Question 1

Why do the complexes [Fe(CN)6]^4- and [Fe(CN)6]^3- have different colors in solution?
Because the different charges on the complexes ([Fe(CN)6]^4- vs [Fe(CN)6]^3-) lead to slightly different ligand field environments and crystal field splitting energies, absorbing different wavelengths of light.

Question 2

Why do the first ionization enthalpies of the first transition series elements show a small overall increase but with notable dips at Cr and Cu?
Because the dips at Cr and Cu correspond to the removal of an electron from a more stable half-filled (Cr: 3d^5 4s^1) or fully-filled (Cu: 3d^10 4s^1) configuration, making the first IE lower than expected.

Question 3

Why do the atomic radii of the elements immediately following the Lanthanoids (Hf, Ta, W, etc.) match those of the elements above them in the periodic table (Zr, Nb, Mo, etc.)?
Because the Lanthanoid contraction causes the elements following the Lanthanoids to be much smaller than expected, making their sizes similar to the corresponding elements in the previous period.

Question 4

Why do the complexes [Cr(NH3)6]^3+ and [Mn(H2O)6]^2+ have different numbers of unpaired electrons despite both being high-spin octahedral complexes?
Because Cr^3+ (d^3) and Mn^2+ (d^5) have different numbers of d-electrons, leading to different numbers of unpaired electrons even in high-spin configurations.

Question 5

Why do the second and third ionization enthalpies of Zn show very large jumps compared to the first?
Because the first electron is removed from the 4s orbital, while the second and third electrons are removed from the much more stable and tightly bound 3d orbitals.