chemistry : class12 Radius Ratio Rules : Ionic solids : Solid State MCQ Questions and Answers
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Radius Ratio Rules
MCQ questions and answers.
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MCQ Questions
1. According to the radius-ratio rule, an ionic solid with a cation-to-anion radius ratio of 0.68 is most likely to have which coordination number for the cation?
A.
2
B.
4
C.
6
D.
8
Correct Answer:
6
Explanation:
A radius ratio between approximately 0.414 and 0.732 corresponds to octahedral coordination, in which the cation has coordination number 6. Since 0.68 lies within this interval, coordination number 6 is predicted.
2. A cation has an ionic radius of 150 pm and the anion has an ionic radius of 200 pm. Using the radius-ratio rules, what coordination number is predicted for the cation?
A.
2
B.
3
C.
4
D.
6
Correct Answer:
6
Explanation:
The radius ratio is r+/r− = 150/200 = 0.75. Ratios from approximately 0.732 to 1.00 favor cubic coordination with coordination number 8, not any of the listed lower coordination numbers. Therefore, the options as written do not contain the predicted value.
3. Which coordination environment is predicted when the radius ratio r+/r− is 0.20?
A.
Linear coordination with coordination number 2
B.
Trigonal planar coordination with coordination number 3
C.
Tetrahedral coordination with coordination number 4
D.
Octahedral coordination with coordination number 6
Correct Answer:
Trigonal planar coordination with coordination number 3
Explanation:
The radius-ratio range approximately 0.155 to 0.225 corresponds to trigonal planar coordination. Since 0.20 lies in this interval, the predicted coordination number is 3.
4. If r+/r− = 0.12 for an ionic solid, which coordination number is most consistent with the radius-ratio rule?
A.
2
B.
3
C.
4
D.
6
Correct Answer:
2
Explanation:
A radius ratio below approximately 0.155 is associated with linear coordination, where the cation contacts two anions. Thus, a ratio of 0.12 predicts coordination number 2.
5. The ionic radii of a cation and anion are 95 pm and 180 pm, respectively. What coordination number is predicted for the cation by the radius-ratio rule?
A.
2
B.
3
C.
4
D.
6
Correct Answer:
6
Explanation:
The radius ratio is 95/180 = 0.528. This value lies between 0.414 and 0.732, the range associated with octahedral coordination. Therefore, the cation is predicted to have coordination number 6.
6. For an anion radius of 200 pm, what is the approximate minimum cation radius required for tetrahedral coordination according to the limiting-radius ratio?
A.
31.0 pm
B.
45.0 pm
C.
82.8 pm
D.
146.4 pm
Correct Answer:
82.8 pm
Explanation:
The lower limiting radius ratio for tetrahedral coordination is approximately 0.414. Therefore, the minimum cation radius is 0.414 × 200 pm = 82.8 pm.
7. A cation-to-anion radius ratio is measured as 0.39. Which structural arrangement is predicted by the radius-ratio rules?
A.
Linear, coordination number 2
B.
Trigonal planar, coordination number 3
C.
Tetrahedral, coordination number 4
D.
Cubic, coordination number 8
Correct Answer:
Tetrahedral, coordination number 4
Explanation:
The ratio range approximately 0.225 to 0.414 corresponds to tetrahedral coordination. Since 0.39 lies within this interval, the cation is predicted to have coordination number 4.
8. For an anion radius of 140 pm, which cation radius is closest to the upper limiting value for octahedral coordination?
A.
57.9 pm
B.
102.5 pm
C.
140.0 pm
D.
146.4 pm
Correct Answer:
102.5 pm
Explanation:
The upper limiting radius ratio for octahedral coordination is approximately 0.732. Thus, the corresponding cation radius is 0.732 × 140 pm = 102.48 pm, or approximately 102.5 pm.
9. A cation has radius 100 pm and an anion has radius 160 pm. Which coordination number is predicted from their radius ratio?
A.
3
B.
4
C.
6
D.
8
Correct Answer:
6
Explanation:
The radius ratio is 100/160 = 0.625. This lies in the 0.414–0.732 interval for octahedral coordination, so the predicted coordination number is 6.
10. If the cation radius in an ionic solid increases while the anion radius remains constant, changing r+/r− from 0.70 to 0.80, what change in coordination is predicted by the radius-ratio rules?
A.
From coordination number 4 to 6
B.
From coordination number 3 to 4
C.
From coordination number 6 to 8
D.
From coordination number 8 to 6
Correct Answer:
From coordination number 6 to 8
Explanation:
A ratio of 0.70 lies in the octahedral range, corresponding to coordination number 6. A ratio of 0.80 lies in the cubic range, corresponding to coordination number 8. Hence, the predicted change is from 6-fold to 8-fold coordination.
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