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PROFESSOR NELSON: Well, so last
time we did a little bit more

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work on thermodynamic cycles,
and basically went around a

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cycle and looked at some state
functions, delta u and delta H.

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Saw that around a closed
cycle those zero because

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they're state functions.
 

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So if you start and end at the
same place, they've got end at

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the same place that
they started.

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There's no change in them, and
then we also looked at some at

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non-state functions, work and
heat, and saw that those aren't

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zero going around a cycle.
 

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Of course you can do work in
a cyclic process, and heat

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can be exchanged with the
environment at the same time.

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So we calculated
those values too.

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And we also looked at this
other funny function that's

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our special function.
 

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We looked at this
integral dq over T.

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It's so special that we called
this derivative dS, and saw

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that at least for the cycle we
looked at, it also behaved as

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a state function behaves.
 

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That is, going around the
cycle, it had no net

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change, and we'll see
this come back later on.

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Then we went on to look at
thermochemistry, and that's

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what I want to continue today.
 

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So really, the main result that
we saw last time is that we can

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describe the enthalpy of
reaction, so if we have

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reactants going to products,
and we'd like to know our heat

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of reaction or enthalpy of
reaction, remember it's a

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constant pressure as we're
considering it, so it's

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equivalent to heat of reaction,
than the way we can do this is

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construct a cycle where we're
going to express these in terms

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of their constituent elements.
 

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We're going to all the
way back to the atoms.

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Right, so if we have the
elements in their standard

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states, that is their most
stable forms at room

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temperature and pressure, then
what we're really doing is

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we're saying let's take the
reactants and let's pull them

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all apart into their separate
elements, they're

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separate atoms.
 

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And then put them back together
this way, and we'll calculate

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the enthalpy of this process,
the enthalpy of this process.

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It's a cycle, so that'll
give us the enthalpy of

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reaction, all right?
 

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So this delta H is our sum
for delta H of formation

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for the reactants, right.
 

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And this is our sum of
the quantity for the

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products, right.
 

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And in this way, then we can
express our delta H of reaction

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is just going to be given a sum
of the heats of formation or

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the difference between the
heats of formation of

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the products and the
reactants, right?

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Now, of course, we have to
weight this by the number of

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moles of each reactant to
each product involved

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in the reaction.
 

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So to write this a little more
carefully, it's, you want to

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write the sum over i of nu i
delta H naught of formation of

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i summed over the products.
 

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This is per mole minus sum over
i, nu i here over the reactants

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in the same quantity.
 

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Delta H per mole f i, right?
 

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So in other words, were taking
each of the products and we're

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going to weight them by their
stoichiomeric coefficients, and

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we're going to have in this
delta H of reaction their heats

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of formation, and then we're
going to have the negative

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heats of formation of the
reactants, because that's

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being subtracted, okay?
 

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So, just to go through a basic
example, let's just look

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at the burning of methane.
 

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So we've got methane gas,
combining with oxygen gas, so

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you have carbon dioxide gas
and liquid water, and we'll

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consider the whole thing at
room temperature and

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pressure, right.
 

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So let's just undertake
this set of processes.

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Let's decompose these
to the elements.

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So in other words, our methane
gas, we're going to write the

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chemical equilibrium between
this and the solid carbon.

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That is to say let's specify
graphite, it's not diamond,

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right, graphite is the stable
form of carbon at room

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temperature and pressure.
 

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And then, hydrogen gas two
moles of hydrogen gas and

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we're going to have a
delta H of formation.

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This is for CH4 in the
gas phase, right?

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And then over here, we have our
oxygen but 2 O2 gas going to,

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well 2 O2 gas -- the point is
oxygen already is in it's

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stable form at room temperature
and pressure, right?

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That is the elemental form of
oxygen, of course, is as oxygen

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molecules in the gas so there's
no delta H formation

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for oxygen.
 

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The gas is zero, right.
 

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And then second phase of this,
now we're going to take the

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elements that we've produced,
and we're going to put them

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back to make products, right?
 

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So there we've got carbon as
graphite, and a solid plus

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an oxygen gas goes to
make CO2 gas, right.

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And we've got our positive
delta H of formation

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associated with that.
 

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And finally we've got hydrogen
gas plus oxygen gas giving us

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two water molecules and this is
in the liquid phase, and

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there's some delta heat of
formation associated

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with that, okay.
 

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So there is our set of
individual processes that's

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going to constitute
our cycle, right.

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If we take the combination of
all those, which is to say we

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just take both steps in this
cycle, then we'll have our net

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reaction, which is to say
we'll have this, right.

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So what that says is our heat
of reaction is our heat of

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formation per mole
of CO2 gas, right.

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Plus 2 times the heat of
reaction or heat of formation

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per mole of liquid water
minus heat of formation per

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mole of methane, right.
 

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And things we can
easily look up.

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So in a simple way, we can
determine, we can calculate

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what the heat of reaction is
for something like this, right.

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And you'll see in the back of
your book, you'll see

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moderately extensive tables of
heats of formation, and if you

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go online you'll see, you can
find extremely extensive

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tabulated values of heats of
formation, that have been

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measured for an enormous
number of compounds.

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And from that, then you can
look at enthalpies of reaction

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for countless numbers
of reactions, right.

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So by using the tabulated data,
we can really determined heats

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of formation for most reactions
that you might contemplate, OK?

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Of course, the cyclic steps
that we've taken to do this

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apply not just for breaking
down reactants and product into

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the elements in their standards
states, but of course we could

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also look at whole sets
of reactions and write

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cycles as well, right.
 

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So for example, if we wanted to
look at the reaction of

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something like carbon graphite
plus oxygen gas to make carbon

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monoxide gas, well normally
this isn't the way the

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reaction would work.
 

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Normally if you just tried to
make this happen what you

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would wind up with the
CO2, not CO, right.

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But one way to approach this
is you could look at the

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individual reactions of going,
you could go to CO2 and then

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you can go with CO2 and oxygen
and combine, or combine CO and

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oxygen to get CO2, right?
 

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So normally, CO2 is formed,
but you could calculate

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the heat of reaction.
 

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Of course you could go back to
the elements, but you can also

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say well, let's just take a
known heat of reaction for, or

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heat of formation for CO2, and
then also combine that with the

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heat of reaction for CO plus
oxygen forming CO2 and

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determine this that
way, all right,

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OK, so once you have done this,
once we've got the heat of

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reaction then there are a few
simple results that are useful.

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One is we know immediately
whether when we run a reaction

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heat is going to be released
in the process out to the

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environment, or whether heat is
going to be taken in, right.

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So, and of course if you ever
used a hot pack or a chemical

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hot pack or cold pack, you've
seen examples of the two of

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those, where the constituents
are selected to give you

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either heat released or
heat taken up, right.

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So in particular delta H of
reaction less than zero, that

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means a negative amount
of heat, which means that

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heat is released, right.
 

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Yes, that is it's exothermic.
 

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Positive enthalpy of reaction,
which is to say a heat

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of reaction is positive.
 

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Remember the way we define heat
is positive it means that there

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is heat that is coming from
the environment into

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the system, right.
 

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In other words heat is
absorbed or taken up by

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the reacting system.
 

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That's endothermic, okay.
 

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All right, one more important
aspect of this that we need to

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be able to deal with, and that
is the heats of formation that

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you'll find tabulated typically
are going to be given for room

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temperature and pressure.
 

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And it's very common that you
might want to know the

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thermodynamic condition for
reactions, especially at other

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temperatures, very
common, of course.

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And it's not hard to see how
the heat of reaction at room

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temperature can be related
to they heat of reaction

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at other temperatures.
 

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So let's just look at that.
 

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So remember your fundamental
relation, dH, if you write that

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as a function of temperature
and pressure, partial of H with

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respect to T, constant
pressure, dT, plus partial of

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H with respect to p at
constant temperature, dp.

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But if we're working
at constant pressure

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then dp is zero.
 

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So we just got the derivative
with respect to temperature.

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That's our heat
capacity, right, Cp.

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And we may have tabulated
values of Cp for an enormous

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number of materials.
 

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So now, if we look at the
temperature dependence of delta

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H for reaction, really what
we're going to need to do is

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look at how that heat capacity
changes going from reactants

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to products, right?
 

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So in other words, d delta
H of reaction, with

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respect to temperature.
 

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That's what we want
to find out, right?

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So how does delta H change if
we change the temperature?

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Well, it's just given by Cp
dT for the reactants and

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00:15:59 --> 00:16:01
the products, right?
 

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00:16:01 --> 00:16:03
For the products minus the
reaction, that is it's

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delta Cp, we need the
sum over the products.

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00:16:15 --> 00:16:33
Nu i, Cp i minus same sum over
reactants, i, nu i Cp i, right.

207
00:16:33 --> 00:16:37
Similar to what we saw before.
 

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00:16:37 --> 00:16:44
Now we need to
integrate, right.

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00:16:44 --> 00:16:51
So if we integrate between some
pair of temperatures, T1 and

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T2, we do this and we have this
quantity, d delta H of reaction

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00:16:57 --> 00:17:02
with respect to temperature,
dT, all this is at

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00:17:02 --> 00:17:05
constant pressure, right.
 

213
00:17:05 --> 00:17:11
Let's just be careful
to specify that.

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00:17:11 --> 00:17:21
Well, so of course, this is
then just delta H of reaction

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00:17:21 --> 00:17:27
at T2 minus delta H
of reaction at T1.

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00:17:27 --> 00:17:28
This is looking good.
 

217
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This is what we want to get,
is our heat of reaction at

218
00:17:30 --> 00:17:33
some new temperature T2.
 

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If we already know it at some
initial temperature, usually

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00:17:35 --> 00:17:36
room temperature, T1.
 

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00:17:36 --> 00:17:40
 


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00:17:40 --> 00:17:44
And it's just given by
the integral from T1

223
00:17:44 --> 00:17:47
to T2 of delta Cp dT.
 

224
00:17:47 --> 00:17:50
 


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00:17:50 --> 00:17:55
Now in general, this is as far
as we can go, but at least if

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00:17:55 --> 00:17:59
the temperature change isn't
too big, for most materials

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that heat capacities doesn't
depend very strongly on

228
00:18:02 --> 00:18:04
temperature, right.
 

229
00:18:04 --> 00:18:08
If you take some material, and
you measure its heat capacity,

230
00:18:08 --> 00:18:10
right, how much heat do I have
to put into it in order to

231
00:18:10 --> 00:18:14
change its temperature
by a degree, right.

232
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And I make that measurement
at room temperature.

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And then maybe I raise the
temperature to whatever, room

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00:18:20 --> 00:18:23
temperature, maybe 20 degrees
hotter than room temperature.

235
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And I again say OK, now how
much heat do I need to raise

236
00:18:27 --> 00:18:30
this thing's temperature
by 1 degree?

237
00:18:30 --> 00:18:33
The amount of heat I need to
put in to do that is not very

238
00:18:33 --> 00:18:36
different from what it was
at room temperature right.

239
00:18:36 --> 00:18:37
In other words the
heat capacity didn't

240
00:18:37 --> 00:18:39
change very much.
 

241
00:18:39 --> 00:18:45
So, the result of that is that
at least for modest temperature

242
00:18:45 --> 00:18:50
excursions, it may be the case
that we can simplify this and

243
00:18:50 --> 00:18:54
simply say it's just the
difference in heat capacities

244
00:18:54 --> 00:18:56
times the temperature change.
 

245
00:18:56 --> 00:18:59
Again, we can't always
be assured of that, but

246
00:18:59 --> 00:19:05
it's often the case.
 

247
00:19:05 --> 00:19:14
Any questions on any
of this so far?

248
00:19:14 --> 00:19:19
OK, now what I want to do is
just describe a little bit of

249
00:19:19 --> 00:19:22
how do you measure all
this stuff, right?

250
00:19:22 --> 00:19:26
So what we've done so far is
just lay out in principle how

251
00:19:26 --> 00:19:29
we should describe heats of
reaction, and of course

252
00:19:29 --> 00:19:31
assuming that we've got
everything in tables we can

253
00:19:31 --> 00:19:33
always look them up, but
sometimes you want to make

254
00:19:33 --> 00:19:36
new compounds, right.
 

255
00:19:36 --> 00:19:39
Sometimes you'd like to know
what the energetics are

256
00:19:39 --> 00:19:42
involved there, right, and so
it's useful to be able to

257
00:19:42 --> 00:19:46
actually measure something.
 

258
00:19:46 --> 00:19:48
So how do we do It?
 

259
00:19:48 --> 00:20:15
This is what's
called calorimetry.

260
00:20:15 --> 00:20:25
So we're going to make
measurements to determine

261
00:20:25 --> 00:20:27
heat of reaction values.
 

262
00:20:27 --> 00:20:30
Actually, calorimetry is used
for all sorts of things.

263
00:20:30 --> 00:20:34
It can be used to determine,
for example, the energetics

264
00:20:34 --> 00:20:35
of phase transitions.
 

265
00:20:35 --> 00:20:37
Maybe you're not looking at a
reaction, but you've got some

266
00:20:37 --> 00:20:39
new compound, and you're
looking at it go from

267
00:20:39 --> 00:20:42
liquid to solid or to gas.
 

268
00:20:42 --> 00:20:45
And you can see what the
heat involved in a process

269
00:20:45 --> 00:20:48
like that is as well.
 

270
00:20:48 --> 00:20:50
So what happens?
 

271
00:20:50 --> 00:21:01
Well, the objective in the
case of a reaction, we have

272
00:21:01 --> 00:21:09
reactants at some temperature
going to products at that

273
00:21:09 --> 00:21:13
temperature, and that is our
heat of reaction at

274
00:21:13 --> 00:21:14
that temperature.
 

275
00:21:14 --> 00:21:18
That's how it's defined, right,
at constant temperature.

276
00:21:18 --> 00:21:23
OK?
 

277
00:21:23 --> 00:21:25
What do we actually measure?
 

278
00:21:25 --> 00:21:31
Well, what we can really do is
we can put the reactants in

279
00:21:31 --> 00:21:37
some container, put the whole
thing in an insulated place,

280
00:21:37 --> 00:21:40
you know, hold things in
a big insulated box.

281
00:21:40 --> 00:21:42
Run the reaction.
 

282
00:21:42 --> 00:21:44
Maybe it produces heat.
 

283
00:21:44 --> 00:21:47
If it does, then the whole
thing will heat up, right?

284
00:21:47 --> 00:21:52
The stuff that's inside the
reacting volume, and whatever's

285
00:21:52 --> 00:21:55
right around it there inside
the big box, it's all

286
00:21:55 --> 00:21:56
going to heat up.
 

287
00:21:56 --> 00:21:58
So I'll start at some
initial temperature, T1.

288
00:21:58 --> 00:22:01
I won't end up at the
same temperature.

289
00:22:01 --> 00:22:02
It'll be hotter.
 

290
00:22:02 --> 00:22:03
How much hotter?
 

291
00:22:03 --> 00:22:06
Well, that depends on how
much heat was produced.

292
00:22:06 --> 00:22:08
So in principle, if I measure
how much hotter, I can

293
00:22:08 --> 00:22:11
determine how much heat was
produced, and from that,

294
00:22:11 --> 00:22:15
I should be able to
calculate delta H at T1.

295
00:22:15 --> 00:22:24
So let's think about how
that's really working.

296
00:22:24 --> 00:22:35
I've really got reactants at
T1, plus a calorimeter at T1,

297
00:22:35 --> 00:22:39
and I'm going to end up with
products -- well let's let

298
00:22:39 --> 00:22:46
me just write that's over.
 

299
00:22:46 --> 00:22:48
In fact, let's start by just
putting a little sketch

300
00:22:48 --> 00:22:50
of the whole thing up.
 

301
00:22:50 --> 00:23:00
So here's my reacting stuff,
maybe it's a liquid.

302
00:23:00 --> 00:23:02
It's going to take
place in there.

303
00:23:02 --> 00:23:04
It's going to be a constant
pressure, it might be open to

304
00:23:04 --> 00:23:06
the air, or even if it isn't,
there might be plenty of room,

305
00:23:06 --> 00:23:09
and it's a liquid anyway, so
the pressure isn't going

306
00:23:09 --> 00:23:11
to change significantly.
 

307
00:23:11 --> 00:23:18
I want to measure
the temperature.

308
00:23:18 --> 00:23:23
And the whole thing
is insulated right.

309
00:23:23 --> 00:23:26
I don't want to have to deal
with heat escaping to the

310
00:23:26 --> 00:23:28
outside environment in a way
that might be difficult or

311
00:23:28 --> 00:23:32
complicated to measure
or calculate.

312
00:23:32 --> 00:23:37
OK, so this, what I've sketched
here would be a constant

313
00:23:37 --> 00:23:39
pressure calorimeter.
 

314
00:23:39 --> 00:23:40
There's a reaction.
 

315
00:23:40 --> 00:23:42
Normally this is used for a
reaction in the condensed

316
00:23:42 --> 00:23:45
phases and liquid usually.
 

317
00:23:45 --> 00:23:58
So this is a constant
pressure calorimeter.

318
00:23:58 --> 00:24:01
It's set up to be
well-insulated so

319
00:24:01 --> 00:24:03
it's adiabatic.
 

320
00:24:03 --> 00:24:04
That's the set up.
 

321
00:24:04 --> 00:24:06
We're going to run the
reactants, the reaction.

322
00:24:06 --> 00:24:08
The reactants are going
to turn into products.

323
00:24:08 --> 00:24:31
Let's look at what happens.
 

324
00:24:31 --> 00:24:44
So what happens is my reactants
at T1 plus calorimeter at T1

325
00:24:44 --> 00:24:57
turn into products at T2 plus
my calorimeter at T2, right.

326
00:24:57 --> 00:24:57
That's my process.
 

327
00:24:57 --> 00:24:59
That's what really happens.
 

328
00:24:59 --> 00:25:03
Now that, the enthalpy of that
process isn't what I want,

329
00:25:03 --> 00:25:07
right, because the temperature
has changed, also the

330
00:25:07 --> 00:25:09
calorimeter is heated up.
 

331
00:25:09 --> 00:25:12
So I need to relate this
to what I do want.

332
00:25:12 --> 00:25:17
Let's label this one.
 

333
00:25:17 --> 00:25:18
It is adiabatic.
 

334
00:25:18 --> 00:25:23
It is taking place inside this
thing, and it's a constant

335
00:25:23 --> 00:25:29
pressure, and we'll do
it reversibly, right.

336
00:25:29 --> 00:25:30
So that's what we've got.
 

337
00:25:30 --> 00:25:39
Now, we can always take these
things the products and the

338
00:25:39 --> 00:25:42
calorimeter at temperature T2
and cool them or warm them

339
00:25:42 --> 00:26:07
to get to products plus
calorimeter at T1, right.

340
00:26:07 --> 00:26:10
Let's label that two.
 

341
00:26:10 --> 00:26:14
It's still at
constant pressure.

342
00:26:14 --> 00:26:16
It's reversible.
 

343
00:26:16 --> 00:26:19
It's a temperature change.
 

344
00:26:19 --> 00:26:22
Now to make that happen,
it's not adiabatic, right.

345
00:26:22 --> 00:26:24
If I wanted to do that, I'd
need a heating element or

346
00:26:24 --> 00:26:28
something to cool, so I
could make that temperature

347
00:26:28 --> 00:26:31
change happen, right.
 

348
00:26:31 --> 00:26:33
Well, so now I can
complete the cycle.

349
00:26:33 --> 00:26:36
I've got reactants and
calorimeter at T1.

350
00:26:36 --> 00:26:40
Fewer products and
calorimeter at T1, right.

351
00:26:40 --> 00:26:44
Calorimeter doesn't
change in this process.

352
00:26:44 --> 00:26:50
So here I've got some
delta H associated with

353
00:26:50 --> 00:26:52
changing the temperature.
 

354
00:26:52 --> 00:26:55
This delta H though,
this is what I want.

355
00:26:55 --> 00:27:02
This is delta H of
reaction at T1, right?

356
00:27:02 --> 00:27:12
It's isothermal, constant
pressure, reversible.

357
00:27:12 --> 00:27:13
Just what I want.
 

358
00:27:13 --> 00:27:17
That's how I've defined
delta H of reaction.

359
00:27:17 --> 00:27:19
This is what I'm after.
 

360
00:27:19 --> 00:27:24
All right, so now let's see how
we execute it, and do the

361
00:27:24 --> 00:27:26
calculations that allow
us to calculate this.

362
00:27:26 --> 00:27:43
So, one, what's delta
H in step one?

363
00:27:43 --> 00:27:49
Yes, exactly, it's
adiabatic, right constant

364
00:27:49 --> 00:27:51
pressure. it's zero.
 

365
00:27:51 --> 00:27:58
Delta H1 is zero, right.
 

366
00:27:58 --> 00:28:01
What we're really going to do
in practice is we're going to

367
00:28:01 --> 00:28:05
measure, we're going to use our
thermometer and say great, how

368
00:28:05 --> 00:28:09
much did the temperature
change, right.

369
00:28:09 --> 00:28:13
So now, then we're going to
use what we're going to learn

370
00:28:13 --> 00:28:16
from step two in order to
calculate this part, what

371
00:28:16 --> 00:28:20
we could call step three.
 

372
00:28:20 --> 00:28:29
OK, so two, that's
the crucial part.

373
00:28:29 --> 00:28:30
It's constant pressure.
 

374
00:28:30 --> 00:28:34
It's just given by the
corresponding heat, and

375
00:28:34 --> 00:28:36
it's just a temperature
change, right.

376
00:28:36 --> 00:28:46
So we know how to do this,
integral from well it's T1 to

377
00:28:46 --> 00:28:52
T2, depending on which way we
go of Cp for the

378
00:28:52 --> 00:28:56
whole system dT.
 

379
00:28:56 --> 00:29:04
 


380
00:29:04 --> 00:29:05
OK?
 

381
00:29:05 --> 00:29:08
It's just how much heat is
involved when we change

382
00:29:08 --> 00:29:09
the temperature.
 

383
00:29:09 --> 00:29:13
Now, the products have some
heat capacity associated with

384
00:29:13 --> 00:29:16
them right, it takes a certain
amount of heat if we make their

385
00:29:16 --> 00:29:19
temperature change, to either
put it in or take it away,

386
00:29:19 --> 00:29:22
depending on which direction
the temperature is changing.

387
00:29:22 --> 00:29:29
Same with the calorimeter, OK.
 

388
00:29:29 --> 00:29:33
In actual practice though, the
calorimeter, is going to be

389
00:29:33 --> 00:29:36
this big hunk of metal, and
really what's going to, there's

390
00:29:36 --> 00:29:38
going to be some stuff in here,
right, they'll be a fluid,

391
00:29:38 --> 00:29:42
it will usually be
some sort of oil.

392
00:29:42 --> 00:29:46
There's a pretty
big thermal mass.

393
00:29:46 --> 00:29:50
Now we run the reaction
and it produces heat.

394
00:29:50 --> 00:29:54
Most of the heat is going
to warm up or cool off

395
00:29:54 --> 00:29:57
all that oil and stuff.
 

396
00:29:57 --> 00:29:59
There's a moderate amount
of material in the

397
00:29:59 --> 00:30:00
actual reaction.
 

398
00:30:00 --> 00:30:03
You want to design the
calorimeter to fulfill

399
00:30:03 --> 00:30:05
that condition,
 

400
00:30:05 --> 00:30:08
Of course, you can't make it so
enormous that even for, that

401
00:30:08 --> 00:30:11
for any ordinary reaction
there's not even a measurable

402
00:30:11 --> 00:30:13
temperature change, right,
because if you have your enough

403
00:30:13 --> 00:30:16
oil to fill up this room, it
would take a huge amount of

404
00:30:16 --> 00:30:18
heat to change it by even
a tiny, it's temperature

405
00:30:18 --> 00:30:19
but even a tiny amount.
 

406
00:30:19 --> 00:30:25
So the calorimeter is designed
sort of to scale to match the

407
00:30:25 --> 00:30:29
maybe the ordinary volume of
reactants that you'll put in

408
00:30:29 --> 00:30:34
there, such that, pretty much
all the heat's just going to

409
00:30:34 --> 00:30:39
heat up the calorimeter, and
there's only a small amount

410
00:30:39 --> 00:30:43
that's going toward heating
up the products, right.

411
00:30:43 --> 00:30:49
So in general, or at least
usually it'll be the case, that

412
00:30:49 --> 00:31:04
this is approximately equal to
integral from T1 to T2 Cp of

413
00:31:04 --> 00:31:09
just the calorimeter dT.
 

414
00:31:09 --> 00:31:22
 


415
00:31:22 --> 00:31:26
And that generally is just
given by the heat capacity

416
00:31:26 --> 00:31:31
the calorimeter times
delta T, right..

417
00:31:31 --> 00:31:34
Because the heat capacity of
the calorimeter just like

418
00:31:34 --> 00:31:41
this thing is not strongly
temperature dependent, OK.

419
00:31:41 --> 00:31:44
So the point is we can
calculate delta H associated

420
00:31:44 --> 00:31:52
with this process
pretty readily, OK.

421
00:31:52 --> 00:32:00
That leaves three, right.
 

422
00:32:00 --> 00:32:07
But delta H for step three must
just be the opposite of this

423
00:32:07 --> 00:32:11
delta H because this was zero
and we know that were going

424
00:32:11 --> 00:32:23
around a cycle, right.
 

425
00:32:23 --> 00:32:28
And that's our
heat of reaction.

426
00:32:28 --> 00:32:44
So we're going to be
able to do this, right?

427
00:32:44 --> 00:32:50
OK, now this is one way to do
calorimetry, and it's practical

428
00:32:50 --> 00:32:53
as long as all the materials
are in condensed phases,

429
00:32:53 --> 00:32:56
solids and liquids.
 

430
00:32:56 --> 00:33:01
If gases are involved it can
work, but it can be tricky to

431
00:33:01 --> 00:33:06
keep the pressure constant,
right, because that means that

432
00:33:06 --> 00:33:10
now the moles of gas might be
changing, and that means

433
00:33:10 --> 00:33:12
in some way the volume
has to be adjustable.

434
00:33:12 --> 00:33:14
You'd need some sort of
balloon or membrane that

435
00:33:14 --> 00:33:16
will allow that to happen.
 

436
00:33:16 --> 00:33:20
Could be done, but easier is to
just do the whole thing at

437
00:33:20 --> 00:33:25
constant volume, right, and
just run the reaction that way

438
00:33:25 --> 00:33:29
and redo the calculation to be
a constant volume rather

439
00:33:29 --> 00:33:32
than constant pressure
calorimeter, right.

440
00:33:32 --> 00:33:33
And it's not hard to do that.
 

441
00:33:33 --> 00:33:37
So let's just look at what
happens in that case.

442
00:33:37 --> 00:34:02
It's almost the same.
 

443
00:34:02 --> 00:34:06
So let's see, just to finish
the job here though, all this

444
00:34:06 --> 00:34:11
says is delta H of reaction is
just negative Cp for the

445
00:34:11 --> 00:34:18
calorimeter times delta T, all
right. so that's what we

446
00:34:18 --> 00:34:29
think we know in constant
pressure calorimetry.

447
00:34:29 --> 00:34:37
Yes, and if we have gases
involved, it's pretty similar,

448
00:34:37 --> 00:34:41
but now what will have
is something like this.

449
00:34:41 --> 00:34:46
We'll have a reaction
vessel that's sealed,

450
00:34:46 --> 00:34:51
it's constant volume.
 

451
00:34:51 --> 00:34:55
That'll be inside
our calorimeter.

452
00:34:55 --> 00:35:06
It's insulated, and there's
still a thermometer, so we

453
00:35:06 --> 00:35:08
can measure the temperature.
 

454
00:35:08 --> 00:35:10
So this is still adiabatic.
 

455
00:35:10 --> 00:35:17
It's insulated, but now
it's constant volume, OK.

456
00:35:17 --> 00:35:20
Now, you know with constant
volume, now it's not going

457
00:35:20 --> 00:35:23
to be delta H that's
straightforward to

458
00:35:23 --> 00:35:27
measure, it's going to be
dealt u, all right.

459
00:35:27 --> 00:35:30
But it's going to be
almost the same, right?

460
00:35:30 --> 00:35:33
So let's just think about
what happens here.

461
00:35:33 --> 00:35:37
Now it's the cycle that we've
got will still basically

462
00:35:37 --> 00:35:37
look the same.
 

463
00:35:37 --> 00:35:44
That is its reactants at T1
plus calorimeter at T1, going

464
00:35:44 --> 00:35:54
to products at T2 plus
calorimeter at T2, right?

465
00:35:54 --> 00:36:04
And it's still adiabatic, but
now it's constant volume.

466
00:36:04 --> 00:36:09
And it's also reversal right.
 

467
00:36:09 --> 00:36:14
So this is our process one.
 

468
00:36:14 --> 00:36:21
Now, process two, we're going
to end up here with our

469
00:36:21 --> 00:36:29
products, again at T1 plus our
calorimeter at T1, right.

470
00:36:29 --> 00:36:37
So now we have a constant
volume reversible

471
00:36:37 --> 00:36:41
temperature change.
 

472
00:36:41 --> 00:36:47
And so this part now isn't
exactly what we want to

473
00:36:47 --> 00:37:04
determine delta H, because it's
a isothermal constant volume,

474
00:37:04 --> 00:37:07
reversible products or
reversible process that takes a

475
00:37:07 --> 00:37:11
reactant to T1 to
a product of T1.

476
00:37:11 --> 00:37:14
What these are going to give
us are delta u values.

477
00:37:14 --> 00:37:20
This'll give us delta u of
reaction, right, T1, right.

478
00:37:20 --> 00:37:25
It's a constant volume.
 

479
00:37:25 --> 00:37:28
All right, so in the end, we're
going to determine delta u

480
00:37:28 --> 00:37:29
here, and then in the end,
we're going to have to relate

481
00:37:29 --> 00:37:32
that to delta H, but that's
straight forward enough to do.

482
00:37:32 --> 00:37:38
So let's look at how we'll
analyze what happens.

483
00:37:38 --> 00:37:48
So one adiabatic, constant
volume process, right.

484
00:37:48 --> 00:37:51
What's zero in that case?
 

485
00:37:51 --> 00:37:53
In this case delta H was
zero in the constant

486
00:37:53 --> 00:37:56
pressure example.
 

487
00:37:56 --> 00:37:59
Now we've got a constant
volume process.

488
00:37:59 --> 00:38:03
What's zero?
 

489
00:38:03 --> 00:38:07
It's u, because u is to q
plus w right, heat and

490
00:38:07 --> 00:38:09
work, but it's adiabatic.
 

491
00:38:09 --> 00:38:14
So there's no heat, exchange
with the environment, and it's

492
00:38:14 --> 00:38:20
constant volume, so there's
no p dV work, right.

493
00:38:20 --> 00:38:29
So q is zero adiabatic.
 

494
00:38:29 --> 00:38:35
Work is zero.
 

495
00:38:35 --> 00:38:40
Delta u1 is zero.
 

496
00:38:40 --> 00:38:45
And again just in the constant
pressure case, what happens

497
00:38:45 --> 00:38:49
that we're going to measure in
step one, which is to say in

498
00:38:49 --> 00:38:53
actually running the reaction
is the temperature's

499
00:38:53 --> 00:38:54
going to change.
 

500
00:38:54 --> 00:38:54
Right?
 

501
00:38:54 --> 00:38:57
The whole thing's going to
come to some new equilibrium

502
00:38:57 --> 00:39:00
temperature between the
products and the oil or

503
00:39:00 --> 00:39:04
whatever's around it, and
we're going to measure that.

504
00:39:04 --> 00:39:13
OK, two, now it's a
temperature change, right?

505
00:39:13 --> 00:39:17
We know how to calculate delta
u for a temperature change.

506
00:39:17 --> 00:39:20
It's very similar here, but
what's going to be different

507
00:39:20 --> 00:39:28
from the case with
constant pressure?

508
00:39:28 --> 00:39:32
There's a real important detail
that's different if you want to

509
00:39:32 --> 00:39:35
calculate what happens at
constant pressure when you

510
00:39:35 --> 00:39:36
change the temperature?
 

511
00:39:36 --> 00:39:40
What happens at
constant volume?

512
00:39:40 --> 00:39:45
Looking at this expression,
what's got to be different?

513
00:39:45 --> 00:39:45
Cv, right.
 

514
00:39:45 --> 00:39:47
We're not going to have the
constant pressure heat

515
00:39:47 --> 00:39:48
capacity, we're going to
have the constant volume

516
00:39:48 --> 00:39:50
heat capacity, right.
 

517
00:39:50 --> 00:39:58
So delta u for step two, that's
our q under constant volume

518
00:39:58 --> 00:40:08
conditions, integral from T1 to
T2 Cv for our whole system dT.

519
00:40:08 --> 00:40:12
 


520
00:40:12 --> 00:40:19
Integral from T2 to T2, and
now I can separate again the

521
00:40:19 --> 00:40:24
calorimeter from the product,
and at least approximately,

522
00:40:24 --> 00:40:34
again, it'll be Cv for the
calorimeter dT, which is to

523
00:40:34 --> 00:40:41
say then it's Cv of the
calorimeter times delta T.

524
00:40:41 --> 00:40:50
Great.
 

525
00:40:50 --> 00:40:55
Three, well delta u1 was zero.
 

526
00:40:55 --> 00:41:03
Delta u2 was there Cv delta T,
so now all we need since the

527
00:41:03 --> 00:41:10
whole thing is going around in
a cycle, Since we know delta u3

528
00:41:10 --> 00:41:17
must be negative delta u2, and
that is our delta u

529
00:41:17 --> 00:41:46
of reaction, right?
 

530
00:41:46 --> 00:41:53
So delta u of reaction is
approximately equal to negative

531
00:41:53 --> 00:41:58
Cv for the calorimeter
times delta T.

532
00:41:58 --> 00:42:07
So, this is what we're going
to measure, and this is what

533
00:42:07 --> 00:42:09
we're going to determine.
 

534
00:42:09 --> 00:42:13
And now we're almost done,
except what we really want is

535
00:42:13 --> 00:42:18
delta H and not delta V, right.
 

536
00:42:18 --> 00:42:25
So now we're going to use the
fact that H is u plus pV.

537
00:42:25 --> 00:42:27
 


538
00:42:27 --> 00:42:38
Delta H is delta u plus delta
pV, and now this is all at

539
00:42:38 --> 00:42:40
constant temperature
in the end, right?

540
00:42:40 --> 00:42:46
We've determined delta u for
some temperature T1, right.

541
00:42:46 --> 00:42:52
So what happens then we're
going to use the ideal gas law.

542
00:42:52 --> 00:42:56
So it's approximately
delta u plus delta nRT.

543
00:42:56 --> 00:42:59
 


544
00:42:59 --> 00:43:01
That's a constant.
 

545
00:43:01 --> 00:43:03
That's a constant.
 

546
00:43:03 --> 00:43:10
So it's delta u plus RT, we can
say T1 is the temperature we've

547
00:43:10 --> 00:43:15
used here, delta n of the gas.
 

548
00:43:15 --> 00:43:18
In other words, what matters
here in changing the

549
00:43:18 --> 00:43:19
pressure volume product?
 

550
00:43:19 --> 00:43:23
What matters is we turned some
reactants into some products.

551
00:43:23 --> 00:43:26
How many moles of gas are
there in each case, in

552
00:43:26 --> 00:43:27
reactants and products?
 

553
00:43:27 --> 00:43:31
If that changes, of course you
know that the pressure in there

554
00:43:31 --> 00:43:33
is going to change at constant
volume if the amount of

555
00:43:33 --> 00:43:35
gas in there is changing.
 

556
00:43:35 --> 00:43:37
And nothing else is going
to make a significant

557
00:43:37 --> 00:43:46
contribution to it, OK?
 

558
00:43:46 --> 00:43:55
So finally, then delta H of
reaction for our temperature T1

559
00:43:55 --> 00:44:00
is approximately minus Cv of
the calorimeter times delta

560
00:44:00 --> 00:44:07
T plus R T1 delta n of gas.
 

561
00:44:07 --> 00:44:12
Change of the number of
moles of gas, right.

562
00:44:12 --> 00:44:17
We're going to measure
that, and now we're

563
00:44:17 --> 00:44:20
going to determine this.
 

564
00:44:20 --> 00:44:25
In practice, we'll already
know the heat capacity of

565
00:44:25 --> 00:44:29
our calorimeter, when
we buy it, right?

566
00:44:29 --> 00:44:32
So we don't really need to put
in a certain amount of heat and

567
00:44:32 --> 00:44:34
change the temperature
of the products and the

568
00:44:34 --> 00:44:35
calorimeter and so on.
 

569
00:44:35 --> 00:44:37
What we need to do is just
measure how much the

570
00:44:37 --> 00:44:45
temperature changed, OK.
 

571
00:44:45 --> 00:44:49
It's worth getting just sort of
roughly calibrated how big is

572
00:44:49 --> 00:44:51
this compared to the
rest of this stuff.

573
00:44:51 --> 00:44:58
That is, how different is delta
u from delta H, all right.

574
00:44:58 --> 00:45:00
And of course it's
straightforward to do this, and

575
00:45:00 --> 00:45:03
I've written this out in the
notes, so I won't re-write

576
00:45:03 --> 00:45:05
the numbers here.
 

577
00:45:05 --> 00:45:09
But I gave an example
looking at combining

578
00:45:09 --> 00:45:11
HCl and oxygen right.
 

579
00:45:11 --> 00:45:18
So 4 HCl plus oxygen gas.
 

580
00:45:18 --> 00:45:23
This two in the gas going
to water and the liquid,

581
00:45:23 --> 00:45:30
plus chlorine gas at
room temperature.

582
00:45:30 --> 00:45:38
Well, what you find out is
delta u of reaction is minus

583
00:45:38 --> 00:45:43
195 kilojoules for the
reaction as written.

584
00:45:43 --> 00:45:47
And it turns out, as written,
if you say OK, how much, what

585
00:45:47 --> 00:45:49
changed for the pV product?
 

586
00:45:49 --> 00:45:52
Well here we've got four moles
of gas, five moles of gas.

587
00:45:52 --> 00:45:55
Here just two, so we changed
the number of moles

588
00:45:55 --> 00:45:57
of gas by three.
 

589
00:45:57 --> 00:46:01
All right, how much
did it matter, right?

590
00:46:01 --> 00:46:02
Well it matters.
 

591
00:46:02 --> 00:46:03
It's measurable.
 

592
00:46:03 --> 00:46:09
So now delta H of reaction
turns out to be minus

593
00:46:09 --> 00:46:12
202 kilojoules.
 

594
00:46:12 --> 00:46:15
So, you know, seven out of a
couple of a hundred, right, a

595
00:46:15 --> 00:46:18
few percent, kind of typical.
 

596
00:46:18 --> 00:46:20
In other words, if you look at
energetics of ordinary

597
00:46:20 --> 00:46:23
reactions where you're, you
know, you're making and

598
00:46:23 --> 00:46:26
breaking covalent bonds,
there's a fair amount of energy

599
00:46:26 --> 00:46:28
stored in those, right?
 

600
00:46:28 --> 00:46:32
The additional change due to
changing pressure volume

601
00:46:32 --> 00:46:34
is certainly measurable.
 

602
00:46:34 --> 00:46:38
You don't want to just ignore
it, but in cases like

603
00:46:38 --> 00:46:40
that, it's usually a small
fraction of the total.

604
00:46:40 --> 00:46:47
A few percent is typical, okay.
 

605
00:46:47 --> 00:46:51
All right, let me just go
through one numerical

606
00:46:51 --> 00:46:58
example of a calorimetry
calculation, OK.

607
00:46:58 --> 00:47:01
I won't put all the numbers
up on the board because our

608
00:47:01 --> 00:47:04
time is running short, but
I just want to outline it.

609
00:47:04 --> 00:47:08
All I really want to do is
calibrate you a little bit for

610
00:47:08 --> 00:47:13
what happens with ordinary
calorimeter heat capacities

611
00:47:13 --> 00:47:16
that makes the calculation turn
out to be relatively

612
00:47:16 --> 00:47:18
easy, right.
 

613
00:47:18 --> 00:47:22
So let's just write it out.
 

614
00:47:22 --> 00:47:30
Let's take iron sulfide as a
solid, plus 11 halves oxygen

615
00:47:30 --> 00:47:40
gas to make iron oxide,
also a solid, plus

616
00:47:40 --> 00:47:43
sulphur dioxide gas.
 

617
00:47:43 --> 00:47:46
All right.
 

618
00:47:46 --> 00:47:53
We'll start at T1
is 298 Kelvin.

619
00:47:53 --> 00:47:59
T2, maybe we don't
know it yet, right.

620
00:47:59 --> 00:48:12
OK, so we know how to calculate
what's going to happen, delta H

621
00:48:12 --> 00:48:15
and delta u, because we can
look up the heats of formation

622
00:48:15 --> 00:48:19
and so forth of all
the compounds, right.

623
00:48:19 --> 00:48:24
So if we do that, what we
discover is that delta

624
00:48:24 --> 00:48:30
H of formation whoops,
something's wrong here.

625
00:48:30 --> 00:48:35
This is sulphur -- what am I
doing, boy, S and it's a two,

626
00:48:35 --> 00:48:40
sorry, and the heat of
formation is minus 180

627
00:48:40 --> 00:48:47
kilojoules per mole,
that's oxygen, it's zero.

628
00:48:47 --> 00:48:52
Boy, I'm, I don't know what is
about this reaction that's

629
00:48:52 --> 00:48:53
vexing me but it's not
that complicated.

630
00:48:53 --> 00:49:00
Here it's minus 824 kilojoules
per mole minus 297

631
00:49:00 --> 00:49:01
kilojoules per mole, right.
 

632
00:49:01 --> 00:49:07
So that's our input
thermodynamic data.

633
00:49:07 --> 00:49:16
So first of all, let's just
do a heat of reaction

634
00:49:16 --> 00:49:16
calculation, right.
 

635
00:49:16 --> 00:49:20
Taking the product minus
the reaction, right.

636
00:49:20 --> 00:49:29
So it's minus 824 plus 4
times minus 297 minus

637
00:49:29 --> 00:49:33
2 times minus 180.
 

638
00:49:33 --> 00:49:34
Right?
 

639
00:49:34 --> 00:49:36
In other words I've got the
stoichiometric coefficients in

640
00:49:36 --> 00:49:39
there and the values, and I'm
subtracting the reactants from

641
00:49:39 --> 00:49:49
products wind up with minus
1652 kilojoules per mole.

642
00:49:49 --> 00:49:52
Well, it depends on what we
write, what we consider mole,

643
00:49:52 --> 00:50:04
right, maybe I should just
write kilojoules as written.

644
00:50:04 --> 00:50:16
OK, I'm going to skip the
delta and get the change in

645
00:50:16 --> 00:50:18
moles of gas calculation.
 

646
00:50:18 --> 00:50:19
It's straightforward to do.
 

647
00:50:19 --> 00:50:21
What I really want to do is
just give an example of what

648
00:50:21 --> 00:50:24
happens when you throw the
thing, the material into a

649
00:50:24 --> 00:50:26
calorimeter and see how much
the temperature changes.

650
00:50:26 --> 00:50:38
So let's imagine we start with
0.1 moles of our iron sulfide,

651
00:50:38 --> 00:50:40
and then we have a
stoichiometric amount of

652
00:50:40 --> 00:50:43
oxygen, and the whole thing is
done in a constant volume

653
00:50:43 --> 00:50:45
calorimeter, and we
see what happens.

654
00:50:45 --> 00:50:47
Now the crucial element is
what is the heat capacity

655
00:50:47 --> 00:50:49
of the calorimeter, right?
 

656
00:50:49 --> 00:50:53
And it's, again it's a
macroscopic pretty big thing,

657
00:50:53 --> 00:50:58
so typical might be 10
kilojoules per Kelvin, and

658
00:50:58 --> 00:51:00
that's pretty big, right?
 

659
00:51:00 --> 00:51:02
Noticed that's not
per mole, right.

660
00:51:02 --> 00:51:06
I mean the calorimeter is a big
thing filled the little oil or

661
00:51:06 --> 00:51:08
whatever is inside it, right?
 

662
00:51:08 --> 00:51:11
And it's for that whole
unit that you've got

663
00:51:11 --> 00:51:12
some heat capacity.
 

664
00:51:12 --> 00:51:14
How much heat does it take the
warm the entire thing up or the

665
00:51:14 --> 00:51:18
insides of the thing
up by a degree?

666
00:51:18 --> 00:51:20
It's that number right.
 

667
00:51:20 --> 00:51:24
Ordinary heat capacities are
in Joule's per Kelvin mole,

668
00:51:24 --> 00:51:25
not kilojoules, right.
 

669
00:51:25 --> 00:51:28
And what that's telling you is
probably your reactants and

670
00:51:28 --> 00:51:31
products, so the amount of heat
that's involved in changing the

671
00:51:31 --> 00:51:33
air temperature is going to be
negligible compared to

672
00:51:33 --> 00:51:36
what happens to the
whole calorimeter.

673
00:51:36 --> 00:51:39
OK?
 

674
00:51:39 --> 00:51:46
So now if we say, OK, we we've
done this calculation starting

675
00:51:46 --> 00:51:48
with 2 moles of this, but now
we're going to be at 0.1

676
00:51:48 --> 00:51:51
mole, so we're going to need
to divide by 20, right.

677
00:51:51 --> 00:51:57
So instead of minus 1652, it's
going to turn out delta u is

678
00:51:57 --> 00:52:07
minus 1648 kilojoules, so, and
then divide by twenty, we end

679
00:52:07 --> 00:52:17
up with minus 82.4 kilojoules,
that is, that's the delta u of

680
00:52:17 --> 00:52:21
reaction for what happens if
you'd put in not two moles of

681
00:52:21 --> 00:52:24
this, but 0.1 mole
of this, right.

682
00:52:24 --> 00:52:26
Practical amounts is the
reason I'm using numbers

683
00:52:26 --> 00:52:28
like this, right.
 

684
00:52:28 --> 00:52:32
So now, what's delta T?
 

685
00:52:32 --> 00:52:41
Well here's Cv, right, so
delta T is just our minus 10

686
00:52:41 --> 00:52:59
kilojoules per degree oh sorry,
it's our minus 82.4 kilojoules.

687
00:52:59 --> 00:53:06
That's the heat released,
divided by minus 10 or 10

688
00:53:06 --> 00:53:11
kilojoules per Kelvin, right.
 

689
00:53:11 --> 00:53:14
It's 8.2 Kelvin.
 

690
00:53:14 --> 00:53:18
In other words, how much does
the temperature of the whole

691
00:53:18 --> 00:53:20
thing change when you put an
ordinary amount of material

692
00:53:20 --> 00:53:22
in there and run a
reaction, right.

693
00:53:22 --> 00:53:23
Well, what do you do?
 

694
00:53:23 --> 00:53:27
You calculate how much heat
is released in the reaction.

695
00:53:27 --> 00:53:30
And then what's going to matter
is what's the heat capacity of

696
00:53:30 --> 00:53:32
the whole, of the calorimeter?
 

697
00:53:32 --> 00:53:35
I didn't even need to know
that heat capacity of

698
00:53:35 --> 00:53:38
the product, right.
 

699
00:53:38 --> 00:53:42
Because it's effect the thermal
mass of the product is

700
00:53:42 --> 00:53:43
negligible compared to
the thermal mass of

701
00:53:43 --> 00:53:46
the calorimeter.
 

702
00:53:46 --> 00:53:50
Now in real practice, I'll do
the calculation in reverse.

703
00:53:50 --> 00:53:53
I'll measure how much the
temperature changed in

704
00:53:53 --> 00:53:56
the calorimeter, right.
 

705
00:53:56 --> 00:53:58
I'll know the heat capacity,
and what I'll really be

706
00:53:58 --> 00:54:02
calculating is OK, how much
heat must have been released

707
00:54:02 --> 00:54:06
in the reaction to make that
temperature change happen?

708
00:54:06 --> 00:54:09
And that in the case of
constant volume, in this case

709
00:54:09 --> 00:54:11
that's my delta u, and then
I'll add my little delta

710
00:54:11 --> 00:54:16
n term to get delta H.
 

711
00:54:16 --> 00:54:20
Any questions on calorimetry?
 

712
00:54:20 --> 00:54:20
OK.
 

713
00:54:20 --> 00:54:21
See you Friday.
 

714
00:54:21 --> 00:54:26
We'll finish on calorimetry and
thermochemistry and then we'll

715
00:54:26 --> 00:54:30
start in on one of the really
most difficult topics that

716
00:54:30 --> 00:54:33
we'll deal with all semester,
which is a second law and our

717
00:54:33 --> 00:54:38
special function that we've
seen just a little bit so far.

718
00:54:38 --> 00:54:38