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ROFESSOR CIMA: So Pauling said we can measure the percent--
so partial ionic character. He said we can measure the percent ionic character
as 100-- because it's going to be in percent--
as the experimental dipole. When I say "experimental dipole," it's what
you actually measure, the dipole that you measure divided by the calculated
dipole if the charge was completely transferred.
In other words, if I look at my molecule A-B here, if this were really
A+ and this were B-, in other words, I transferred one [electron]
charge-- and I multiplied that by the bond length,
that would be the denominator here.
That would be the fully ionic bond. So you couldn't have a dipole moment greater
than that for that bond. And so the ratio should be that.
And what he ended up doing was he ended up showing that you could
correlate this percent ionic character to a formula that looked like this,
that this percent ionic character was related to the difference in
electronegativity. Sort of simple function.
I'll plot this out. So this was his prediction.
Now, let's see how it works in practice. Let's look at this first one here.
STUDENT: Is that to the second power? PROFESSOR CIMA: Did I square it?
Yep. Yes?
STUDENT: Is that a Q or a 4? PROFESSOR CIMA: That's a 4, 1/4.
STUDENT: Sorry. Back on the other board, the [INAUDIBLE],
what were those spiraling lines meant to represent?
PROFESSOR CIMA: The spiraling lines. OK, I'm going to have to pass on that.
I'm getting a little bit behind, so I'll have to hold on the questions.
So let's do an example, HF gas. It has a measured dipole moment of 1.83 debye.
And if you want it in coulomb meters, you have to take this into account.
We know that the bond length is 92 picometers. So we can calculate the bottom part here.
If you had completely H plus and F minus, you'd know the distance is 92 x
10^ -12 meters. The charge that would separate is one fundamental
charge because we're moving it completely to the fluorine, if it
were fully ionic. And so you'd put in 1.602 x 10^ -19 meters.
That gives you 1.47 x 10^ -29 meter coulombs. And if you convert that to debye, it's 4.47
debye. So for this bond length, the maximum dipole
moment you could get was 4.47 debye.
The ratio of this measure to this one is 100 times 1.83/4.47 gives you 41%.
Now, how about Mr. Pauling's formula here? That one comes up-- well, you need to know
the electronegativity. That's 2.2 for hydrogen.
And for fluorine it's 3.98. And so when you plug that in, you get 55%.
So here's the two. And this is Pauling, 55.
And those are the two. That's the kind of error that you might expect.
Here's what is actually in his book. Oh, good.
You see it here. Down here is the electronegativity difference.
And here is the fraction, not multiplied by 100, of ionic character.
So it goes from 0 to 1. And they've got a bunch of these gaseous molecules
here. And so these dots are calculated just this
way, the experimental dipole moment divided by the maximum calculated dipole
moment you can get, given the bond length of the molecule.
And you can see it generally fits this curve. HF is lower than that curve, just like we
calculated. And this curve, I forgot to mention, is essentially
this equation. So it does a pretty good job of estimating
the percent ionic character.