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Life is chaos.
The whole universe is chaos.
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Whether it's the terrible state of my office
or the slow degradation of my body into dust,
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the universe tends toward disorder.
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But why, why is the universe structured in
this terrible and callous way?
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Well, it turns out that it's not really the
universe's fault.
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If you think about it there's only one way, or at best, maybe a few ways for things to be arranged in an organized way.
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But there are nearly infinite other ways for
those same things to be arranged.
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The simple rules of probability dictate that
it's much more likely for stuff,
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whether it's the stuff on my desk or the particles
and energy that make up my concept of self,
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to be in one of the many disorganized states
than in one of the few organized states.
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It's simple math and it's unavoidable.
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So unavoidable that it is in fact our Second
Law of Thermodynamics, which says that:
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"Any spontaneous process increases the disorder
or randomness of the universe."
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Processes that don't increase the disorder of the universe require work to be done in opposition to the disorder,
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and are in fact often impossible to achieve.
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The very act of putting one system in order
requires that other systems become disordered.
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Think of it this way: Your lunch was composed
of an extremely ordered set of molecules.
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And it gave you the energy to clean up your
house, maybe.
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And it had to be broken down into less ordered
nutrient molecule for you to do that.
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Carbohydrates, proteins, and lipids, and those
molecules were broken down even further as
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they were converted to energy in your cells,
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and your body used some of that energy to
power your muscles as you cleaned your house.
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But a bunch of that energy was used to do things like keep your heart beating, and breathe, and make sweat,
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and some of that was lost to the surroundings in the form of random movement, and most importantly, heat.
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By the time you've finished your house may be orderly but the remains of your lunch molecules are all over the place.
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And that's only one of the many systems that
became less orderly while you worked.
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So yes, cleaning your house in fact increased
the overall disorder of the universe.
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Next time someone gives you a hard time about the state of your house you can tell them that.
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Obviously disorder is a pretty big deal in the universe, and that makes it a pretty big deal in chemistry.
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So scientists have a special name for it:
entropy.
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Entropy is a measure of molecular randomness,
or disorder.
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And even though people complain about
the disorder in their lives, it's not all bad news.
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Entropy helps make chemical reactions possible,
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and it helps us predict how much useful work
can be extracted from a reaction.
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We all have to live with disorder so you might
as well understand it.
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For the next ten minutes I want you to embrace
the chaos.
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[Theme Muusic]
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So what does the Second Law of Thermodynamics
mean when it says:
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"Any spontaneous process increases the disorder
of the universe."
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"Spontaneous" simply means a process that
doesn't need outside energy to keep it going.
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And it goes the other way too, anything that increases the disorder of the universe happens spontaneously.
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That doesn't mean disorderly things will always
happen though, other factors may interfere.
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The reaction to change a diamond into graphite,
for example, would be thermodynamically spontaneous.
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It wouldn't have to be forced along by outside
energy,
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but the bonds in the diamond are so stable
that essentially it never gets started.
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Lots of other chemical reactions are like
this too.
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So even though we think of "spontaneous" meaning sudden and impulsive, like the majority of mall lip piercings,
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in chemistry "spontaneous" doesn't tell you
how quickly something happens,
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it only means a reaction is thermodynamically capable of happening without outside energy to move it along.
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Though come to think of it, I imagine that spontaneous lip piercings cause a fair amount of disorder as well,
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especially upon arriving home.
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Entropy is another state function.
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It doesn't depend on the pathway the system
took to reach its current state.
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So even though we can't measure the entropy of reactants or products directly, we can calculate them.
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We can also calculate the change in entropy during a reaction exactly like we can for the change in enthalpy,
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by subtracting the sum of the reactant values
from the sum of the product values.
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In other words, the formulas look exactly
the same, just substituting "S"
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(which for some reason is used to denote entropy)
for "Delta H F".
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Notice we dropped the "Delta"s on the right
side of the formula
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because we know absolute values for entropy
of individual reactants and products.
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We keep the "Delta" on the left
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because we're calculating the change in entropy that occurs when the reactants rearrange into products.
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What the heck is this good for?
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Well, we can explain a mysterious thing, which
is how reactions occur spontaneously in nature
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even though there's no energy given off, or
even they suck energy out of the environment,
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and seem to go up the energy ladder instead
of down.
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Let's try it out with a real reaction here
on my desk -- this is one of my favorites.
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This is barium hydroxide octahydrate and this
is ammonium chloride.
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Usually we do chemical reactions in aqueous solution because most solids don't interact easily,
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but this pair is exception to that rule; they
react readily in solid form.
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This reaction absorbs a lot of heat from the surroundings, making everything around it feel cold.
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Now to show you how cold it gets, I'm going
to do something here.
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And you're just going to have to assume you
understand what I'm doing.
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"What am I doing? What is happening? Why am
I doing this? That's weird Hank.
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Why are you doing that?" And then I put that
on there.
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So now I've dumped barium hydroxide in this beaker, I'm gonna dump the ammonium chloride in.
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And now one of the by-products of this reaction is ammonia so I'm gonna have to smell that, but you don't.
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Oooh ye-eah, look at that slush.
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I think we've reacted pretty much completely here and so we should, if all things have gone properly --
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yep, that's pretty cool --- sucked enough heat out of the block of wood to actually freeze it to the beaker.
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Normally in chemistry a reaction that proceeds spontaneously and yet absorbs heat is really weird.
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Basically I have a hard time believing what
I just did.
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So what does entropy have to do with this
little freak show?
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You might think it has something to do with taking the heat from the surroundings to make the system colder,
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but while that's counter-intuitive and cool,
that's not all of it.
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You might also think that it has to do with two solids combining to form a whole bunch more liquids and gases,
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and that IS a big part, but still not all.
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To understand what we just saw a little better,
we need to put it all together.
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Let's start by finding out exactly how much heat it did absorb and what happened to the entropy as well.
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First, we'll find the enthalpy change using
Hess's Law and standard enthalpies of formation.
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We can use the coefficients from the balanced chemical equation to fill in the number of moles for each substance.
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Then we have to look up a whole bunch of numbers
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(remember, you can find tables like this online and probably in the back of your chemistry textbook too).
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When we plug the standard enthalpies of formation
into the formula and do the math,
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we find that the change in standard enthalpy
is plus 166 kilojoules.
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It's positive, which makes sense because the
reaction absorbed the thermal energy,
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enough to create about a half a kilogram of ice if it had been surrounded by water instead of air and fingers.
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Next, we'll find the entropy change: remember,
the basic equation is the same.
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We put in the number of moles from the balanced
chemical equation
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and the standard entropies from the table
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and a quick calculation tells us that the change in standard entropy is 590 joules per Kelvin.
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A positive result means the entropy of the
reaction increased,
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meaning the products were more disordered
than the reactants.
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Note that the standard enthalpy is in kilojoules while the standard entropy is in joules per Kelvin.
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The energy units should match, so let's call
the standard entropy 0.594 kilojoules per Kelvin.
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It doesn't look like much right now, but wait,
there's more.
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Those numbers don't explain why the reaction
proceeds spontaneously,
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even though it scavenges all that heat from
the environment.
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But Josiah Willard Gibbs, he found a way to
explain it, and he didn't even mean to.
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Gibbs was interested in the amount of energy in a system that was available or free to do useful work.
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Today, we call this Gibbs free energy or sometimes the standard free energy or simply free energy of the system.
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Like enthalpy or entropy, Gibbs free energy is a state function, so it can be calculated the same way.
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We simply substitute "Delta G," which stands
for Gibbs free energy, for "Delta H" or "S."
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The standard free energy of formation, written
like this,
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is the change of free energy that occurs when a substance is formed from its elements at a standard state.
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It's analogous to the standard enthalpy of formation that we use to calculate change in enthalpy.
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Like enthalpy and entropy, we can't directly
the free energy change of the whole reaction.
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So scientists created a baseline by setting
the standard free energy change of formation
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for an element in its most stable form at
standard state to zero.
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The standard free energy change of formation
for a compound, then,
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is just the difference between its standard
free energy and that baseline.
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But what if you don't know the standard free energies of formation for the products and reactants?
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Well, they're often listed in tables, but
sometimes the ones you need aren't available.
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Never fear, Willard Gibbs has an app for that.
It's actually a formula, but he figured it out.
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In 1873, Gibbs calculated that at constant
pressure and temperature,
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the change in standard Gibbs free energy for
a reaction equal the change in standard enthalpy
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minus the product of the temperature and the
change in standard entropy.
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In other words, the amount of free energy a reaction makes available to do work depends on two
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and only two things: the enthalpy change,
the amount of heat the reaction transfers,
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and the entropy change, the amount of disorder
it creates at a given temperature.
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So which is more important, the heat transfer
or the disorder? Well, it depends.
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A large change in enthalpy can determine the
direction of a free energy change,
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even if the entropy changes in the opposite
direction, and vice versa.
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If the absolute value of the change in enthalpy is greater than the absolute value of the product of the temperature
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and the change in entropy (or "T Delta S"),
then we say that the reaction is enthalpy-driven.
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this means that the flow of thermal energy
provides most of the free energy in the reaction.
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On the other hand, if the absolute value of "T Delta S" is greater than the absolute value of the enthalpy change,
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we call the reaction entropy-driven, meaning increasing disorder provides most of the reaction's free energy.
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Which type was the barium hydroxide reaction?
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Well, I'm gonna say that the temperature in here is about 25 degrees Celsius, or 298.15 Kelvin,
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because I'm awesome like that -- I can just
tell.
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When we multiply that by the change in entropy
that we calculated,
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0.594 kilojoules per kelvin,
we get a value of 177 kilojoules.
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If we compare that to the change in enthalpy
we calculated, 166 kilojoules,
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it is clear that the "T Delta S" is higher than the "Delta H", so the reaction is entropy-driven -- no surprise there.
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Even though the reaction absorbed a lot of thermal energy, this phenomenon was dwarfed by the increase in entropy.
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And this makes sense, because the balanced
equation goes from three total moles of solids,
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with their molecules locked in place, to one mole of solid, ten moles of liquid, and two moles of gas.
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This is a massive increase in disorder,
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because in addition to the fact that there are now 13 moles of particles to move around instead of just 3,
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the liquid and gas are particularly good at
moving around,
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so most of those particles are in random motion,
no longer stuck in one spot,
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causing a large increase in disorder, or entropy.
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But here's the coolest part, Gibbs formula also tells us whether the reaction is spontaneous or not.
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We know all systems tend toward the lowest possible energy state, whether its a ball rolling down a hill,
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elastic springing back into shape, or positive
and negative ions forming a bond.
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"Delta G" is a type of energy, obviously, so it spontaneously approaches the minimum possible level.
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So if the value for "Delta G" is negative, that is if the free energy decreases, the reaction is spontaneous.
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Reactions that are able to release free energy
don't need external energy to make them proceed,
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and that's the very definition of a spontaneous
reaction.
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So if "Delta G" is positive, the reaction is non-spontaneous, but the reverse reaction is spontaneous.
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If "Delta G" is zero, the reaction is in an equilibrium state and no discernible occurs in either direction.
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So what about the reaction I just did?
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Is it spontaneous at room temperature? Can
it occur without energy driving it along?
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Well, yes because we just watched it happen,
but let's do the math!
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Using Gibbs Formula and plugging in the numbers
we've calculated so far,
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we see that the Gibbs free energy for this
reaction is negative 11 kilojoules.
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It is indeed spontaneous, because it releases energy instead of requiring it in order to get started.
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The energy that was produced was used to rearrange
the bonds in the reactants,
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to make smaller product molecules, to break
attractions between molecules,
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and to push some of the particles apart from
solid form into liquid and gas form,
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which increased the entropy of the system.
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So even though the reaction absorbed a lot of thermal energy, it didn't NEED that energy to make it proceed,
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because the large change in entropy alone
was enough to keep things moving along.
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So Gibbs formula confirms our earlier results with just one little subtraction -- pretty smart guy.
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And now, some of his smartness has been transferred
into you,
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now that you've watched this episode of Crash
Course Chemistry.
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If you paid any attention, you learned:
00:12:41
that it's hard to stay organized because there
are so many ways to be disorganized,
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that the second law of thermodynamics says
disorder, or entropy, happens everywhere,
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and that the change in entropy ultimately depends on how much room molecules have to move around in,
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how much heat heat energy they have to give off in reactions, and the temperature around them.
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You learned about Josiah Willard Gibbs and his formula to calculate the Gibbs free energy for a reaction,
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that both entropy and Gibbs free energy are
state functions,
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and that the sign of the Gibbs free energy
tell us whether or not a reaction is spontaneous.
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This episode of Crash Course Chemistry was
written by Edi Gonzalez.
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The script was edited by Blake de Pastino, and our chemistry consultant was Dr. Heiko Langner.
00:13:20
It was filmed, edited and directed by Nicholas Jenkins. Our script supervisor was Caitlin Hofmeister.
00:13:25
Our sound designer is Michael Aranda, and
our graphics team is Thought Cafe.
