Tungsten is hard and has a very high melting point
(3422 °C), an...

Question

Tungsten is hard and has a very high melting point (3422 °C), and gold is soft and has a relatively low melting point (1064 °C). Are these facts in better agreement with the electron-sea model or the MO model (band theory)? Explain.

Accepted Answer

Hello. In this problem we are given most hardness values for some period for transition metals. Were asked to determine if the trend that is seen in the table is best explained by the electron C model or the molecular orbital model let's begin by considering the electron C model, electron C model proposes that we have cat lines surrounded by a sea of electrons. More electrons would mean greater electrostatic forces in the middle which should lead to increasing partners as we go from left to right in the periodic table, the number of electrons increases. And so if the electron C model were to describe this trend, we would expect to see then more hardness values increase as we move from left to right. What we observe is that from titanium to chromium. The more hardness values do increase but once we get to manganese and move through to zinc we see that the Moh hardness values are decreasing. Therefore the metal hardness shown in the table does not follow the trend that we would predict based on the electron C. Model. So let's move on then to consider the next model, the molecular orbital model. To understand the molecular orbital model, it's best if we consider what's taking place in period four. So in period four filling forest orbital and we're filling three D orbital's This four s orbital And these three D orbital's overlap to form an sp band sp band is composed of three bonding orbital's and three anti bonding orbital's partners increases with the number of electrons in bonding orbital's and the hardness decreases with the number of electrons in anti bonding more beetles. So let's go back up and look at our table of most hardness values. So as we go from titanium, vanadium chromium, we see that we have an increase in the mo hardness values. And this is explained by the fact that as we go from titanium, vanadium chromium, we are adding electrons to the bonding orbital's. So titanium, let's go back up here a moment. So titanium In Group four B has four valence electrons. Vanadium has five. Chromium has six valence electrons, manganese has seven. Iron has eight. If you look at the periodic table, we see that there are other transition metals that follow iron. Before we get to copper, copper has 11 valence electrons and zinc has 12. So as we are adding electrons beginning with titanium through chromium, we have then going to our bonding and anti bonding orbital's. So with titanium we have four valence electrons. Vanadium has five and we get to chromium we have six. So as we go from titanium vanadium chromium, we are adding additional electrons to the bonding orbital's. The more bonding orbital's, the greater the hardness. So we look at the table again, the most hardest values increase as we go from titanium to chromium which is associated with an increase in the number of electrons in these bonding orbital's as we then move to manganese manganese has seven valence electrons, iron again has eight. And then we moved to copper and zinc which have 11 and 12. Once we have more than six valence electrons, we start adding electrons to the anti bonding orbital. So with manganese we'll start adding electrons to the anti bonding orbital's will continue to do so with iron which has eight. And then copper has 11 and zinc has 12. So as we move from manganese to iron, we are adding more and more electrons to these antibiotic orbital's. And so we expect the hardness value to go down, which is what we see in this table. We see that the more hardness values are decreasing as we add more and more electrons to those anti bonding orbital. So the molecular orbital model then seems to be a good fit for describing the trend that we see with the most hardness values for these period for transition metals. While we are forming these Are filling these bonding orbital's with electrons, we see an increase in the mo hardness value for titanium through chromium. Once we start adding electrons to those anti bonding orbital's with manganese, we see that the most hardness values decrease with zinc having the most electrons in the anti bonding orbital and having the lowest most hardness value of 2.5. I hope this helps explain. Um This trend. Thanks for watching Goodbye

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