JANET: One of the advantages of a state function
is that whatever property you are looking at
depends only on the initial and the final states,
it does not matter how that property got there.
So in this screen cast,
we're gonna look in particular at enthalpy,
which is our H-bar, and that bar signifies
that it is specific enthalpy per mole or per kilogram.
And so if we have to find the change in enthalpy
during a process, we take here's our enthalpy
and we wanna find the change
and so that's equal to the enthalpy of the final state
minus the enthalpy of the initial state.
But what happens if you don't know these two numbers?
That's where this hypothetical process path
for state functions works.
You can construct this process path
where you know all the states in between you sum them up
and you end up with the Delta H
or the change in enthalpy for the same process.
Does that sound complicated?
Yes, so let's look at an example.
So let's say that we wanna find the change in enthalpy
of some substance A,
and it be it is a solid at one atmosphere and 50 degrees C.
So that's its initial state.
And we wanna know the change in enthalpy
for it becoming a vapor still at one atmosphere,
but now at 110 degrees C.
Now, normally you just take this enthalpy
and subtract from it this enthalpy,
and there's your Delta H.
However, what if we don't have either of those enthalpies?
So what we do is we construct a hypothetical path
where we do know the values and then add them all up.
So this right here is what's known as the true process path.
What we're gonna do is take a convoluted path
to get from the initial state to the final state
and add up all of these enthalpies.
So here's what we're going to do.
We're gonna start with our solid
and all of this is gonna be at one atmosphere
so we won't worry about any changes in pressure,
and 50 degrees C.
And the first thing we're gonna do to that
is raise it to its melting point.
So now we have a solid, which is at its melting point,
and now we're gonna melt it.
And so now it becomes a liquid at its melting point.
Then we take this liquid at its melting point,
raise it so that it becomes a liquid at its boiling point,
vaporize it, so now we have a vapor of A
at its boiling point,
and then we raise the temperature
so we end up with a vapor at 110 degrees C.
And so what we do is we calculate this enthalpy,
this enthalpy, this enthalpy,
then to this enthalpy, which we'll call four,
and this enthalpy,
and if we add all of these together
we will get that change in enthalpy for the entire process.
So what do we need in order to calculate these enthalpies?
So there are two types of heat
when you're doing this enthalpy process.
We have what's known as sensible heat,
and that's where you take a substance
and raise its temperature without changing its phase.
And to calculate it, you take a specific heat
and you multiply that by the final temperature
of that particular process minus the initial.
We also have a phase change,
and so that's what's known as latent heat,
and here it's no calculation
what you do do is you look up the heat of melting,
or you look up the heat of vaporization.
So let's put together some representative values
for this particular process, and do the calculation.
Please note that these are example values
and do not correspond to any particular substance.
So our heat capacity specific heats
are in units of kilojoules per mole degree celsius.
And for the solid, it's going to be 0.15,
for the liquid, it's gonna be 0.25,
and for the vapor, it's gonna be 0.1.
We also need these phase change latent heats,
and they'll be in kilojoules per mole,
and so the heat of melting
is going to be equal to 10 kilojoules per mole,
and that of vaporization
is going to be equal to 25 kilojoules per mole.
So, let's construct a path using these values.
We basically have to calculate
our H one, H two, H three, H four, and H five.
So let's try it out,
and we'll put a table together to keep track of our values.
Please note that we also need the melting point
and boiling point of substance A.
So our melting point is equal to 60 degrees C,
and our boiling point is equal to 95 degrees C.
So here the different enthalpies
that we're going to need to calculate.
H one right here goes from the solid at 50 degrees
to the solid at 60 degrees,
and if you know that sensible heat
so we use the heat capacity.
Next we do the phase change, so that is the heat of melting.
And then we have to go from the melting point of 60 degrees
to the boiling point of 95 degrees C,
again this is sensible heat, so we use a heat capacity.
Now we vaporize it, and we use the heat of vaporization.
And finally we take our substance A
from that boiling point to its final temperature,
110 degrees C as a vapor.
And again since that's sensible heat,
we use our heat capacity.
So let's do some of these calculation.
So first we'll do our H one, and this is equal to 0.15,
and remember, this is in kilojoules per mole degrees C,
and that's 60 degrees minus 50 degrees celsius,
and this ends up being 1.5 kilojoules per mole.
Now our H two is just that heat of melting
and that's equal to 10 kilojoules per mole.
Our H three, again, is going to be a calculation,
it's a sensible heat,
and now we use the heat capacity of the liquid,
so that's equal to 0.25 kilojoules per mole degree celsius.
And now we multiply it by the difference in temperature
from the melting point to the vapor,
the melting point to the boiling point,
which is 95 degrees C minus 60 degrees C,
and that's equal to 8.75 kilojoules per mole.
Our H four is that heat of vaporization,
again, all we have to do is look it up
and that's equal to 25 kilojoules per mole.
And finally the sensible heat of bringing the vapor
from its boiling point to the final temperature
and that's equal to 0.1 kilojoules per mole degrees celsius.
And now the difference is 110 degrees C minus 95 degrees C
and that's equal to 1.5 kilojoules per mole.
And so when we add up all of these enthalpies
we come up with our change in enthalpy for our process,
and that's equal to 46.75 kilojoules per mole.
So one thing you might note from this calculation
is the significant amount of heat
is gotten from the latent heat
as opposed to the sensible heat.
So whenever you're putting together one of these process
pass you have to be very careful
to include that phase change in your calculations.