I just found this one, which also does a good job.]]>

I may add a few things.

I also will have answers before the test.

Sorry. Here is the not quite complete answer sheet.

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As we have noted, elements in a column (group) on the periodic table tend to have similar chemistry. We posited earlier in the year that this has to do with similarities in how their electrons are arranged. We derived this just by thinking about the fact that chemistry happens at the level of electrons interacting or trading places, always to find a lower potential energy (PE).

Now, we are starting to use quantum to define the energies of these electrons. We have also learned (or, at least are beginning to learn) that there is periodicity in the pattern of the outermost electrons…all fits together.

So, we will be talking about "Valence" electrons, which are the ones on the outermost shell that is occupied (corresponds to the period on the table), and "inner" electrons, which we will call "shielding" electrons. They are in between the nucleus and the valence electrons, shielding the attraction between the valence electrons and the nucleus. In each group, the atoms have similar valence structure

This idea seems harder than it is. It is a simple bookkeeping step to determine how much the outermost electrons of an element are attracted to that atom's nucleus: more nuclear charge, more attraction. Nuclear charge (z) is the same as the atomic number: the number of protons. However, the attraction will be reduced (shielded) by the presence of inner (non-valence) electrons. To restate, a valence electron is any electron in the outermost shell, or principle quantum number. By the process of elimination, a non-valence electron is one that is in one of the inner shells (has a principle quantum number less than that of the valence. So, take any element in period 3: any electron in either the S orbital or the P orbitals of level 3 is valence. For all period 3 elements, there are 10 non-valence, or shielding electrons. These are the electrons in the 1S, 2S, and 2P orbitals and are in the same configuration as Neon's ten electrons.

The equation for effective nuclear charge is:

z

Core electrons are those of the previous noble gas plus any d and f electrons added since that noble gas. More on that later.

These are also called “shielding electrons” or the “shielding constant” because they interpose between the valence electrons and the nucleus, effectively shielding the attraction.

For sodium, there are 11 protons, but 10 shielding electrons. So, Zeff is 11-10 or 1. For potassium it is 19-18 or 1. For all elements in group 1, the effective nuclear charge will be 1.

For Mg, Z

- Atomic Radius: outermost electrons are mores strongly attracted the more the z
_{eff}. ∴ radius gets smaller moving left to right. Note also that a smaller radius gives rise to still greater attraction (the closer the electron is to the protons, the more attracted it is). - 1st ionization energy (the energy required to remove an electron to make the atom a 1+ ion): electrons more strongly attracted ∴ harder to remove as you move left to right.
- Electron affinity (how easy it is to add an electron to make the atom a 1- atom): more attraction ∴ easier to add another electron as you move left to right
- Electronegativity (how tightly they horde electrons when in a bond with another atom): more attraction as you proceed left to right ∴ more likely to steal or hog electrons in bond.

These follow the rule. However, electrons are being added to inner levels and thus the shielding constant is increasing at the same rate as the number of protons. Thus, Zeff is essentially the same for all the transition metals (Z

As noted, the closer two charges are, the more they are attracted. As you move down a group Z

- Atomic radius goes up as n goes up.
- 1st ionization energy: larger radius, less attraction, easier to remove ∴ loer 1st ionization energy
- Electron affinity: less attraction ∴ harder to add another electron
- Electronegativity: less attraction ∴ less likely to steal or hog electrons.

These require you to consider the exact electron under consideration. For this, we will look in more detail at the quantum description.]]>

Everything you know is wrong. Well, not everything. Just most of it. If there is one take-home lesson from this is that the assumption we all make that two opposite conditions cannot both be true at the same time is not valid, or at least not useful, when examining the world of subatomic particles and EM radiation. Think of it this way: our interaction with the BIG world averages out all the little events and we don’t notice them. Think about atmospheric pressure. The collisions of air molecules with your body average out and you don’t feel like you are being pummeled. But, if you were a spec of dust...you might have a different experience. Matter and energy, as we experience them, seem to be two different things with different properties. Actually, they are manifestations of the same thing.

- All electromagnetic (EM) radiation travels a the same speed in a vacuum (2.9979x10
^{8}m/sec. 3.00x10^{8}m/sec will do ) - We characterize EM radiation in terms of two parameters other than speed, wavelength, which is given the Greek symbol λ, (lower case lambda) and frequency, which is given the Greek symbol ν (lower case nu)
- Wavelength is exactly that, the distance from the peak of one wave to the peak of the next and is given in meters (visible light has wavelengths in the 4-7x10
^{-7}range, while UV light is shorter and X-rays much shorter. FM radio has values in the 3-10 meter range. - Frequency is “cycles per second;” just how many waves will pass a given point per second. It has units of 1/seconds or sec
^{-1}. - Logically, if I multiplied λ in meters by ν in 1/s I would get m/s, which is speed. Therefore νλ=c, the speed of light. Also λ∝1/ν That is, as wavelength goes up, frequency decreases.
- Light has a dual nature. In some ways, it behaves like a wave (shows diffraction patterns and refraction), in others it behaves like a particle (can travel in a vacuum, and has a measurable momentum).

Max Planck did an experiment in which he heated objects until they glowed. He then increased the energy he put in (by electricity) and expected the total energy he got out to go up as a straight line. Instead, it went up as a step function (that's not quite true…I'm presenting a clarifying view). More properly, the total energy was always some multiple of the same value for any frequency. That is, the height of the step was always the same for any wavelength.

He found that the value was equal to hν where “h” is Planck’s constant and ν is the frequency of light emitted. The value of Planck’s constant is 6.63e-34 J*s. The total energy emitted is given by nhν where “n” is some integer. Note, since λν=c, hν=hc/λ.

Einstein interpreted an experiment in which others shined light of different wavelengths onto a metal surface and found that electrons could be ejected from the surface. If one turned up the intensity of the light, more electrons were ejected, but they all had the same kinetic energy. If one increased the frequency of the light (lowered the wavelength), the electrons came off at higher velocity, therefore higher kinetic energy (since the mass of the electron is constant, higher KE means higher velocity). Einstein found that the kinetic energy of the electrons was related to frequency by the equation hν=BE+KE where ν is the frequency of light used and BE is the ionization energy (Binding Energy). It may seem obvious now, but it was not always clear how a ray of light could impart energy to a particle. In order to make sense of these results, and those of Planck, Einstein proposed that energy was transferred to the electron by a particle of light called a “photon” and that the energy of a photon was given by the equation Ephoton=hν. Therefore, the reason light was quantized is that each quantum of energy corresponds to the energy of a photon. One electron was ejected by a collision with one photon. The kinetic energy of the electron after the collision was equal to the kinetic energy of the photon after the collision minus that amount needed to remove the electron. Based on this, it was possible to calculate what the momentum of the photon had to be in order to impart energy to the electron at the measured level. Using the equations one could show that the momentum (p) of the photon was given by p=hν/c=h/λ. This suggests that a photon has mass, which it really doesn’t. It does have momentum.

I don’t want to lose track of the big picture in the details of some fairly simple calculations. The actual calculations are not hard, they just involve some numbers that seem non-sensically small.

Here is the big picture: we treated light like a wave, using standard equations that describe any wave and diffraction and got a number for the wavelength. Then, we looked at light as a particle (photon) with momentum, a completely different way of looking at it, and we got the same answer.

How can two completely different ways of viewing light both be right. This is one of those “Jimmy Moments” where you want to look at me and say: “No, the blue dog is up, damn it!” It underscores the point that a theory’s job is not to make you feel better about understanding things. Its job is to make predictions that can be tested. Bohr’s theory is clearly inadequate for the reasons I stated earlier. It does, however, make some astonishing predictions that turn out to be correct.

The equations:

You use trigonometry to figure out theta and from that, you figure out the wavelength from the diffraction angle and width of the slit (5.15E-6 in this case). First you have to figure out what theta is. For each bright line, you measured the length of the opposite in the right triangle (let’s say it was 37 cm for the red). You measured the adjacent , which was the same for each (100 cm). The ratio of opposite over adjacent is therefore 0.37. That’s related to the angle though the “tangent.” So you use the inverse of tangent (which is usually called “atan” for arctan or tan-1). arctan 0.37 is 20.3 degrees. So that’s theta. Then you take sin of that times 5.15e-6, and you get finally the wavelength at 6.59e-7m (659nm or rounded to 660nm).

The other numbers should be about 490nm for green and 430nm for Blue/violet.

This is not too hard. We'll cover it later in the week.

In fact, the math is easier.

Step 1 is to figure out the energy of each level in the Bohr atom. The amount of energy on level 1 is The answer is in joules because the ionization energy is (2.18x10

For Level 2 it is and for level 3 it’s 1/32 times 2.18 E

Now, find the difference between the value for 2 and the value for 3 (it should be about 3.03x10

Now that you have the Energy of each photon, use that to solve for the wavelength using “h” is Planck’s constant (6.63x10-34 J*s) and c is the speed of light (3.00x108m/s). Multiply hxc (you should get 1.99x10-25) and divide that by each of the energies you got for the differences between 3 and 2 etc. You should get wavelengths that are similar to the red, teal and blue lines.

The Bohr model has a lot of truth in it:

- Bohr’s idea that the electron exist only in discrete energy states is correct.
- He is also correct that the emission or absorption of a photon occurs when an electron transitions from one energy state to another.
- Where he was wrong was in that his mathematical approach did not explain the emission spectra of any other atom, and he had no real explanation as to why the electron should only be in discreet states.

- de Broglie and Schröedinger decided that they could take the equations developed to describe the energy of waves of fluid, or sound, and apply them to the behavior of the electron.
- The result was what is known as a “wave function,” which is abbreviated Ψ (psi) and is also known as an orbital. For each electron of an atom, there is a unique form of wave equation, which describes the energy of that electron. While this in not an “orbit,” this serves the same role as the “orbit” in the Bohr model, and so is called an orbital.
- An orbital does not tell you much about where an electron is, or where it is going. However, there is a form called Ψ
^{2}, which predicts the probability of an electron being in any particular place. - Since we have had to rely on the wave mechanical model to describe the electron, it is difficult to then solve for the position of the electron (position implies it is a particle).

Werner Heisenberg came up with the following equation

Δx X Δmv≥h/4π

where Δ

SO…we now can calculate the energy of an electron of other elements at any energy state (orbital)

What is the test of this?

We look to see whether it accurately tells us the wavelength of the bright-line spectrum of other elements…

We also now know why an electron only exists in discreet states: this is a characteristic of waves. Once you define certain parameters (like, where the nodes are, like in a guitar string), the distribution of the electron is constrained.

- The wave function describes the energy of an electron. What are the types of energy we need to take into account? a. Kinetic Energy of the electron (it’s moving and it has mass)
- Potential Energy attracting the electron towards the nucleus (opposites attract).
- Potential Energy resulting from the
*repulsion*from other electrons. - Bohr dealt pretty well with the first two. However, he never was able to deal with the third. The reason his equations work for hydrogen is that there
*are*no other electrons to repulse. - The wave function can be thought of as a “ticket” for a seat in a theater.

Level 1 is closest to the stage, and has only section “s” which has only 1 box. Those are the best seats, but there are only two of them.

When you go to level 2, you have section “s” which has only one box (2 seats in it) and section “p” which has three boxes, total of six seats. The next best seats are on level 3, again there is a section s (one box), a section p (three boxes) and now even a section d with 5 boxes in it. This goes on. Oh, one last thing: the ticket printer has a perverse sense of humor in terms of how he names each box and seat. The single box in any ‘s’ section is called box “0,” the three boxes in the ‘p’ section are called -1, 0 and +1; the 5 boxes in section ‘d’ are called -2, -1, 0, 1, 2 and the 7 sections in section f are -3, -2, -1, 0, 1, 2, 3. And the seats (remember, only two per box) are called either +1/2 or -1/2. So, if you get a great seat, you might be in level 1, section s, box 0 and seat +1/2. Maybe I’m in level 2, section p, box -1, seat +1/2. And, just confuse things more, section “s” is also known as section “0,” p is known as 1, d as 2 and f as 3....yeah, we needed that complication. But, remember, these are really part of equations, so they have to have some numerical value.

The first or principle quantum number is known as “n,” and can have positive integer values: 1; 2; 3; 4 etc. These play the same exact role as “n” in the Bohr equation. What Bohr missed is that at each primary level, there were multiple possible states for the electron to be in, and each differs slightly in energy. 2. Second quantum number is the angular momentum number and is symbolized as

Rather than determine the ΔH for every reaction, we have tables of standards involving all sorts of chemicals. These are called “Standard Enthalpies of Formation” abbreviated ΔH

The enthalpy of formation is the enthalpy involved in forming one mole of a compound from its elements in their most stable state. So, for water, it would be the enthalpy of the reaction H

All types of energy are interconvertible. The when a reaction takes place that releases energy, such as the burning of paper in air to produce CO

Energy comes in many forms, and can be converted among the forms, but not created or destroyed (this is known as the First Law of Thermodynamics). In order to keep track of energy, we need to define how to follow the changes and define a set of terms.

Here’s how: There is the

Okay, so here’s the somewhat odd part: we can only directly measure the changes in the surroundings; however, we like to report what has happened to the system. So, let’s say the surroundings (the water in a calorimeter, or your hand, for example) gain in heat. That must mean the system (the chemical reaction)

In a calorimeter, as I said, we aim to be totally

But, the total energy change of the system that is not in such a calorimeter has to be viewed as the total heat and work.

So, the explosion that goes on in the cylinder of your car's engine heats up the engine block, which heats up the radiator fluid, which passes the heat to the atmosphere. I can quantify that. But also, there is work done moving the car. Or, more directly, there is work done as PV work (remember, PV has units of energy).

Total energy change is heat plus work:

E

That's true no matter how you measure the work. However, when using PV work, there is a sign convention you must follow. Since work done by the system on the surroundings will

E

We went through a lot of derivations, but the take-home lessons are really not that complicated. There are three basic rules relating to the volume of a gas, all of which are intuitive.

- If you add more molecules (or moles, so that they are easier to count) to a balloon, the volume increases. If you remove molecules, the volume decreases.
- If you raise the temperature of a gas in a balloon, the volume will increase. If you decrease the temperature, the volume will decrease.
- If you increase the pressure on a balloon, the volume will decrease. If you decrease the pressure on the outside of a balloon, its volume will increase.

Increasing the number of moles of gas will increase the volume. In fact, if you double the number of moles, the volume will double. You can plot this on a graph of Volume (on Y) versus “n” (number of moles, on X), you get a straight line. This is a simple process. Put in some air, measure the volume. Then put in more, measure the new volume. You then plot the volume (in liters) at each number of moles. The slope of that line is in units of L/mol and is a proportionality constant relating volume to moles. The equation is V = k(n), where k is the slope of the line. A plot is included below. The number (22.4L/mol) is what the slope of the line would be for a gas at 1.00 atmosphere of pressure and 273K. You may note from that statement that we would have a different slope if we did the same experiment at a different temperature or pressure. This equation works only if temperature and pressure are constant. At other temperatures or pressures, you would have different equations.

If you increase the temperature, the volume also should increase. If we use the absolute scale, we get a graph that looks just like the one we got for volume versus “n.” In this case, the line would be V = k

You may notice that there is a point at which the volume is predicted to go to zero. We really don’t expect that to happen, of course. Sooner or later, we would expect that the gas would condense and become a liquid, or even a solid, at which point the volume would not decrease much more. However, that point at which the volume is

Using Kelvin, you have no negative temperature values. Also, we get a straightforward relationship that if we double the temperature (in K), we double the volume. Once again, we get a straight line with a slope in units of Liters/Kelvin (liters per Kelvin). That slope is the proportionality constant. Again, this line is derived for a particular number of moles and particular pressure.

If you increase the pressure, in this case, the volume will decrease, while volume will increase if the pressure is decreased. This is known as an “inverse relationship.” So, to get a straight line for this plot, you have to plot Volume versus 1/P.

You can the equation V=k3*1/P, which can also be written as P*V =k3, where k3 is the slope of the line and has units of Liter * atmospheres (or liters x whatever unit we use for pressure). All three of these “special” gas laws work only if the other two quantities are held constant.

In other words, the line for volume being proportional 1/P assumes that the temperature and number of moles are constant.

It would be great if we could derive a single equation that relates all of the parameters. That turns out to be pretty easy: you multiply the three equations and simplify the result. In the end, you get PV=nRT The ideal gas law. P is “pressure (usually in atmosphere in this class), V is volume (always in Liters in this class), ”n“ is number of moles and T is temperature ALWAYS in Kelvin). R is the Ideal Gas constant. The units of R, for us, will usually be liter*atmospheres/mol*Kelvin. In those units, the value is 0.08206 L*atm/mol*K. Using this equation is really quite simple. If I give you any 3 of the unknowns, you can solve for the fourth. For example, if I tell you that pressure is 1.2 atm, temp is 278K and volume is 22.0L, you can calculate how many moles of gas there are in the balloon. As you would for any equation, you just rearrange the equation to get the unknown thing on one side, and leave all the known parameters on the other. Then plug in the values.

Using this equation is really quite simple. If I give you any 3 of the unknowns, you can solve for the fourth. For example, if I tell you that pressure is 1.2 atm, temp is 278K and volume is 22.0L, you can calculate how many moles of gas there are in the balloon.

As you would for any equation, you just rearrange the equation to get the unknown thing on one side, and leave all the known parameters on the other. Then plug in the values. so, in this case, you are solving for “n” and the equation is which would be.

Notice that the units cancel properly.

There are also times in which I will not give you enough of the unknowns for you to solve for the last one. Instead I will ask you to tell me the change in one of the parameters given a change in some others. An example would be if I had a 0.57L balloon that was at 285K and I increased the temperature to 305K, what would be the new volume? Once again, the approach would be to rearrange the equation to get all of the parameters that are changing (in this case volume and temp) on one side and the ones that are not changing on the other. So, PV=nRT becomes:

At the first condition, the value is:

But, the values of n, R and P are all constant, so the value of nR/P has to be constant also. That means, that for

If you want to skip a step or two, you just set the two conditions equal to each other. That is, you don't even have to know that V/T=.002. Even if you didn't know the pressure and couldn't solve for the value, you would still know that V/T would be constant, as long as P or n do not change. So, as long as that is true:

Just solve for V2.

You can do the same for other "special" cases. Suppose I am holding temperature and number of moles constant, but changing pressure. Let's say, I put a sealed balloon in an oven (code phrases: sealed means "n" is constant…"rigid" means "V" is constant..which doesn't apply here).

You have 0.45L of volume in the balloon at 1.0 atm. Assuming temperature is constant, what is the new volume if I increase the pressure in the room to 1.8atm?

Here, we know n, R and T are constant. PV is changing. So, even though I don't know the temperature and therefore cannot solve explicitly for "n," I do know that P times V will remain constant, just as I showed in the demo today.

So, you can write P

In this case, PV=1.0x0.45=1.8xV

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I'm being pretty lazy here and using the Washington University, St. Luis website

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There were some problems with the program. As an additional place to see the questions, I'll place them here:

- True or false: The pH and the pOH are always equal
- You have a solution of 0.0125M HCl, which is a strong acid. Calculate the pH of that solution (be careful with sig figs on this).
- You make a solution in which you dissolve 0.20g of NaOH in water to a total volume of 500. mL (3 sig fig). What is the pH?
- You mix the 10.0mL of each of HCl and NaOH solutions. What is left in "excess."-(OH- or H+)
- What is the final pH of the solution of this mixture?

Answers:

false

1.90

12

H+

2.9

(the previous version was wrong…sorry)

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We are going to be looking at reactions in aqueous solutions (in water). The reason for this is that in order for a reaction to occur, the atoms, molecules and ions have to be able to interact with each other. They can do this if they are in either liquid or gaseous phase, but it is harder for this to happen if the compounds in question are in solid phase. While you can have solutions of solids, liquids or gases, but we will speak almost entirely on liquids. By convention, we call the thing that is present in greater concentration the "solvent" (this is the thing doing the dissolving) and the thing that is dissolved in it is called the "solute" (this is the thing dissolved).

BTW, here are the pages from the white board today.

The definition is functional: a solution that conducts electricity. In practice, this means that there are ions in solution, as opposed to molecules, since it is the presence of positive and negative ions that allows conductivity. Any electrolyte must involve some ions separating from each other. If a compound produces a lot of ions in solutions, such as when an ionic compound like NaCl dissolves, it is a strong electrolyte. Things that ionize only a little, like weak acids, will be weak conductors. Weak electrolytes, weak acids and weak conductors should be linked in your mind. A strong acid results in a low pH and will be good a conductor. Strong and weak bases will be analogous.

Solutions of ionic compounds in water are not "molecules" in solution, but were rather the separate ions of the compound. If an ionic compound dissolves, it does so by separating into its component ions which are "hydrated," or surrounded by water molecules. The partially negative oxygen crowds around the positive ion and the partially positive Hydrogens crowds around the negative ion. Solubility implies that the condition of hydration is lower-energy for that compound than the crystal. If the bonds between the ions is too strong, the compound will not be soluble, because the water cannot break the bonds.

There are a few we will consider:

- Precipitation reactions: In these, two solutions of ions are mixed. When the cation of one compound interacts with the anion of the other, the bonds of this new compound are too strong for the water to keep in solution, and the new solid precipitates.
- Acid-base reactions: in these, you mix the acid and base, which will result in a solution of intermediate pH. The product of these is generally water and some soluble salt.
- Oxidation/reduction reactions. These involve the trading of electrons, and are most notable in that they are the underlying chemistry of batteries and you.

We write equations usually as what we call balanced molecular reactions. For example

MgCl

In this notation, the small "s" in parentheses is "solid" and the "aq" is the aqueous form. But, we know that there are not molecules in solution, they are ions. So we can write the "complete ionic reaction:

Mg

C

First you have to balance that equation. Now, imagine I mix 5.45g of C

Answers 1C5H12 + 8O2 --> 5CO2 + 6H2O C5H12 is 72.15 g/mol water is at 18.02g/mol O2 is 32g/mol For C5H12, 5.45g x 1mol/72.15=0.0755mol 11.42g of O2 is 0.3569mol. You clearly have more O2 than C5H12. However, you don't have 8x as much. In other words, for 0.0755 mol of C5H12 you would need 0.604mol. You don't have that, so Oxygen is limiting. So, for 0.3569 mol of oxygen, you would use 1/8 that in C5H12 or 0.0446 mol. To answer the last part first, that means you would have left 0.0755-0.0446 mol of C5H12 which is 0.309 mol or 2.23g left over. For water, you have 0.3569 mol O2 x 6 mol H2O/8molO2 x 18.02g H2O/mol for 4.82g H2O.]]>

When we label an atom, the most important thing is it's atomic number, which is the number of protons. The number of protons determines the atoms identity. Carbon always has 6 protons. There is no form of carbon that has a different number of protons. If I were to add a proton to carbon, I would have 7 protons, and that would be some form of nitrogen (which has 7 protons, always. The atomic number usually is listed below the symbol for the element and to the left (the 6 is the number of protons, and, did I mention: carbon

Why don't we have to specify the number of protons? Because, calling it carbon already does that (you may recall that all forms of carbon have 6 protons...Okay, I'm done with that for a while). Isotopes have more or less identical chemistry. That's not surprising since they have only changed in the nucleus (which is the marble in the center of the stadium, while it is the electrons in the cheap seats that do the chemistry).

You can remove or add electrons from an atom without changing what type of element it is (but

1 Suppose I start with nitrogen-15, which has 7 protons. What would the symbol for that be?

2 Suppose I add 3 electrons, what would the symbol for that?

3 Suppose I started with nitrogen 15 and took away 2 neutrons, what would the symbol for that be?

4 Finally, suppose I started with the result from question 3 and took away a proton (left the same number of neutrons and electrons), what would the symbol for that be?

Borrowed from https://chem.libretexts.org/Reference/Periodic_Table_of_the_Elements

First, let's remember that chemistry will happen at the level of changes in the number of or interactions among electrons. Remember too that everything happens because of energy. Everything that happens will do so because it satisfies our second law and spreads out energy (Usually through enthalpy, or "heat"). So, it stands to reason that when bonds form, electrons will end up in a lower potential energy state, releasing energy to the surroundings. note also that there are elements called "Noble gases," which do not engage in chemistry at all. They are the ones in the last column on the right. It stands to reason that they, or rather their electrons, are already in as low an energy state as they can get to. Maybe chemistry happens in ways that get other elements to an arrangement of electrons more nearly like noble gases. That will provide our first working model for how bonds will form. ]]>

Mr. Potato Head from "Toy Story." Used without permission.

Okay, you have been told for years that all matter is made of atoms, and you probably have been told that atoms are in turn composed of a nucleus, in which there are protons and neutrons, and electrons in "orbit" around the nucleus (that last part is not quite correct). But, what evidence have you ever been given that any of this is true? I know that you had to memorize this stuff to get good grades quizzes and such, but I really don't want you just to accept stuff on faith in my class. You cannot see atoms. We cannot “see” them ever, really. So, how can we ever show that something we cannot see even exists, let alone makes up all of matter?

The idea of the atom goes back a long way. It was a minority view in the time of the Greeks, which is where the term Atom (which means “uncuttable”) comes from. It's a simple idea: I have some carbon, and I divide it in half. I still have carbon in each half, with no differences in behavior. I do the same thing again, and again, the two halves are carbon. Imagine doing this over and over until we are down to sizes we can no longer see, and even smaller. One school of thought was that sooner or later, we would come down to some really small thing that we could no longer cut in half. That is an "Atom." The other school of thought is that the four "elements" (earth, air, fire, water) could be combined in continuous amounts to make all things we see.

1. Elements are made of atoms.

2. All the atoms of an element have the same properties (they are essentially identical), and the atoms of different elements have different properties. They are different in some fundamental way.

3. Chemical compounds are formed when atoms combine with each other. A given compound always has the same relative numbers and types of atoms.

4. Chemical reactions involve reorganization of the atoms - changes in the way they are bound together. The atoms themselves are not changed in a chemical reaction.

That fourth one is the big one. It is our first real model for how chemistry happens.

It turns out that carbon has the mass of 12 and oxygen is about 16 (which preserves the 3/4 ratio). Since I have focussed a lot on units, you would be justified in asking "12 what?" or "16 what?" Well, we call it the "AMU" which stands for Atomic Mass units. Years later, we know the conversion to grams. But, before we did, we could still talk about relative masses. Carbon atoms weigh 12 times the mass of a hydrogen atoms.

Another key point is that chemical reactions cannot change the number of atoms of each element. They all have to be there both before and after the chemical reaction. their connections…we'll call them "bonds," to each other change.

An example of how Dalton drew his conclusions:

Suppose I didn't tell you how many heads I made, would you be able to tell what each piece weighed? Well, no. However, you would be able to tell that the head was 4 times the mass of the noses. Also, you would be able to tell that the head is 5 times the mass of each eye and therefore, the mass ratio of the nose to that of the ear is 5:4. So, even without knowing how many you have, you can get the mass ratios. Well, Dalton used the law of definite proportions like that.

Dalton had a really good model explain what was going on in chemical reactions-atoms are bonded in different patterns to make different molecules with new properties-but no idea how bonding would take place. Moreover, what was an atom made of anyway?

If you forget the names of the famous dead guys who did the experiments, I'll forgive you (and it won't hurt your grade much). However, I do expect you to know, at least for the cathode ray experiment (Thomson) and the Rutherford (gold foil) experiment, how what they did demonstrated what we think. The absolutely key thing is

Interestingly, however, the recognition that atoms are made of generic particles whose number differs from atom to atom, re-opens the old alchemy idea of changing one form of matter into another. It can be done, after all. But, instead of increasing the amount of "fire" in iron to make it gold, we have to increase the number of protons, neutrons and electrons.

Of course, the real trick is showing that the static electricity and other electricity is carried by particles that have mass. Thomson performed experiments with a cathode-ray tube.

The fact that the beam had inertia (it resisted a force applied) and that its inertia varied with the square of its speed suggests that there must be particles that have mass. Thomson was able to to determine the charge/mass ratio of the electron, which proves in principle that it has mass. It's simple enough: the heavier it is, the more difficult it will be to deflect. The more charge it has, the easier it will be to deflect. By doing a series of experiments, he determined a determined the charge/mass ratio that fit the deflection. Millikin did a more difficult experiment that comes to this: Charge a drop of oil, which would require you to either add or subtract some electrons from the oil. He would suspend the drop in an electric filed. The strength of the force on the drop from the field is equal to E*Q, where E is the voltage applied and Q is the charge on the drop. The force making the drop fall is of course m*g (mass times gravity). When the drop hovers suspended, E*Q=m*g. He could determine the mass of the drop (from density and volume), he knew "g" and knew E (the voltage he applied). He could solve for Q, which is the charge on the drop. Some sample data were:

In a perfectly run experiment, the difference in charge between drops would be some integer multiple of 1.6x10-19 Coulombs (C, the unit of charge we use after another famous dead guy). That suggests that this must be the charge on a single electron. Actually, his data were a little off because he didn't account properly for the viscosity of air. From this, and Thomson's mass/charge result, we can calculate the mass of the electron as about 9.1x10-28g. Really tiny.

So, the next big experiment is Rutherford. In this one, a set of charged (positive) particles (alpha particles) are fired at a thin sheet of gold foil. Almost all of them go through.

You and your friends are members of an alien species that is fascinated by a dead planet known as E-rth and in particular with the extinct species called Huemon. In particular, you are interested in understanding a peculiar aspect of Huemon society, known as monee. It is thought by many that everything in the Huemon society is somehow made of monee. One of the problems that you face in understanding monee is your vision, which detects light only in the short wave radio range. As a result of this, you and members of your species can only resolve, that is, see, objects that are larger than about 7 cm in size. Therefore, while many of you suspect that there is fine structure to monee, no one has been able to discern what that structure is.

Among the things known about monee are:

- Collections of monee behave as a dense liquid. That is, when poured into a container they have a defined volume, but adopt the shape of the container.
- When poured, monee makes a characteristic "jingling" sound.

You are the planets leading expert in monee (since scientists are revered on your planet, that makes you kind of a big deal…kind of like basketball players are here). You have attained the status for two main reasons. First you have found a way to purify different types of monee based upon their optical properties. You have, to date, isolated three distinct types: type "A," is extremely shiny; type "B" is somewhat dull in appearance but similar in color to A; type "C" has two forms, a shiny one and a dull one, but both are darker in color than either A or B. The second reason for your success, is that you have discovered a Huemon device known as the "Kandimusheen." When specific combinations of monee are put into the Kandimusheen, various tasty treats come out (this is part of why your species thinks that everything on E-arth is made of monee). You have combined these two advantages to determine that specific combinations of each form of monee results specific treats.

Since you cannot handle money directly, you have a robot to carry out your experiments. In a typical experiment, you begin with a known mass of each type of monee in each of three cups. The robot then takes monee from each of two cups and combines them with the help of the Kandimusheen, yielding a particular substance. After that, you can determine how much of each type of money is used by determining mass remaining in each cup.

The results of typical experiments are shown below:

Experiment | Mass of "A" used | Mass of "B" used | Mass of "C" used | Yield |

1 | 0g | 5.0g | 3.0g | peessogum |

2 | 0g | 10.0g | 6.0g | 2 peesogum |

3 | 2.5g | 5.0g | 0 | chalklatkiss |

4 | 5.0g | 10.0g | 0g | 2 chalklatkiss |

5 | 5.0g | 5.0g | 0g | Kookie |

6 | 10g | 10.0g | 0g | 2 Kookie |

7** | 5.0g | 5.0g | 0g | chalklatkiss AND 2.5g of A left over |

The key observations you make are:

Your task is to come up with a detailed theory of monee, and explain to me, an amiable but somewhat dim King, as much as you can about how monee works.John Dalton 1766-1844

John Dalton lived in England, on planet Earth, where scientists are not revered nearly enough. Among nerds like myself, Dalton is famous for many things. He also trained a graduate student who went on to become famous, named James Prescott Joule, who distinguished himself working on energy. Dalton worked on matter, and is perhaps best known for his Atomic Theory of Matter.

Dalton's notebooks show that he based it on data and observations such as this:

From this, Dalton came to very similar explanations as you did for monee.

The ratio of the masses of Carbon to Oxygen is 3:4. Hydrogen was found to be the lightest (it is given the weight of one Dalton), then oxygen is 16 times that mass, and therefore oxygen must be 16 daltons, and Carbon must be 12 (to maintain the 3:4 with Oxygen). Notice, you don't know the actual mass in grams. But, you know the ratios.

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The important thing to remember here, is that units are usually chosen to be convenient. I made a couple of jokes about needing a unit for distance that is about the width of your thumb or a unit of volume that’s the right amount to order for a glass of beer (or orange juice, in your case). So, using the units you are more used to, a “cup” of orange juice or a “pint” of beer may seem about right. Measuring out gasoline in cups would be a little less convenient than gallons. Similarly, measuring distances between your home and downtown San Diego in inches would be inconvenient. Thus, we try to have units such that the amount we are measuring provides us with a number that makes sense in our feeble brains. (No offense intended, no humans are any good at comprehending really large or really small numbers.) The problem with the system that you grow up with is that there is no consistent relationship between units that are optimized for measuring out a cup of orange juice, a gallon of gasoline, or a barrel of oil, just as there is no consistent relationship between an inch, a foot, a yard and a mile. You have to remember all of the unit conversions. At this point you probably know most of them however, I have to say it is a bit of pain in the butt. We will be using the SI Units. That stands for the “international system” of units (or rather, it stands for the French version of that). The great advantage here is that in each case we have one base unit, say, the meter for distance, and then units derived from that as factors of 1,000 larger or smaller. In some cases, factors of 10 or 100 may be used if we have need for a unit in that range. A meter is about the length from the tip of your nose to the tip of your finger, that is, if you are an average male in the 17th century (actually, the definition of a meter has been updated many times over the last couple of hundred years). The common unit “centimeter” is one 100th of a meter. Normally, as I said, we would multiply or divide by factors of 1,000. So we have: a millimeter, 1/1000 of a meter; a micrometer, 1/1000 of a millimeter; a nanometer, 1/1000 of a micrometer, and so on. Whether we are speaking about meters, grams, liters, or volts, or any other basic unit, milli means 10

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The basic idea is this: the units must cancel out to give you the proper units for your answer. If you want your answer to be in grams, the other units in the calculation must cancel. The nice thing about this is that it shows you how to set of the calculation. Rather than try to remember whether two numbers should be multiplied, or one divided into the other, you set up the equation

How do we know things? Fundamentally, what is the basis of knowledge? This is a completely separate class. However, it is essential that we address it a bit. Science is not about certainty, but about testability. It is a system of knowledge that is based on testing one's ideas against observation. The only untestable assumptions we allow are: that there is something we call reality; and that we can interact with that reality in some meaningful way. That is the core of what an experiment is: an experience of reality from which we extract meaning.

One could fairly point out that science is therefore based ultimately on untestable assumptions. However, it is also fair to say that anyone interacting with the world at all—walking, talking to others, any interaction at all—makes these same two untestable assumptions. In science, these two untestable assumptions are the only two we make.

Every other assumption can be tested by comparing the predictions of your assumptions to the reality you experience. There will be mistakes and dead ends, that's true. However, by continuing to check our predictions against reality, we can assess how well our explanations fit. You may notice that in this system, there are no "absolutes" accept for rare instances where they arise as part of a definition (as in “absolute zero” in temperature). Otherwise, we merely define and limit our uncertainty. The very idea of certainty is somewhat out of place in science. A few years back at the dedication of our Science building, Nobel Laureate David Baltimore put it like this: “in science, we move from uncertainty to

A fact is something observed reproducibly in the physical world. Facts are our measurements. As absolute as the term "fact" may seem to you, the reliability of facts depends on the precision of the measurement. Thus, our appreciation of facts can change. You may say it is a fact that the desktop is solid matter. However, it is, like all objects you see, mostly space. Small particles pass through the desktop as though it isn't there. If your level of detection (resolution) is that of your eye, or your finger, objects do not pass through the desktop. If your level of resolution is considerably smaller (the size of a proton or electron), the is more "space" for particles to pass through than there is matter for them to hit. Anything outside your limits of resolution cannot be detected. That does not mean your measurements are meaningless. It just means that it is extremely important to know what your limit of resolution is. In a very meaningful way, the desktop is solid. Your conclusions from your interaction with the desktop were not wrong. We have just refined our understanding of what "solid" means.

A theory can be disproved. However, when a theory that has proven extremely useful fails to work in some context, we usually don't talk about disproving it, but rather finding its limits. For example, Dalton's Atomic Theory, which we will discuss soon, is right in many ways. However, one of Dalton's claims is not correct: that atoms are indivisible. So, we modify the theory a little and say that dividing an atom makes it a fundamentally different thing. An atom is not the smallest unit of matter (as Dalton would have said) but the smallest unit of an element that still has the properties of that element.