A chemistry course to cover selected topics covered in advanced high school chemistry courses, correlating to the standard topics as established by the American Chemical Society. Prerequisites: Students should have a background in basic chemistry including nomenclature, reactions, stoichiometry, molarity and thermochemistry.
5.10 Standard versus Nonstandard Free Energy Change
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From the course by University of Kentucky
Advanced Chemistry
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From the lesson
Thermodynamics
The overarching theme of thermodynamics is the prediction of whether a reaction will occur spontaneously under a certain set of conditions. Entropy and Free Energy are defined and utilized for this purpose.
Meet the Instructors
Dr. Allison SoultLecturer
Chemistry
Dr. Kim WoodrumSr. Lecturer
Chemistry
In this learning objective we're going to be looking at the difference between
a standard delta G in a non-standard delta G.
Students are often don't see the nuances in the differences between these two
so I am going to try to help you work through
thinking about the difference between them. We know that this equation Delta
G equal delta
H minus T delta S would apply whether you are in standards state
conditions or not and standard state conditions.
What is the difference between standard state non-standard state? Well, let's
review what it means to be in standard state conditions.
That means that the pressures is at one atmosphere
and if it is a solution
then it will be 1 molar and when you look in tables for standard
value at thermodynamics there are usually at 25 degrees Celsius
but they don't have to be to be considered standard state.
Now, if we started out
every reactant and product in a reaction
in the standard state conditions. Lets say they are all gases and every gases was at
one atmosphere in there.
Not just to reactants, but your reactants and your products.
This system is very unlikely to be at
equilibrium under those conditions. So
if it's not an equilibrium that is going to proceed either to the right or is going to
proceed to the left. Now remember
if delta G standards is negative we know it's gonna go to the right to get
to equilibrium, it is spontaneous in the forward direction.
If standard GG is positive it's going to proceed to the
left in order to get to equilibrium.
The reverse reaction is spontaneous. Now if you wanted to know what standard delta
G at a temperature
other than 25 degrees Celsius then this is the equation that we would use.
You would look up in tables the delta H standard and the Delta S standard.
From that information these values don't change very much with temperature.
Delta G is very affected by temperature. So if you put those
standard delta H and standard delta S, even thought they are at 25 degrees Celsius.
You put in your temperature and don't forget to use Kelvins when you do so
then this is going to give you the standard delta G at a temperature
other than 25 degrees Celsius. If you needed delta G at 25 degrees Celsius
and its standard then you might as well just go to the tables and determine the standard
delta G for the reaction
and not use this equation. So we have a series of questions that I want you think
through in order to figure out
the connections between what is delta G standard telling you
and how does it change when you leave standard state conditions.
So I have a reaction and in this reaction chamber I'm starting with
every gas at one atmosphere.
So that's what's being represented in that picture. That is a standard a condition.
We see here that the standard delta G is a negative value
a -190.5. So if I started everything out at one atmosphere which
statement would be true?
Would the reaction shift to the right to get equilibrium, or shift to the left to get equilibrium,
or neither, it is already an equilibrium?
If you said A you would be correct.
A negative value for a standard delta G says,
and this is all it says, it is snapshots that says, if we started
everything at at 1 atmosphere this reaction would proceed
to the right because it's negative. Let's again start this system out at equilibrium.
I mean start the system out with everything in its standard state
conditions with 1 atmosphere.
So we're here. We know according to this standard delta G that if we start
everything and a standard state conditions
the reaction will proceed to the right. Now if it gonna proceed to the right.
What is going to happen to the pressure HCl?
Well if you said it will increase
you would be correct. The HC; pressure is going to go up.
These pressures are going to go down as it proceeds to the right.
So it's always going in the forward direction and reverse reaction are always happening
but more of the forward is happening then the reverse when you have a -190.5
kilojoule, we have a negative value for that standard delta G. Now as soon as it
starts proceeding to the right
my question for you is, is it still under standard state conditions?
Well no, because if the pressure is going up it is no longer one atmosphere
it is greater than one atmosphere. And if its greater than one atmosphere
then we are not under standard state conditions and this number
of - 190.5 no longer applies. It
only applies when when we are in standard state conditions.
Just to think about this,
does it really give us a good connection between standard and non-standard delay G?
What's going to happen to the total pressure on the system
as you establish equilibrium from the point
at the beginning where everything is one. Starts proceeding to the right
and it finally get equilibrium and the foreign reverse and reaction are happening at the
same rate, what is going to happen to the total pressure?
If you said stay the same, then you're correct? The pressure of
HCl is going up as it proceeds to the right. The pressure of H_2 is going down
the pressure Cl_2 is going down
because the number of moles on the left which we have two moles and gas not just
is not just moles its moles and gas
there's two moles gas in the left and there's two moles a guess on the right
then as this reaction shifts the total pressures not changing.
Okay now here is a question I really want you to think about.
When the equilibrium is finally established, ok so what's happening here?
We started everything at one atmosphere. We saw that at one atmosphere we know
that the standard delta G is negative
that tells me this reaction is going to proceed to the right to establish equilibrium
and it finally gets there. Once it
establishes equilibrium what is going to be the value
of the standard delta G. Will it increase to get equilibrium?
Will it have decreased to get to equilibrium? Or will it stay the same?
Students often miss this.
So don't feel bad if you didn't you've got to get to the
understanding of why would stay the same. A standard delta G
is a snapshot of where where it would be
if everything were at one atmosphere. So standard delta G never changes.
Its value is the - 190.5 kilojoules per mole for this reaction.
So as a reaction release these one atmosphere conditions
we no longer have a standard state condition
but the standard delta G is the snapshot of what it is when everything is that.
So don't think that your standard delta G is going to change.
Which Delta G without the circle
it certainly will change. So our next question is to think about
what is happening to Delta G. Once
you establish equilibria. Will it be positive will be negative?
Will be equal to 0. Well it you said it would be equal to 0 you are correct and that's exactly what happens.
Delta G equals zero an equilibrium.
Not standard delta G the only way
standard delta G could equal 0
is if when everything was that was at one atmosphere
this thing happened to be at equilibrium. Very, very unlikely.
Very unlikely. Well this reaction certainly isn't it had a negative value
we know it wi'll proceed to the right. We will build up more and more
of these two. We will use up some of this and some this and finally get to equilibrium.
When he gets the equilibrium, at that point
the Delta G for the reaction is no longer standard state conditions
is 0, That is true for every reaction it's Delta G is equal to 0
at equilibrium. So what happened to the Delta G?
The Delta G started out when we were all at one atmosphere
with this number. It gets to equilibrium
Delta G non-standard is equal to 0
so the negative Delta G is increasing
as the reaction keeps working its way closer and closer
to equilibrium. Now we will look at the mathematical relationship between the standard
in a non-standard delta G, there is a connection. So anytime you need in
non-standard delta G
is when you're not in standard state conditions.
We have this equation help us get to a non-standard.
So if we want to know what the reaction was at
going to proceed to the right or proceed to the left and we had conditions other than
standard state conditions
then this is the equation that we would use. The R that we use in this equation
is the 8.314 because it has the
energy unit a joule, and you actually probably have to convert it to
kilojoules before you could add those terms together.
We see that a Kelvin is here in this K and that's what we have to use for the temperature
and our Q is a reaction quotient.
The reaction quotient if we remember for reaction is just like a K
equilibrium constant. Its products and concentrations if there aqueous
pressures if it is
gases, but its products over reactants
raised to the power of their coefficients. So there's some coefficients of the
balanced equation is raised to those powers.
So that's what the reaction quotient is so
we can look at this reaction and say OK at this point in time
there is this much product, there is this much reactant. Let's put those numbers in there
and let obtain a value for a non-standard
delta G. Now if everything were 1 then Q would be 1.
And if Q is one the natural log of Q is 0 and this term goes away
and that make sense.
So we're just gonna think through this equation.
In terms of what how does change in Q affect the Delta G?
So let's start with a standard Delta G that's negative.
This means that the reaction is spontaneous in the forward direction.
if you we in standard state conditions. We put everything in a
reaction chamber
and this is kinda like our little questions that we went through
are standard delta G was negative the reaction spontaneous in the forward direction.
So the question is what would happen, we have to do, in terms of conditions?
What would we have to do in terms of Q here in order to make Delta G positive?
Well if the delta G is positive we know that it's no longer spontaneous in the forward
direction is now spontaneous the reverse direction.
How do we make Delta G positive? Well, the only way we can make delta G positive
is to make this term positive.
Well this term is positive when Q is what? How do we make the natural log of Q
be positive value? Well
if Q is greater than one
it's a value that is bigger than one then the national log of Q is positive.
That is the first thing. As long as Q is greater than 1 then when we take the natural
log it will be positive in this term
that I have circled up there is going to be a positive term. We just gotta make
positive enough.
So anytime that the products are greater than the reactants because remember what Q is?
It is products over reactants.
Remember? Raised to the power of their coefficients.
So anytime products is greater than reactants
then the Q is going to be bigger than 1 and a national log of Q will be a
positive value
and we can get it positive enough to overcome all the negative that we have here.
We can turn a reaction that was spontaneous in the forward
direction to be spontaneous instead
in the reverse direction. Well lets go through that same mathematical logic
in the revers. What if the standard up to G was positive
the reaction is not spontaneous in the forward direction
it is only spontaneous in reverse reaction direction
if everything were under standard state conditions.
So we start everything is standard state conditions. We know the reactions going to proceed
to the left. That is when a positive
means its spontaneous in the reverse direction.
What conditions would we have to have in order to make
this negative. We want this reaction proceed in the forward direction
instead of in the reverse direction. Well lets think about what has to happen to this term.
In order to make this reaction becomes spontaineous the forward direction
this term is going to have to be very negative. It is going to have to be negative enough to
overtake the positive of the standard delta G.
How can we make that term negative?
Well, the only way we can affect that term R cannot change it's always the same.
Temperature is Kelvin and there's no such thing as a negative Kelvin so the only
way we can make this term negative
is to make the natural log of Q negative.
So if Q is less than one, it is a fraction
less than 1. Then anything can you take the natural log of a number less than 1
its negative. So how do we make Q less than one?
Once again we remember that Q is products
over reactants raised to the power their coefficients.
As long as you have a lot of products so this is a big number.
and this is a small number. So products
is an smaller than the reactants and you want to have a number
less than 1 and as long as it is small enough
this natural log of Q would be negative enough that we would
have more negative than we have positive and that would make my
non-standard delta D negative and we can for force this reaction to become spontaneous
in the forward direction. Now you going to
be doing mathematics numbers for this it's not a big deal.
You just gotta watch for signs if you're given a standard delta G
and they want to know a non-standard delta G this is the equation you will pull out.
Watch you units if Delta G which is typically in kilojoules is given to you
and then we're going to have to make sure that this term gets converted
kilojoules before we convert it.
The thing you have to watch is your T and make sure it is in Kelvin.
Then you will be able to easily convert between a standard delta G
and a non-standard delta G.
So this is the enough are learning objective number 9 in which we are
seeing the connection between the Standard delta G and a non-standard delta G.
We see that they're not the same thing we have to understand their differences
and we have an equation that will help us
convert between them.
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