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visit MIT OpenCourseWare at ocw.mit.edu. CATHY DRENNAN: So
now, we're going to move on to talk about
spontaneous change. And so this is today's handout. So spontaneous
reaction is a reaction that proceeds in the
forward direction without any kind of
outside intervention, like heat being
added, for example. It just goes in that direction. So we can talk about
the following reactions are spontaneous at
constant pressure. And we'll see later
that temperature can make a difference between
whether something's spontaneous or not. But constant pressure, here's
an example, iron plus oxygen. And what is this in
layman's term an example of? AUDIENCE: Rust. CATHY DRENNAN: Rust, yes. And many of you are
probably aware of this, rust is a spontaneous process. It's something that people
try to do something about. You don't want your car to rust. If you're new to New
England and you're from a part of the country
that doesn't get so cold, you'll look at people's
cars and you're like, wow, look at all that
rust all over them. Yes, rust happens,
especially in New England. And delta H here is negative. Is this endothermic
or exothermic? AUDIENCE: Exothermic. CATHY DRENNAN:
Exothermic, minus 824. Here is another
spontaneous process. This molecule is ATP. And it will hydrolyze, which
means react with water, forming ADP. So ATP is triphosphate. ADP is diphosphate. So one of the
phosphates-- and here's the phosphate-- comes off. It hydrolyzes off. And this is a
spontaneous process. And we also have a delta H0 of
minus 24 kilojoules per mole. And remember, when we
oxidize glucose in our body, we store that energy in ATP. And we want that
ATP to be around. And then when we break ATP
apart, it releases the energy. So this is a very important
biological process. And you have a negative
value, exothermic reaction. But there's a few other examples
of spontaneous reactions. One of them is this one. And we've probably
all experienced this. If you're from New
England, you've seen snow melt or ice
melt, solid to liquid. If you're from a hot
part of the world, you probably had ice cubes in
your nice, refreshing drink with maybe a little
umbrella on the top. Anyway, everyone, I
think, has seen ice melt. But here, delta H0
is of positive value. It's endothermic. Also, if you have
ammonium nitrate, this will just come apart
in a spontaneous reaction. Delta H here is plus
28 kilojoules per mole. So is delta H the
key to spontaneity? It is not-- plays
into it, but it is not the determining factor. So if delta H0 is not the
key to spontaneity, what is? It is free energy, yes,
particularly Gibbs free energy, or delta G. And I'm
really happy they decided to add the Gibbs free energy,
because another thing of energy would be a lot. So having this free energy
having abbreviation of G, I think is a good thing--
so Gibbs free energy. So Gibbs free energy
depends on delta H. But it also depends
on another term, which is T delta S-- temperature
and delta S, change in entropy. So delta G is the predictor
of whether a reaction will go in the forward direction in
a spontaneous fashion or not. So let's just think
about the sign of delta G and what it means. So again, at constant
temperature and pressure here, delta G less than
0, negative delta G, is that spontaneous or not? AUDIENCE: Spontaneous. CATHY DRENNAN: Spontaneous. Positive delta G is not
spontaneous, non-spontaneous. And delta G equals 0. It's one of the other things
that I am very fond of, which is equilibrium. So delta G indicates whether
something is spontaneous or not. Negative value, spontaneous
in the forward direction. Positive value, not spontaneous
in the forward direction. And equilibrium, the thing we
all try to reach in our lives. So let's look at an
example and calculate what delta G is going to be. So we saw this equation already. We have a positive delta H0. And now, I'm telling you
that delta S0 is also a positive value. So we can use this equation. And this is really one of
the most important equations in chemistry. Figuring out this equation was
really a crowning achievement. And you'll be using it a lot. Not just in this
unit, but pretty much in every unit from now on, you
will be using this equation. So room temperature, pretty much
we're not doing-- occasionally, we'll do something not
at room temperature, but we like room temperature. And we like it in Kelvin. So delta G0, so we plug
in our delta H value. So it's going to equal delta
H minus the temperature. And if the temperature
isn't given in a problem, you can assume that it's 298. And now we need to
plug in delta S. But I left a blank here
to make a point, which is that delta S's are
almost always given in joules per kelvin per mole. But everything else is
given in kilojoules. So you want to make sure
you convert your units, or you're going to come up with
very funky answers at the end. So from joules to kilojoules,
so now plus 0.109 kilojoules per kelvin per mole. And we can do this out now. So we have plus 28 minus 32.48. And why don't you tell me
how many significant figures this answer has. 10 more seconds. So at least some
people got it right. We've identified once
again a weakness, so rules of adding and subtracting. So we have 28 here minus 32. There are no significant figures
after the decimal point here. So we're just left with 4. So when we're doing
multiplication or division, we consider the total number
of significant figures. But with addition
and subtraction, you gotta pay attention to
where the decimal point is. And when we get into the
next unit, there are logs. And those have special rules
of significant figures. Yes, very exciting. So delta G0 is negative here,
although delta H is positive. So this reaction is spontaneous. It's not hugely. It's a pretty small number,
but still, it's spontaneous. So let's consider
our friend over here that we've been talking
about-- glucose being oxidized to CO2 and water. You practically should
have the delta H memorized for that at this point. Now, I'm telling you
what the delta S0 is. And it's positive 233
joules per kelvin per mole. And we can plug this
into our equation to calculate a delta G0, again
remembering to convert joules to kilojoules to do this. And so now, we see that it has
a very negative delta G0 here, minus 2,885 kilojoules per
mole at room temperature. So at room temperature,
this reaction is spontaneous but slow. We saw that with the candies
that had glucose in it. We opened them up,
and no water or CO2 were obviously being
liberated in this reaction, because it is slow. And now, a clicker question. I want you to tell
me whether it would be spontaneous at different
temperatures or not? 10 more seconds. Yep. So it is spontaneous
at all temperatures. Not all reactions
are, but this one is. So if we go back
here, the reaction is spontaneous at
all temperatures. And that's because,
to be spontaneous, you want a delta
G that's negative. If delta H is negative
and delta S is positive, then you'll have a
negative minus a negative. So it doesn't matter
what temperature is. This will always yield
a negative delta G0. So other reactions, that
might not be the case. But if you have negative delta
H and a positive delta S, it will be spontaneous. So negative delta H, again,
exothermic, heat release. And a positive entropy
is a favorable thing. Entropy is always increasing. So if this reaction has
increased in entropy, it will be much more
likely to be spontaneous. So let's talk about entropy. So entropy is a measure
of disorder of a system. Delta S is the
change in entropy. And delta S, again,
is a state function. So one example of
entropy in New England are these stone walls that do
not look absolutely beautiful. There are often stones
falling everywhere. And it doesn't matter if these
stone walls that were probably built in 1600s or 1700s in
New England fell totally apart and were rebuilt, now we just
care about how the wall is compared to the way it started. So delta S, again,
is a state function. It doesn't depend on path. And so if you get
out and walk around and go like on the
Minuteman Trail and see some of the
historical sites where Paul Revere rode his horse
along a lot of stone walls, there's a New England
poet who writes about this, Robert Frost. And he said, "something there
is that doesn't love a wall." And that something is entropy. AUDIENCE: [LAUGHTER] CATHY DRENNAN: Entropy
does not love a wall. Entropy does not like order. Another example, those of you
who are learning more about me as a person know that
I am a fan of dogs. This is my dog Shep. Shep does not like going to
the groomers, does not like it. And I think that this is because
he's been at my office hours and he knows that increasing
entropy is favorable, decreasing entropy is not. And he says, really,
this violates the laws of thermodynamics,
what you're doing to. Me and you should
cease and desist. But anyway, he
still get haircuts. So entropy, again,
is this measure of disorder of a system. You have a positive
delta S, which is going to be an
increase in disorder. And a negative delta S is going
to be a decrease in disorder. And disorder, you
can be thinking about this as internal degrees
of freedom in your molecule, thinking about
this as vibrations. All sorts of
different things can lead to increase or
decrease in entropy. But we often think
about changes in entropy depending on if the reaction
is changing in phase. So gas molecules have
greater disorder than liquid. And liquid has greater
disorder than solids. And so a solid has all
its molecules lined up. And liquid can move
around a little bit more. But gas really can
spread all out. So in terms of entropy
and changes in entropy, we can think about the phase
change that's happening and even predict if
something's going to be an increase in entropy or not. So let's just look
at one example. So without a calculation,
predict the sign of delta S. And this is a clicker question. Let's just take 10 more seconds. And can our demo TAs come down? Yep, good. So you predicted positive,
which is the correct answer. And so here, we're going from
a liquid to a liquid and a gas. And so going to the
gas, that will increase the disorder of the system. So delta S will be positive. So now, we're actually
going to do a demo of this particular reaction. And so we have
hydrogen peroxide, which can just be bought at
a CVS or local drugstore. And it will go to liquid
water and also oxygen gas. And so how do you see a gas? And you can see it by putting
it in with soap bubbles. So as bubbles of oxygen
form, the soap bubbles will bubble out. And so you can see it. And you can also add
some kind of food color. And we have yeast as
a catalyst to make it go a little bit faster. So let's see if we can
actually see disorder increase. I don't want the mic. If you want to just say-- if you
want to talk at the same time, here's a mic. AUDIENCE: I might do that. CATHY DRENNAN: You're
not going to do that, OK. AUDIENCE: Yeah, we will. CATHY DRENNAN: Oh, you do. OK. AUDIENCE: Is this on? This on? Yes, it is. OK, great. So what we have going on here
is we've got this container. It's filled with water. And what I did was I added
about 4 teaspoons of yeast. The yeast, as Cathy said, is
going to act as a catalyst. It's actually a
biological species. It's a living species
that's actually going to catalyze this reaction. What Erik is doing is Erik is
pouring some hydrogen peroxide. He added some soap. So as you see in the
reaction, the H2O2 is going to break down
into water and gas-- the gas being oxygen. And what we don't
want to happen is we don't want just
the gas to escape, because then you
guys can't see it. So what Erik is doing right
now is he's adding some soap. The soap is actually going
to catch, if you will, the escaping gas and
turn it into a foam. And what we should
be able to see is the foam kind of escape
from this container. You ready? OK. So hopefully, this will work. We should put on our goggles. [LAUGHTER] Smells really bad. OK, ready? And-- get out of
there, look at that. Hey! Wow, that worked a
lot better than we thought it was going to work. CATHY DRENNAN: And
so this is sometimes called the elephant
toothpaste demo, because that is sort of, if
you were an elephant, what you would probably be brushing
your teeth with, I don't know. Yes. So this is-- [APPLAUSE] --entropy increasing. So let's just see
if we can quickly talk a little more about
entropy and then we'll end. So entropy of reactions
can be calculated from absolute values. And again, we can use
this equation here. So we have a delta S for
a particular reaction, can be calculated
from the delta S's of the product minus reactants. So again, we have
products minus reactants. The absolute value, or
an absolute delta S, S equals 0 for a perfect crystal
at a temperature of 0 kelvin. You never really talk
about S by itself. It's always really
delta S. And S of 0, this is like the saddest
thing for a crystallographer, because you know
you're never going to have a perfect crystal,
even if you go to 0 kelvin, I feel like at least
experimentally. So S equals 0, to me
that's kind of sad. So if we just put in for this
reaction that we just did, we can put in our values here. And we can put in we're
forming liquid water. And we're forming O2 gas. And we're using two molecules of
hydrogen peroxide-- H2 O2 here. And so now, we can calculate
what that delta S0 is. And it's a value of 125
joules per kelvin per mole. So again, products, water
and gas, minus reactants, pay attention to
the stoichiometry, and you can get
your delta S value. And why is it positive? Again, we already
talked about this. It's because it's going from
liquid to a liquid plus a gas. And then, if we plug
these values in again to see if it's
spontaneous, we can use this equation and
plug in our values, making sure we change our units. And we can see that, in fact,
this is a spontaneous reaction, because it's negative here. But you already knew
that, because you watched it go spontaneously. So most of the time,
you can't do the demo. So then you can use this
awesome equation right here. So that's where we're
stopping for today. And we'll see you all on Friday. So if you take out your Lecture
16 notes, the bottom of page 3, we had an example about
the melting of ice at room temperature. So we did a little demo for you
at the end of class last time and calculated that
the reaction was spontaneous for
hydrogen-- hydrogen peroxide is pretty reactive. And we watched the O2 bubble go. And we did that calculation. So we're thinking
about, not just delta H, but we're thinking
about delta S. And we're now thinking
about delta G as well and how they all play together. So when we started
last lecture, we had talked about the fact
of some reactions that were spontaneous where
delta H was negative, where it was exothermic,
where heat was released. But then we also
gave some examples where delta H was
positive and said, but these are also
spontaneous reactions. We all know that at room
temperature ice will melt. We know that that's a
spontaneous reaction. But the delta H
for that reaction is actually a positive value. It's an endothermic reaction. So when we're thinking
about these reactions and spontaneity, we have to
be thinking about delta G, no just delta H. And delta G has
to do with delta H and delta S. So sometimes, delta S
is the driving force behind whether a reaction
is going to be spontaneous. Whether the delta G will
be negative or positive, delta S is making
that determination. So we can calculate what
a delta S for reaction is if we know the entropy
values for the products. And it's the sum of
the entropy values for the products minus
the sum for the reactants. So when we're doing
heats of formation, we also had products
minus reactants. But we have one exception
to this products minus reactant rule, and
that's when we're using what? What thing are we going to
do reactant minus products? AUDIENCE: Bond-- CATHY DRENNAN: Bond? AUDIENCE: Bond enthalpy. CATHY DRENNAN: Enthalpy, right. But here, we're products
minus reactants. So we can plug those numbers in. Our product is our liquid water. Our reactant is our
solid water, or our ice. And we can calculate what the
delta S0 is for this reaction. We can put in our values. And we get a positive
value, positive 28.59 joules per kelvin per mole. And delta S's tend
to be in joules. Everything else
is in kilojoules. So keep that in mind. And why do you think this
reaction has a positive value? Why is delta S greater than 0? What would be your
guess for that? What's happening? AUDIENCE: [INAUDIBLE]. CATHY DRENNAN: Yeah, so we're
going from a solid to a liquid. So we're increasing the
internal degrees of freedom. The molecules of water can
move around more in a liquid than they can in a solid. So this is increasing the
disorder of the system. You're increasing entropy here,
because the water molecules can move around more. There's more freedom of motion. So delta S is positive. It's increasing. And then we can use that
to calculate delta G0, Gibbs free energy. We can plug in our delta H
value minus T, room temperature, times delta S, which we
just calculated, making sure that we convert from
joules to kilojoules. And then our units will
be kilojoules per mole. And here, delta G0
is a negative value. So it is spontaneous. We all know it's spontaneous. We've observed this happening. So even though delta
H0 is positive, it's an endothermic reaction. Ice melts at room temperature,
because the delta G is negative. So let's talk a little
more about delta G. So let's talk about
free energy of formation and the last page
of this handout. So free energy of
formation, delta G sub f. And so this is analogous
to delta H of formation-- so the change in
enthalpy of formation. So again, when you have
a little value here, this is standard Gibbs free
energy of formation for the f here. And that's the
formation of 1 mole of a molecule from its
elements in most stable state and in their standard states. So we can have tables in
your book of these values. So your book, in the back,
if you haven't explored, the back of your book gives
lots of tables of things, including information about
delta G's and delta H's and bond enthalpies and
all sorts of other things. Redox potentials, we
haven't talked about yet, lots of tables. So you can look this up. Or if you have
already, say, looked up your delta H of formation, you
can use this handy equation-- delta G equals delta
H minus T delta S. But if we plug in our
delta H's of formation, we can get our delta
G's of formation. So how you're going to
calculate delta G of formation depends on what
information you're given. So let's think a
little bit about what it means for particular
delta G's of formation-- if they're positive or
if they're negative. So let's look at an example. And we saw this before. This is the formation of
carbon dioxide from elements in its most stable state, which
is graphite carbon and O2 gas. So these are the elements
in their most stable state, forming CO2. Now, I'm telling
you that the delta G0 is minus 394.36
kilojoules per mole. And we can think about what
this information tells us, that this is a fairly
large negative number. So if delta G of
formation is less than 0, what's going to be
true thermodynamically? And this is a clicker question. Let's just take 10 more seconds. Interesting. So let's think about
why this is true. This might be a deciding
clicker question. We'll see. So if it is negative
value for delta G, a negative value
for delta G means that it's spontaneous in
its forward direction. So here, the formation from the
elements in their most stable state, if this is spontaneous
in the forward direction, it also means that
it's non-spontaneous in the reverse direction. That means once CO2
forms, it's going to be stable compared to the
elements from which it came, because it's non-spontaneous
going in the reverse direction, or at least that's the way
that I like to think about it. So relative to its elements,
it's stable-- spontaneous forward, non-spontaneous
in reverse. So this is kind of
bad news for us, because there's too much CO2
in our environment right now. It's a greenhouse gas. And wouldn't it be awesome if
we could just encourage it all to go back to its
elements, form more oxygen, which we could breathe. How lovely? Make some nice graphite. Maybe compress it,
make some diamonds. But no, it is quite stable
compared to its elements. So CO2 is in our environment
causing global warming. And it's going to be hard
to solve that problem, not easy to solve that problem. So this is unfortunate news
that thermodynamics gives us. So then we can
look at the other. If you have a positive value
for delta G of formation, then it's
thermodynamically unstable compared to its elements. So it's spontaneous going
in the reverse direction. So it's unstable. So thermodynamics tells
us whether something is stable or unstable. And kinetics tells us
about whether things will react quickly or not. So something can be
kinetically inert-- it might take a long time to react. But thermodynamics tells
us stable, unstable. So thermodynamics is great,
but it doesn't tell us anything about the rates of reactions. So nothing about the
rates, and that's kinetics. So really thermodynamics
and kinetics are very important for
explaining reactions. And we'll talk about
more kinetics at the end. So to calculate a
delta G for a reaction, it depends, again,
what you're given. You can sum up the delta G
of formation of your products minus your reactants. Or you might use this. You'll find yourself
using this equation a lot. This, again, was a crowning
achievement of thermodynamics, that delta G equals delta H
minus T delta S. So, again, whatever information
you're given, you can use that to
find these values. So we're not done
with this equation. We're going to switch handouts. But we're going to continue
with that exact same equation.
