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Given the cation radius is 148 pm and the anion radius is 195 pm, determine the coordination number and crystal structure.

Chemistry

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Answer

d

a) Body centred cubic\text{a) Body centred cubic}

Step-by-step solution

4 steps
  1. Identify the given radii of the cation and anion.

    The radius of the cation A+^+ (rcr_c) is 148 pm148 \, \text{pm}.
    The radius of the anion B−^- (rar_a) is 195 pm195 \, \text{pm}.

  2. Calculate the radius ratio (rcra\frac{r_c}{r_a}).

    rcra=148 pm195 pm\frac{r_c}{r_a} = \frac{148 \, \text{pm}}{195 \, \text{pm}} rcra≈0.75897\frac{r_c}{r_a} \approx 0.75897
  3. Determine the coordination number and crystal structure based on the radius ratio.

    The radius ratio rules for ionic compounds are:

    • 0.155−0.2250.155 - 0.225: Coordination number 3 (Trigonal planar)
    • 0.225−0.4140.225 - 0.414: Coordination number 4 (Tetrahedral)
    • 0.414−0.7320.414 - 0.732: Coordination number 6 (Octahedral, NaCl type)
    • 0.732−1.0000.732 - 1.000: Coordination number 8 (Cubic, CsCl type)

    The calculated radius ratio of approximately 0.759 falls within the range 0.732−1.0000.732 - 1.000. This indicates a coordination number of 8.

  4. Relate the coordination number to the given options.

    A coordination number of 8 for an ionic compound typically corresponds to a cubic arrangement, such as the CsCl structure. In the CsCl structure, one type of ion (e.g., cation) is located at the body center of a cube formed by eight ions of the other type (e.g., anions). This arrangement is often referred to as a Body-Centered Cubic (BCC) structure in the context of ionic compounds.

    Comparing this with the options:

    • (a) Body centred cubic: This matches the expected structure for a coordination number of 8.
    • (b) Face centred cubic: This corresponds to a coordination number of 6 (e.g., NaCl type).
    • (c) Tetrahedral: This corresponds to a coordination number of 4.
    • (d) Octahedral: This corresponds to a coordination number of 6.

    Therefore, the ionic compound AB will have a Body-Centered Cubic structure.

    The final answer is a) Body centred cubic\boxed{\text{a) Body centred cubic}}.

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