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How many total cations (A and B) and anions (X) are there in the unit cell below? = A = B = X

How many total cations (A and B) and anions (X) are there in the unit cell below? = A = B = X

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Question:** How many total cations (A and B) and anions (X) are there in the unit cell below? **Diagram Explanation:** The diagram depicts a cubic unit cell structure. The structure includes different colored spheres representing cations and anions: - Blue spheres represent cations A. - Red spheres represent cations B. - Yellow spheres represent anions X. **Unit Cell Composition:** - Cations A (Blue): Located at the corners of the unit cell. There are 8 corner spheres, and each is shared among eight adjacent unit cells. - Cations B (Red): Positioned at the center of each face of the cube. There are 6 face-centered spheres, and each is shared between two unit cells. - Anions X (Yellow): Situated at the edges of the unit cell. There are 12 edge-centered spheres, and each is shared among four adjacent unit cells. To determine the total number of each type of ion within a single unit cell: - Cations A: \( \frac{1}{8} \times 8 = 1 \) - Cations B: \( \frac{1}{2} \times 6 = 3 \) - Anions X: \( \frac{1}{4} \times 12 = 3 \) **Summary:** - Total Cations (A and B): 1 (A) + 3 (B) = 4 - Total Anions (X): 3 This illustrates the balanced distribution of ions within the unit cell, ensuring neutrality and stability in the crystal structure.
Transcribed Image Text:**Question:** How many total cations (A and B) and anions (X) are there in the unit cell below? **Diagram Explanation:** The diagram depicts a cubic unit cell structure. The structure includes different colored spheres representing cations and anions: - Blue spheres represent cations A. - Red spheres represent cations B. - Yellow spheres represent anions X. **Unit Cell Composition:** - Cations A (Blue): Located at the corners of the unit cell. There are 8 corner spheres, and each is shared among eight adjacent unit cells. - Cations B (Red): Positioned at the center of each face of the cube. There are 6 face-centered spheres, and each is shared between two unit cells. - Anions X (Yellow): Situated at the edges of the unit cell. There are 12 edge-centered spheres, and each is shared among four adjacent unit cells. To determine the total number of each type of ion within a single unit cell: - Cations A: \( \frac{1}{8} \times 8 = 1 \) - Cations B: \( \frac{1}{2} \times 6 = 3 \) - Anions X: \( \frac{1}{4} \times 12 = 3 \) **Summary:** - Total Cations (A and B): 1 (A) + 3 (B) = 4 - Total Anions (X): 3 This illustrates the balanced distribution of ions within the unit cell, ensuring neutrality and stability in the crystal structure.
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