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Boyle鈥檚 Law .txt
So in order to explain exactly how individual gas molecules behave, scientists came up with something called a kinetic molecular theory.
Boyle鈥檚 Law .txt
And what this theory is is it's basically a bunch of assumptions that they make about gases that helps us understand how individual gas molecules interact.
Boyle鈥檚 Law .txt
So the kinetic theory is used to explain the behavior of gases on a nanoscale level.
Boyle鈥檚 Law .txt
Now, in order to look at the macroscopic level or explain gas behavior on a macroscopic level, much larger level, we have to look at something else.
Boyle鈥檚 Law .txt
Now, scientists came up with different equations and formulas to explain macroscopic gas behavior.
Boyle鈥檚 Law .txt
The first formula we're going to look at and discuss is called Boils Law.
Boyle鈥檚 Law .txt
Now, Boils Law works under certain conditions.
Boyle鈥檚 Law .txt
Now, if we have a constant temperature and constant number of moles or N constant number of molecules, then we can use something called Boils Law.
Boyle鈥檚 Law .txt
And what Boils Law relates is it relates volume and pressure.
Boyle鈥檚 Law .txt
And what it states is that volume is directly proportional to the inverse of one over P. Or said another way, volume is inversely proportional to one over P. And we can represent this as VP equals constant.
Boyle鈥檚 Law .txt
In other words, if we rearrange this and multiply this by some constant, we get this formula.
Boyle鈥檚 Law .txt
And what this basically says is that under these conditions of constant temperature and constant number of moles, v times p will always be a constant.
Boyle鈥檚 Law .txt
So when B increases, p decreases, or when P increases, V decreases and so on.
Boyle鈥檚 Law .txt
And our constant depends on the temperature and the number of moles.
Boyle鈥檚 Law .txt
So if temperature increases or its temperature changes or N changes, this constant will also change.
Boyle鈥檚 Law .txt
In other words, the number that you get when you multiply D times P will also change.
Boyle鈥檚 Law .txt
Now, suppose we have some gas or some sample of gas.
Boyle鈥檚 Law .txt
And suppose we have one set of conditions and a second set of conditions.
Boyle鈥檚 Law .txt
So suppose I have the following.
Boyle鈥檚 Law .txt
Suppose I have some container with pressure one and volume one.
Boyle鈥檚 Law .txt
And I have the same container, but with a smaller volume and a different pressure.
Boyle鈥檚 Law .txt
So one set of conditions and second set of conditions.
Boyle鈥檚 Law .txt
Now, what this law does is it explains macroscopic phenomenon.
Boyle鈥檚 Law .txt
Like, for example, why is it that when I take a balloon filled with air and I push it hard enough, it explodes?
Boyle鈥檚 Law .txt
Well, why did that occur?
Boyle鈥檚 Law .txt
Well, this can be explained by Boyle's Law and I'll show you in a second.
Boyle鈥檚 Law .txt
Well, this equation can be rearranged in this format if we're dealing with two different sets of conditions.
Boyle鈥檚 Law .txt
Notice that p times V will always give you a constant when you're talking about the same temperature and the same number of mole.
Boyle鈥檚 Law .txt
So if I have one set of conditions p one times v one, that will give me a constant.
Boyle鈥檚 Law .txt
And if I have the second set of conditions p two times v two, it will give me the same constant, right?
Boyle鈥檚 Law .txt
So I can set them equal.
Boyle鈥檚 Law .txt
This guy is equal to the same constant that this number represents.
Boyle鈥檚 Law .txt
So this is my equation for two sets of data or two sets of conditions.
Boyle鈥檚 Law .txt
Now let's look at this picture.
Boyle鈥檚 Law .txt
Well, once again, why is it that a balloon explodes?
Boyle鈥檚 Law .txt
Well, when the balloon is when you're not compressing the balloon, when you're just dangerous up, it has a certain pressure and a certain volume.
Boyle鈥檚 Law .txt
When you take it in your hand and you begin squeezing it, you begin decreasing the volume.
Boyle鈥檚 Law .txt
Boils law states that if you decrease volume, pressure must increase because our constant remains the same.
Boyle鈥檚 Law .txt
And that means pressure will begin to increase and the ball or the balloon will pop when the pressure is large enough for it to burst open and pop.
Boyle鈥檚 Law .txt
And that's exactly why balloon, when squeezed, will eventually pop.
Boyle鈥檚 Law .txt
So let's look at ventral sensation.
Boyle鈥檚 Law .txt
Suppose that this is our balloon and this is our compressed balloon.
Boyle鈥檚 Law .txt
Well, our gas molecule in this condition are further in part than they are in this condition.
Boyle鈥檚 Law .txt
And that means if they're further apart here, they will make less collisions than here.
Boyle鈥檚 Law .txt
And that means that there are less collisions.
Boyle鈥檚 Law .txt
Less of the molecules are colliding with the walls.
Boyle鈥檚 Law .txt
And so with less collisions, that means we have less pressure.
Boyle鈥檚 Law .txt
So the bigger the volume, the smaller the pressure.
Boyle鈥檚 Law .txt
So once again, we see that we can use the kinetic theory to explain nanoscopic or nanoscale behavior of these molecules.
Boyle鈥檚 Law .txt
And once again, the kinetic theory explains boiler's law.
Boyle鈥檚 Law .txt
A smaller volume means less room to navigate and increase in number of collisions.
Boyle鈥檚 Law .txt
This increase in collisions will increase our pressure because by definition, pressure is forced per unit area.
Boyle鈥檚 Law .txt
And if we have more molecules hitting the walls, we have more force and so a higher pressure.
Boyle鈥檚 Law .txt
So this is Boyle's Law and Boyle's Law is used to explain macroscopic behavior.
Boyle鈥檚 Law .txt
So let's examine the graphs of Boyle's Law or a graph of Boyle's Law.
Boyle鈥檚 Law .txt
Now, we can have two graphs.
Boyle鈥檚 Law .txt
We can graph volume and pressure.
Boyle鈥檚 Law .txt
Or we can grab volume and one over pressure.
Boyle鈥檚 Law .txt
So let's graph this guy first.
Boyle鈥檚 Law .txt
So recall that I said that volume is inversely proportional to one over P. Now mathematically what that means is we have this type of a graph in which as we increase our volume, our pressure decreases.
Boyle鈥檚 Law .txt
Or if we decrease our volume, decrease that volume in the balloon, our pressure will begin to increase.
Boyle鈥檚 Law .txt
If we continue to increase or decrease the volume, that pressure will begin to increase exponentially, right?
Boyle鈥檚 Law .txt
And that's what this represents.
Boyle鈥檚 Law .txt
Now instead, suppose that I graph volume over one over P. Well, how would that look?
Boyle鈥檚 Law .txt
Well, if I grab the volume over one over P, whenever this guy increases, this guy increases by the same ratio amount.
Boyle鈥檚 Law .txt
And that's because volume times pressure gives you a constant.
Boyle鈥檚 Law .txt
If this increases by say, two times, then this must decrease by two times.
Boyle鈥檚 Law .txt
That's why this guy is a straight line, the slope is constant, versus on this graph, the slope varies, it changes.
Boyle鈥檚 Law .txt
And if you wanted to find the slope, you would have to use calculus and approximate it using lines tangent to any point on the line.
Boyle鈥檚 Law .txt
Now, this is Boiler's law.
Boyle鈥檚 Law .txt
Once again, boiler's Law explains macroscopic behavior gases versus the kinetic theory, which explains nanoscale behavior of individual molecules.
Structure of Atoms .txt
Today we're going to go into detail about atomic structure.
Structure of Atoms .txt
Now, all matter and mass is composed of very tiny units called atoms.
Structure of Atoms .txt
Everything we see, we touch, we feel is composed of atoms.
Structure of Atoms .txt
Now, atoms themselves are composed of nucleuses surrounded by electrons.
Structure of Atoms .txt
Now, a nucleus is composed of two types of particles called protons and neutrons.
Structure of Atoms .txt
Now, protons and neutrons have approximately the same weight.
Structure of Atoms .txt
A neutron is a tiny bit heavier than protons, but for all purposes we can approximate that these guys have the same exact mass.
Structure of Atoms .txt
Electrons, however, have a very small mass, much smaller than that of protons or neutrons.
Structure of Atoms .txt
In fact, it's 1800 times smaller than a proton or a neutron.
Structure of Atoms .txt
Now, if we look at this table and we look at their masses, a proton has one AMU, a neutron has one AMU.
Structure of Atoms .txt
Now, AMU is simply atomic mass unit.
Structure of Atoms .txt
We're going to discuss that in detail in another lecture.
Structure of Atoms .txt
But an electron has a mass of 5.5 times ten to negative four AMU that's much smaller than that of proton or a neutron.
Structure of Atoms .txt
The charge, however, of a proton, an electron has the same magnitude 1.6 times ten to negative 19 Coulombs.
Structure of Atoms .txt
However, the sign of a proton is positive, while the sign of an electron is negative.
Structure of Atoms .txt
A neutron has VR charge.
Structure of Atoms .txt
It's a neutral charge.
Structure of Atoms .txt
Now let's look at the structure.
Structure of Atoms .txt
Now, in the illustration above, we see our atom.
Structure of Atoms .txt
Now, this whole guy is our nucleus.
Structure of Atoms .txt
And our nucleus is composed of two particles, protons and neutrons.
Structure of Atoms .txt
In this atom we have two protons and two neutrons.
Structure of Atoms .txt
The protons are quantitatively charged, while the neutrons are neutrally charged.
Structure of Atoms .txt
Now, the electron is found orbiting our atom, our nucleus.
Structure of Atoms .txt
And the distance between our nucleus and the electron is quite large.
Structure of Atoms .txt
And in fact, atoms are mostly composed of empty space.
Structure of Atoms .txt
And in fact, if our atom with the size of a football field, our nucleus will be the size of a marble.
Structure of Atoms .txt
So you can imagine that our entire atom, for the most part, is composed of empty space.
Structure of Atoms .txt
And that's because our electrons are very, very small and they orbit our nucleus at a very, very great distance compared to the size of the nucleus itself.