A four-coordinate complex of Co2+ labelled A has a spin-only magnetic momentof 3.87 BM. Another four-coordinate complex of Co2+ labelled B has a spin-only magnetic moment 0f 1.73 BM. Use the magnetic moments to deduce thegeometries of complexes A and B

To deduce the geometries of complexes A and B based on their spin-only magnetic moments, we can use the following steps:

Step 1: Understand the relationship between spin-only magnetic moment and geometry. The spin-only magnetic moment is related to the number of unpaired electrons in a complex. The formula to calculate the spin-only magnetic moment (μ) is given by: μ = √n(n+2) BM where n is the number of unpaired electrons.

Step 2: Calculate the number of unpaired electrons for complexes A and B. For complex A, the spin-only magnetic moment is given as 3.87 BM. Using the formula, we can solve for n: 3.87 = √n(n+2) Squaring both sides, we get: 15 = n(n+2) Simplifying the equation, we have: n^2 + 2n - 15 = 0 Factoring the equation, we find: (n + 5)(n - 3) = 0 This gives us two possible values for n: -5 and 3. Since the number of unpaired electrons cannot be negative, we take n = 3.

For complex B, the spin-only magnetic moment is given as 1.73 BM. Using the same formula, we can solve for n: 1.73 = √n(n+2) Squaring both sides, we get: 3 = n(n+2) Simplifying the equation, we have: n^2 + 2n - 3 = 0 Factoring the equation, we find: (n + 3)(n - 1) = 0 This gives us two possible values for n: -3 and 1. Again, since the number of unpaired electrons cannot be negative, we take n = 1.

Step 3: Determine the geometries based on the number of unpaired electrons. For complex A, with 3 unpaired electrons, the possible geometries are octahedral and square planar. However, since the coordination number is given as 4, the geometry of complex A must be square planar.

For complex B, with 1 unpaired electron, the possible geometries are tetrahedral and square planar. Again, since the coordination number is given as 4, the geometry of complex B must be tetrahedral.

Therefore, based on the spin-only magnetic moments, we can deduce that complex A has a square planar geometry, while complex B has a tetrahedral geometry.