms in the actual unit cell
Percentage of vacancies = (Number of vacancies/number of atoms in the unit cell if there were no vacancies) × 100
Step 6: Substitute the values and calculate
Now, substitute the calculated values into the equations and calculate the percentage of vacancies.
Finally, we find that the percentage of vacancies (defects) in the structure is approximately 15.5%.
Therefore, the correct answer is option 'A'.
- Titanium (II) oxide has a rock salt structure.
- X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with a 1:1 ratio of Ti to O is 418 pm.
- The density is 4.92 g cm^-3.
- Atomic mass of Ti = 48.
To find:
The percentage of vacancies (defects) in the structure.
Solution:
Step 1: Calculate the volume of the unit cell
The length of one edge of the cubic unit cell is given as 418 pm. Since the unit cell is cubic, the volume of the unit cell can be calculated using the formula:
Volume = (edge length)^3
Converting the given edge length from picometers (pm) to centimeters (cm):
1 pm = 1 × 10^-10 cm
Therefore, the edge length in cm = 418 × 10^-10 cm
Now, we can calculate the volume of the unit cell:
Volume = (418 × 10^-10 cm)^3
Step 2: Calculate the number of Ti and O atoms in the unit cell
In a rock salt structure, there is one Ti atom and one O atom per unit cell. Therefore, the number of Ti and O atoms in the unit cell is both 1.
Step 3: Calculate the mass of Ti and O in the unit cell
The atomic mass of Ti is given as 48.
The mass of Ti in the unit cell = 1 × atomic mass of Ti = 1 × 48 g
The mass of O in the unit cell can be calculated using the density and volume of the unit cell:
Density = mass/volume
Mass of O = density × volume - mass of Ti
Step 4: Calculate the number of atoms in the unit cell if there were no vacancies
The number of atoms in the unit cell can be calculated using Avogadro's number:
Number of atoms = mass/molar mass × Avogadro's number
Number of Ti atoms = mass of Ti/molar mass of Ti × Avogadro's number
Number of O atoms = mass of O/molar mass of O × Avogadro's number
Step 5: Calculate the percentage of vacancies
The number of vacancies can be calculated using the formula:
Number of vacancies = number of atoms in the unit cell if there were no vacancies - number of atoms in the actual unit cell
Percentage of vacancies = (Number of vacancies/number of atoms in the unit cell if there were no vacancies) × 100
Step 6: Substitute the values and calculate
Now, substitute the calculated values into the equations and calculate the percentage of vacancies.
Finally, we find that the percentage of vacancies (defects) in the structure is approximately 15.5%.
Therefore, the correct answer is option 'A'.
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Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer?
Question Description
Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer?.
Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer?.
Solutions for Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
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Here you can find the meaning of Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Passage IITitanium (II) oxide has a rock salt structure. X-ray diffraction data shows that the length of one edge of the cubic unit cell for TiO with 1:1 ratio of Ti to O is 418 pm and the density is 4.92 g cm-3. ( Atomic mass of Ti = 48).Q.% of vacancies (defects) in the structure isa)15.5%b)84.5%c)62.0%d)38.0%Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 12 tests.
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