CHM 501

10. Use Slater's rules to calculate Z* for Ru, Rh, Pd, Os, Ir, and Pt. What are the periodic trends? Compare the trends in the first ionization potential, the electron affinity, the metallic radius, the Pauling electronegativity, and the density for these six elements. Does Z*, as calculated by Slater's Rules, adequately explain the trends in each of these properties? Why or why not?

Answer

Find the electron configurations and write them according to Slater's prescription. Then use the rules to find the screening constant and then Z*

Ru: (1s)2(2s2p)8(3s3p)8(3d)10(4s4p)8(4d)7(4f)0(5s5p)1

For the 5s valence electron: S = (15)(0.85) + (28)(1.00) = 40.75 so Z* = 44 - 40.75 = 3.25

Rh: (1s)2(2s2p)8(3s3p)8(3d)10(4s4p)8(4d)8(4f)0(5s5p)1

For the 5s valence electron: S = (16)(0.85) + (28)(1.00) = 41.60 so Z* = 45 - 41.60 = 3.40

Pd: (1s)2(2s2p)8(3s3p)8(3d)10(4s4p)8(4d)10(4f)0(5s5p)0

For the 4d valence electron: S = (9)(0.35) + (36)(1.00) = 39.15 so Z* = 46 - 39.15 = 6.85

Os: (1s)2(2s2p)8(3s3p)8(3d)10(4s4p)8(4d)10(4f)14(5s5p)8(5d)6(5f)0(6s6p)2

For the 6s valence electron: S = (1)(0.35) + (14)(0.85) + (60)(1.00) = 72.25 so Z* = 76 - 72.25 = 3.75

Ir: (1s)2(2s2p)8(3s3p)8(3d)10(4s4p)8(4d)10(4f)14(5s5p)8(5d)7(5f)0(6s6p)2

For the 6s valence electron: S = (1)(0.35) + (15)(0.85) + (60)(1.00) = 73.10 so Z* = 77 - 73.10 = 3.90

Pt: (1s)2(2s2p)8(3s3p)8(3d)10(4s4p)8(4d)10(4f)14(5s5p)8(5d)9(5f)0(6s6p)1

For the 6s valence electron: S = (17)(0.85) + (60)(1.00) = 74.45 so Z* = 77 - 74.45 = 3.55

Z* generally increases from left to right on the Periodic Table, but Pt appears to be an exception to this rule. Going down the Periodic Table gives a slight increase in Z* because of the poor shielding abilities of the f electrons, but again Pt appears to be an exception, at least based upon Slater's Rules.

Element

Z*

IP (eV)

EA (eV)

rmetal (Å)

Pauling Electronegativity

Density (g/cm3)

Ru

3.25

7.361

1.05

1.34

2.2

12.41

Rh

3.40

7.459

1.137

1.34

2.28

12.41

Pd

6.85

8.337

0.562

1.37

2.20

12.02

Os

3.75

8.438

1.1

1.35

2.2

22.57

Ir

3.90

8.967

1.564

1.36

2.2

22.42

Pt

3.55

8.959

2.128

1.39

2.2

21.45

Z* tracks with IP reasonably well, both across a period and between periods. In contrast, there appears to be little correlation between Z* and EA. The metallic radius and Pauling Electronegativity are essentially constant for all six of these metals, so Z* appears to have no influence. However, since n is larger for Os, Ir, and Pt, the radial function would expect one to expect a larger radius. This is not observed because of the poor shielding of the f electrons, which is a Z* effect. The densities in each period are close to constant and the difference between the two periods is solely based on mass.