Let's talk about what total strain means and what calculations look like involving total
strain including chair conformations. Total strain as we define it as "strain total" here
is the equal of the sum of its parts so we could say it's the sum of strain due to angles
so like if we have a cyclopropane or butane or pentane, any other size ring. Except cyclohexane
or a 14 membered ring are strain free. We have to be given a table of values that give
us these total strain amounts for angle strain and so 6 and 14 being strain free, so angle
strain is a component. We also have torsional strain which is due to eclipsing interactions
say we have a Newman projection with dihedral angles that are non ideal so less than 60
degrees where we have overlapping, eclipsing that's torsional strain. Then we also have
steric strain which can be one of a couple of things early in our course the first being
a Gauche type strain, so if we have a staggered conformation of an ethane type molecule or
any linear alkane where we have groups such as methyls which are near each other 60 degrees
apart in dihedral angle we have bumping that occurs between these groups that we will call
Gauche strain. And it's a long distance interaction so it's a form of steric strain. Bumping between
eclipsing interactions/torsional strain is right next door 0 degree dihedral angle and
we have long distance interaction or bumping for Gauche strain. We can also have in the
case of a cyclohexane, we can have 1,3 diaxial interactions which I'm going to call Ax here,
axial stain, diaxial strain. When we have groups that are axial such as this methyl
can interact 3 carbons apart so this is 1,3 diaxial because it happens 1,2,3 positions
away and you always get two at a time when you have a big group in the axial position.
Ok so we are going to have a couple of components of steric strain, but the sum is all the different
parts added together. With an alternate way of defining total strain is we can say that
total strain is equal to the difference between the actual heat of formation of a compound
minus the predicted heat of formation using a calculation based on strain free molecules.
So this difference between what we predict and it's an absolute value here because it's
always greater so we could say the other way around . The actual minus the predicted should
be positive, but it is absolute value because the total strain left over from what we would
predict as strain free. We should end up with a number greater than zero. But we can always
get it if we assume it's always positive. So that's two ways to find strain, let's look
at an example where we put together the total strain of two conformations of cyclohexane,
a trisubstituted cylclohexane. So we have a couple of questions....and then which one is less strained is more stable. So we need to be able to identify
all the parts of strain here. If we put all our parts of strain in kind of a column here,
we've got angle, we've got torsional, we've got steric, with steric we can have Gauche
strain, Gauche interaction and we can have diaxial interactions for steric strain. So if we look at our compounds cyclohexane
means we are not going to have angle strain for either one of these. The chair conformation
exists in the way that it does because it achieves 109.5 bond angles and creates staggered
conformations for every bond in the molecule so we eliminate angle and torsional. What
we are looking for Gauche strain and 1,3 diaxial strain as the ring flips from one ring flip
to the other. What we've got to do, is we've got to define our positions so if we number
this thing we would end up putting the lowest number by going 1,2,3,4, so we can lower the
numbers on our groups by going 1,2,3,4 so as we name it in nomenclature, those are our
1,2,3, and 4 carbons. We 've got to turn around here and label 1,2,3, and 4 on our template
somewhere and like to put carbon 1 at on end or the other at on corner so we go here or
here. We'll go top left just for fun, and we have to number around clockwise here because
that's the way it's drawn out in our skeletal structure preview here. So we've got to go
carbon 1, carbon 2,3, and 4 and we do the same thing after the ring flip 1,2,3, and
4. That happens here as well so we've got to be consistent for both the ring flipped
up and the ring flipped down on one side. Then we define our axial position so the corner
that's pointed up, is always axial up. The corner pointed down is always axial down.
the axial position alternates at every carbon so we'll just draw the ones that matter here.
Just the ones we have groups attached to in our final molecule, we now have axial down,
axial up, then down and back up again. So everything else is equatorial, we want to
make those as close as possible to being parallel to the bond two away. So as we do these....and
so we've defined our axial positions first so that we can define our equatorial positions
and axial up means we have equatorial down. Anytime axial's down then we have equatorial
up and so forth. That's important for when we are translating our structure so at carbon
1 we have methyl up at us with the wedge so we want to put the methyl here up in the axial
position. likewise, chlorine is up on the skeletal structure, I want to put it equatorial
up at carbon 2. Then 3,4 we are down relative to the ring at carbon 4 so I want to put the
final methyl down as we are on our structure. We've got carbons 1,2,3, and 4 defined here
in the correct orientation for our structure. Anything left over that is not shown is a
hydrogen so we draw those in. And then we ring flip so we go from axial up to equatorial
up, but we stay in the same relative positions relative to our original structure, and then
equatorial down becomes axial down. likewise the chlorine becomes axial up and then at
carbon 4 we become equatorial down as we were axial down. So we've got our 2 conformations
successfully drawn out here. Now we've got to determine the other types of strain that
we have. If we are looking for Gauche strain, what we have to do is look for carbons that
are side by side. So as we make a Newman projection and we circle a bond to make a Newman projection
the bonds on the Newmans have to be at neighboring carbons. So carbon 4 which is down here is
not going to participate in any type of Gauche interaction so really it's carbon 1 and 2
so as we define that here, we would have to look at the 1,2 bond and see if we have a
gauche interaction. I'm going to draw a Newman projection with axial up for carbon 1, axial
up is methyl, there it is, then the back carbon axial down is a hydrogen and so I'm going
to put that there, define the staggered Newman projection. The ring connects to itself on
the right hand side and then we have an equatorial chlorine on carbon 2, there it is on the back
carbon so we fill in all the structures. We do indeed have a methyl to chlorine Gauche
interaction in the structure on the left. In the structure on the right the 1,2 bond
is here after the ring flip we can draw it in as well. So carbon 1 we have axial down
now so I draw it upside down from the way we had before, put the hydrogen axial down,
and the back carbon, carbon 2, we have a chlorine that is axial up, the ring connects off to
the right and then we have on carbon 1 in the front we have the methyl and then in the
back carbon we have a hydrogen. So what I've got here is another Gauche interaction, methyl
to chlorine, that we have to account for in this structure. Then now that we've got our
Gauche interactions taken care of, we look at 1,3 diaxial strain. So as I see...I'm going
to erase this so we can see a little better...ok so as I see on the structure on the left,
I've got a methyl axial here, I've got a methyl axial here, so I've got to look at my other
axial positions, here are the other two axial ups, we have a methyl interacting with those
above the ring, the ups, they are above the ring, hydrogen is too small to interact with
itself so we have nothing here, so methyl to hydrogen we have two of those. On the bottom
we also have axial down hydrogens that we have to account for below the ring, that are
interacting with the axial methyl below the ring. So we end up with 4 Methyl to hydrogen
1,3 diaxial strain interactions. On the right hand conformer we have methyls that are in
the equatorials, but we do have a chlorine that is axial so we have to account for it,
find all the axial ups since chlorine is axial up. Chlorine to hydrogen, chlorine to hydrogen,
so we have two, chlorine to hydrogen 1,3 diaxial interactions so the total strain then is the
sum of these. And so we end up with one methyl to chlorine, 4 methyl to hydrogen diaxial,
one methyl to chlorine Gauche, four methyl to chlorine diaxials. The same methyl to chlorine
gauche and then 2 chlorine to hydrogen diaxials. When you add these up from a table, you would
end up getting that this is a higher number of kJ/mole than the structure on the right.
so it turns out that the structure on the right is lower energy, less strain, and thus
more stable. And because its more stable, a more negative delta G or lower delta G that
means its equilibrium constant is going to be bigger, which means it exists more of the
time, it has a higher equilibrium constant than the conformer on the left because it's
more stable.