All right guys, so in these videos I'm going to teach you how to use free energy in kilojoules
per mole to calculate the exact percentages of each conformation that you would get of
a cyclohexane.
Again, these videos might be beyond the scope of what your professor wants you to know for
your test, so I'm going to leave it up to you to decide if you need to know this or
not.
So you've been warned, so it's time to get into this.
It turns out that we can use that delta G value that we get from our A values to calculate
those exact percentages at any given temperature.
Now the way we do this is through the Gibbs free energy equilibrium constant equation.
Just so you guys know, if this equation looks familiar, it's not unique to this type of
problem.
In fact, pretty much any process that you can describe a free energy difference in can
be – you can determine an equilibrium through this equation.
This is a very important equation for all of chemistry, not just for cyclohexanes.
As you can see, what it says is that – let's just go through one term at a time.
It says that the delta G or the change in free energy is equal to the negative R. Now
remember that R is the gas constant that we used to use in general chemistry.
And there were two different values of R that we used to use.
Well, just note that the one we're using is in joules per mole so that's 8.134.
That's going to be important in a second.
Then temperature.
Temperature is in Kelvin.
Remember that – it's been a while since we've dealt with temperature, but remember
that 0 degrees Celcius is equal to 273.15 degrees Kelvin.
That's going to be a conversion that we have to use in a little bit.
Then you're going to multiply that by the natural log of the equilibrium constant.
Well, in order to solve any of these problems for percentages, we need to know the value
of the equilibrium constant because equilibrium constant, by definition, tells you what's
your products over your reactants.
I need to know that fraction.
If we go ahead and we solve for Ke – I did the math for you.
Don't worry.
What we get is that the Ke is equal to the negative delta G over the R times the T all
to the e.
If we can just plug in these variables, we're going to get the equilibrium constant.
Now we know what R is.
We know what T is.
Your calculator tells you what e is.
All we need is negative delta G. Do we have a way to find that?
Yes, guys, that's through our A values.
Our A values tell us what the free energy change is as we go axial.
All right?
Awesome.
Now I do want to make one note of the delta G. Notice that this is negative delta G, but
everything that we solved when we were doing A values, we were actually solving for positive
delta G because we were actually looking at the less stable one.
We were looking at how much energy do I have to put into the system to go to axial.
So when we use this equation, we're actually going to be inputting the positive delta G
here and that's fine.
What we're going to be getting is a number that describes basically how we're going to
that less stable value.
So then over here what we have is that – then we get that Ke and now we can solve for the
percentages using the definition products over reactants.
Now once we get that positive Ke number, that positive Ke number means that we're actually
going toward the favored direction.
I'm not sure if you guys remember, but if you have a Ke over 1, that means you're going
to the more favored direction.
I'm just telling you guys right now, if we use a positive number for delta G, we're going
to get also a positive number for – I'm sorry, we're going to get a number that's
above 1 for Ke.
We're going to get this greater than 1.
It's going to be equal greater than 1.
What that means is that our definition of Ke has to be the products over the reactants
meaning the more favored conformation over the less favored.
Just letting us know that the way we've arranged this equation, the way that your textbook
does it, is that it always does the more favored over the less favored, meaning that when you
get this positive value, it's going to tell you what percentage you're going to have of
the equatorial.
Then that minus 100 will be your axial.
Here it says that Ke is equal to x over 1 over x.
Guys, that just has to do with the definition of equilibrium constant, how x is what you're
making.
That's your product, so then 1 minus whatever you made would be your reactants.
Then we don't really want Ke here.
We want x because we're really trying to figure out how much of this product we're going to
get.
If we solve for x, I did that for you, what you're finally going to get is that x is equal
to Ke over Ke plus 1.
And if you want to put it in a percentage term, it's times 100.
Now that was a tons of words and I just said a lot of numbers and symbols.
I do not need you guys to perfectly understand this as much as I just need you to memorize
it and know how to use it.
If your professor wants you to solve this on your exam, then these equations should
be in your mind.
You should have memorized this equation.
You should have memorized the definition of Ke or how to solve for x.
Now we're going to focus on the actual working part, on the actual part that we determine
percentages, which is so cool.
I'm a huge orgo nerd as you guys know, so this is fun.
Getting to determine the exact percentage of each cyclohexane.
This first one will be a worked example.
We'll go ahead and start off with this first one.
So I'm just going to pause the video and then we'll come back and we'll solve this one together.