This course will cover the topics of a full year, two semester General Chemistry course. We will use a free on-line textbook, Concept Development Studies in Chemistry, available via Rice’s Connexions project. The fundamental concepts in the course will be introduced via the Concept Development Approach developed at Rice University. In this approach, we will develop the concepts you need to know from experimental observations and scientific reasoning rather than simply telling you the concepts and then asking you to simply memorize or apply them. So why use this approach? One reason is that most of us are inductive learners, meaning that we like to make specific observations and then generalize from there. Many of the most significant concepts in Chemistry are counter-intuitive. When we see where those concepts come from, we can more readily accept them, explain them, and apply them. A second reason is that scientific reasoning in general and Chemistry reasoning in particular are inductive processes. This Concept Development approach illustrates those reasoning processes. A third reason is that this is simply more interesting! The structure and reactions of matter are fascinating puzzles to be solved by observation and reasoning. It is more fun intellectually when we can solve those puzzles together, rather than simply have the answers to the riddles revealed at the outset. Recommended Background: The class can be taken by someone with no prior experience in chemistry. However, some prior familiarity with the basics of chemistry is desirable as we will cover some elements only briefly. For example, a prior high school chemistry class would be helpful. Suggested Readings: Readings will be assigned from the on-line textbook “Concept Development Studies in Chemistry”, available via Rice’s Connexions project. In addition, we will suggest readings from any of the standard textbooks in General Chemistry. A particularly good free on-line resource is Dickerson, Gray, and Haight, "Chemical Principles, 3rd Edition". Links to these two texts will be available in the Introduction module.
CDS 14 Physical Properties of Gases II
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Del curso dictado por Rice University
General Chemistry: Concept Development and Application
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Ideal Gas Law and the Kinetic Molecular Theory
One of the powers of chemistry is the ability to relate the properties of individual molecules to the physical and chemical properties of the compounds of these molecules. In other words, we want to relate the atomic molecular world to the macroscopic world of materials. We begin this study by observing the physical properties of gases and deriving an equation which relates these properties. From this law, we can devise a model which describes how these physical properties result from the properties and motions of individual molecules. Understanding the significance of temperature is a critical part of this study.
Conoce a los instructores
John Steven HutchinsonDean of Undergraduates and Professor of Chemistry
In lecture, we're going to continue our study of the physical properties
of gases, building on the material and concept development study number 14.
This will also build upon the material from
lecture one, in which we studied the relationship between
pressure of the gas and the volume of
gas for fixed samples of gas at fixed temperatures.
You'll recall that what we observed
experimentally was something called Boyle's Law.
Boyle's Law told us that the pressure is inversely related to the volume of
the gas for a fixed sample of gas at a fixed temperature.
If we vary the sample of the gas, we vary the proportionality.
That's most commonly written in the form that pressure
times volume is a constant, as we've written here.
But we know that, that constant depends upon
what the sample of the gas actually is.
What though, if we were to change the temperature of the gas?
That's actually the subject for today's lecture.
To study
the variation of the properties of the gases we change the temperature.
We're going to use the same apparatus that we used before.
This is just a cylinder, fitted with a piston.
But in this particular case, what we're going to do is now apply a constant
pressure to the piston, to the ex, to the end of the piston here.
And in doing so, we're going to hold the pressure of the gas itself constant.
The pressure of the gas has to equal the applied
pressure outside, otherwise the piston will move.
So we fix the pressure of the gas and we're going to vary the temperature of
the gas and measure that variation with a thermometer on the end of the apparatus.
We could vary the temperature of the gas by for example heating the cylinder
or by immersing the entire cylinder into
an ice bath and taking various temperature measurements.
What we'll discover is that the volume of the gas
trapped inside here varies as we vary the temperature.
We'll collect that volume versus temperature data and
this particular set of data looks something like this.
For one particular trapped sample, and one particular pressure we get,
oh, a half a dozen or so data points and if we
draw a line through those data points what we discover is
that beautifully, they form an almost perfect straight line, it would seem.
Implying that there's a simple relationship
between the volume and the temperature.
Notice that this is not a proportionality.
It doesn't pass through zero.
It passes through some non zero intercept down here.
What happens if we vary the sample of the
gas, or measure, or vary the pressure of the gas?
Let's actually sketch out what is observed
experimentally, back over here on the tablet.
If
I take the volume of the gas, as
a function of the temperature of the gra, gas
in degrees centigrade, here is in fact the
function that we have already gotten from our data.
This is for sample n1 at pressure P1.
What would happen if we increased the number of moles of the gas?
It turns out, in fact, that we get a new straight line relationship for n2 larger
than n1. At the same pressure.
Notice that the slope of the line changes.
Notice also that the y-intercept of the line changes.
The volume at zero degrees centigrade is not the same for these two samples.
You might think for a moment, why did the graph go up?
It's because from Avogadro's hypothesis, the more moles
there are, the larger the volume is going to be.
What if we were to change the pressure of the gas instead?
Let's draw a graph of that one as well.
Volume versus temperature.
Here's our original data. I'll reproduce it again here.
n1 and P1.
Now if we're going to increase the pressure of the gas and in
this particular case what we've discovered, we get a new straight line
relationship, not parallel to the first one and again with a different y-intercept
and different than either of the previous y intercepts that we observed.
What that tells us then,
is that although we get a straight line relationship, both the slope and the
y-intercept vary with the sample size and with the pressure.
What's an interesting surprise, though, is if we go to the trouble to try to
extrapolate what this data might look like as we go back in
the direction towards zero volume both
of these two curves, it turns out, extrapolate back to the
same point on the temperature axis. That particular point is minus
273.15. Likewise, let's
put all of these on the same graph together, but give ourselves
room to extrapolate below the temperature equal to zero
degrees centigrade.
Here is the data that we're looking at on the graph on the screen, n1 and P1
Here is the graph if we increase the number of moles, here is
the graph if we increase the pressure,
while holding the number of moles constant.
If I extrapolate each of these curves back to the point where the volume is
zero, each of them in fact extrapolate back to
exactly the same point, regardless of the pressure, regardless of the sample size.
All of these straight line relationships go back and intersect the t axis
at minus 273.15 degrees centigrade. The x intercept
does not vary with either the sample size or the pressure size.
That suggests that there's something rather important
about this x-intercept or temperature intercept, minus
273.15. It seems to be a constant.
Furthermore, relative to a temperature at minus 273.15, all of these are
proportionalities, the volume is proportional to
the temperature, relative to minus 273.15.
That
suggests that we should define a new temperature
scale, we should just shift the zero over.
Rather than taking the zero to be zero degrees centigrade, we'll
take the zero to be this new temperature, minus 273.15 degrees centigrade.
To do that is actually relatively simple. We'll simply define a new temperature
by adding 273.15 to every temperature in degrees centigrade,
as shown in this equation. Notice that minus 273.15 becomes 0 on the
new temperature scale, and 0 becomes 273.15 on the new temperature scale.
This new temperature scale is called the Absolute Temperature Scale and the units
are called Kelvin for Lord Kelvin. In this new set of data now,
notice that when we've shifted the temperature over, we're going to wind
up with graphs which are straight lined proportionalities passing through zero.
This is actually a result which is referred to as Charles' Law.
That the volume is proportional to the
absolute temperature as we have defined it here.
Here is our proportionality with a slope which is
alpha, the proportionality constant we've now called alpha.
If we extrapolate this particular straight line back to zero
it passes through the 0,0 so this is in fact a proportionality.
You might ask the question, why do we have to extrapolate?
Why don't we just take some more data down here, and see if
we can in fact get data that would fit all the way down?
The answer is straightforward.
As we lower the temperature of the gas, eventually we reach the
point that it will condense into a liquid, or possibly a solid.
And as a consequence we can't actually collect data on
the volume of the gases once the temperature is too low.
So in fact we do have to extrapolate but
that extrapolation does carry us back through zero, zero.
So here we have Charles' Law.
It says that the volume is proportional to
the absolute temperature but of course, the data that
we have drawn here are for a single sample, at a single pressure.
So alpha then is going to depend upon what
is the sample size and what is the pressure.
Here's Charles' Law expressed as an equation now.
The volume is proportional to
the temperature and the proportionality constant
depends upon what is the sample size and what is the pressure.
As we've seen back over here, though, that proportionality constant
will vary if we vary either n or vary the pressure.
What happens if we vary n?
How will alpha change?
Well, we know.
For one thing, we've observed experimentally.
That the slope becomes greater so alpha must go up.
How much does it go up?
Let's answer that question by using Avogadro's hypothesis.
Let's fix the pressure and
fix the temperature.
And now let's say double the number of moles here.
I know from Avogadro's hypothesis that the volume's proportional to the
number of moles when the pressure and the temperature are constant.
That means, if I doubled n, I have doubled V.
But if I doubled V then I have to in this equation, have doubled alpha.
So when I double n, I double alpha and therefore I can
conclude alpha is proportional to n by Avogadro's hypothesis.
Well that unlocks the n part of the
problem what about the pressure part of the problem.
If we vary the pressure instead, how is alpha going to change?
To find out let's use Boyle's law.
This time let's hold the number of moles of the gas and the temperature constant.
Let's do like we did before.
Let's say we doubled the pressure.
What do we think is going to happen to the proportionality constant?
Well, from our data we know that the slope
of the line actually decreases when we increase the pressure.
But that is consistent from what we've learned from Boyle's Law.
Because if I doubled say the pressure here I know that the volume
must be cut in half because the pressure and the volume are inversely proportional.
And according to this equation,
if the volume is cut in half, then alpha is also cut in half.
Therefore, if I double the pressure, I've cut
alpha in half, and what does that tell me?
It tells me that this proportionality constant
alpha is inversely proportional to the pressure.
Let's put all this together now.
Here is our expression of Charles's Law with the
volumes proportional of the temperature with the proportionality constant depends
on n and P.
We know that alpha is inversely proportional to P and proportional to n.
We can express that in this particular equation, alpha is proportional to
n so it's in the numerator inversely proportional to P so its in
the denominator and the new proportionality
constant now, we're just going to
call that r because it turns
out conventionally that's what chemists call it.
It doesn't have to have any other particular name.
If I just take this
alpha and insert it into the equation above, which
is Charles's law, what do I wind up with?
I have v is equal to r times n divided by P multiplied by T.
That in combination just becomes PV is equal to the nRT.
Something which chemists refer to as the ideal gas law.
It summarizes the relationships of the pressure and volume
together, the pressure and the temperature together, the volume and the
temperature together and the volume of the number of moles together.
In sum then what we've observed is that the ideal gas law is
includes all of the experiemental observations
that we've made over these two lectures.
Boyle's law, Charles' law and Avogardo's law.
Where Boyle's law is the pressure volume relationship.
Charles' law is the volume temperature relationship.
And Avogadro's Law is the volume relationship with the number of moles.
Why do we call this thing the Ideal Gas Law?
The answer has to do with the fact that we have observed that
this relationship is independent of the type
of gas molecules that we have captured.
It wouldn't matter whether we had contained helium
or neon or oxygen or nitrogen or fluorine gas.
Or perhaps complex hydrocarbons like methane, or
ethane, or propane, or butane into our cylinder, we get exactly
the same relationship for pressure, volume, number of moles, and temperature.
It's in that regard that we call this ideal.
It begs the question somewhat, why would this be true?
Why would the relationship of these physical variables be exactly the same
for all gases regardless of what the structures of the molecules are?
We're going to deal
with that question at length in the following concept development study.
In the next lecture though first, we're going to consider some applications
of the Ideal Gas Law predicting pressures particular, particular samples of gases.
Or even using pressure volume and temperature data
to determine the number of moles of the gas.
We'll pick that up in the next lecture.
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