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ZwsWjelzqDA-054|N equal 3.
ZwsWjelzqDA-056|Zero probability are the places where the wave function goes to 0.
ZwsWjelzqDA-057|After you square 0, you still get 0.
ZwsWjelzqDA-058|So the probability of finding the particle at these crossings is zero.
ZwsWjelzqDA-059|And that's a strange characteristic of particles that behave like waves.
ZwsWjelzqDA-060|There's portions of the box where the particle is forbidden to be.
ZwsWjelzqDA-061|So this is interesting.
ZwsWjelzqDA-062|I'll have two nodes, 1, 2.
ZwsWjelzqDA-063|Node a, area where the wave function goes to 0 in the high energy state, one node here, and zero nodes here.
ZwsWjelzqDA-064|When the number of nodes increase, the energy state increases.
ZwsWjelzqDA-065|That's a higher energy situation.
ZwsWjelzqDA-066|So here's what I have.
ZwsWjelzqDA-067|I have a wave.
ZwsWjelzqDA-069|Only certain wavelengths can exist.
ZwsWjelzqDA-070|So half a wavelength, one full wavelength, 1 and 1/2 wavelengths.
ZwsWjelzqDA-072|So if I fix the ends of the box, I put boundaries on a wave.
ZwsWjelzqDA-073|I naturally get what I call quantization.
ZwsWjelzqDA-074|Not every wave can fit in these boxes.
ZwsWjelzqDA-075|Only certain waves can fit in these boxes.
ZwsWjelzqDA-076|And there's a gap.
ZwsWjelzqDA-077|I go from here, n equal 1, all the way up to here, and I skip all those energies in between.
ZwsWjelzqDA-078|I can only have this energy state for the box or this energy state for the box and no energy states in between.
ZwsWjelzqDA-079|The energy is quantized.
ZwsWjelzqDA-080|And waves naturally do this.
ZwsWjelzqDA-081|It's not unusual to see it.
ZwsWjelzqDA-082|We can demonstrate it with audio waves.
ZwsWjelzqDA-083|Audio, sound, is a wavelike property, and here's a tube of fixed length.
ZwsWjelzqDA-084|So if I want waves to exist on this tube, only certain wavelengths will fit.
ZwsWjelzqDA-085|I'll be able to fit a full wave on this, a wave on this, a wave and a half on this.
ZwsWjelzqDA-086|So only certain sounds will fit in this tube.
ZwsWjelzqDA-087|That's interesting characteristic.
ZwsWjelzqDA-088|I can demonstrate a couple of the sounds that fit in this tube.
ZwsWjelzqDA-089|We won't hear when we figure the sounds that fit in this tube.
ZwsWjelzqDA-090|We won't hear a continuous sound.
ZwsWjelzqDA-091|We won't hear [MAKING SOUND EFFECT] continuous wavelengths.
ZwsWjelzqDA-092|We'll have [MAKING SOUND EFFECT] and [MAKING SOUND EFFECT],, two individual wavelengths that fit in this box.
ZwsWjelzqDA-093|Let's actually demonstrate that.
ZwsWjelzqDA-094|I'll try to spin this, and you guys can listen.
ZwsWjelzqDA-095|There is one wave that fits.
ZwsWjelzqDA-097|And there's that low frequency, long wavelength, two energy levels.
ZwsWjelzqDA-098|And you can see energy.
ZwsWjelzqDA-100|I wonder if I get a higher one.
ZwsWjelzqDA-102|That's a beautiful acoustic example of waves and quantization.
ZwsWjelzqDA-103|All you need to get quantization is take a wave and force it to exist in a certain area of space.
ZwsWjelzqDA-104|If you fix the ends of a wave, you get quantization.
ZwsWjelzqDA-106|And when waves are bounded, you get quantization.
ZwsWjelzqDA-107|You get a particle in a box.
sY-0uDLNYmk-000|Let's look at the bromination of diene.
sY-0uDLNYmk-002|Now, as these reactions go, there's an equilibrium here, so these two products can interconvert.
sY-0uDLNYmk-005|Notice that the 1-bromo is the same throughout.
sY-0uDLNYmk-012|We're looking at the bromination of a diene.
sY-0uDLNYmk-013|It can be brominated in the 1 position or the 3 position, and we have some data about the chemical reaction.
sY-0uDLNYmk-014|So as the chemical reaction occurs initially, the 1-bromo is favored, so it's kinetically favored.
sY-0uDLNYmk-015|It has a short pathway or a low activation energy to forming relative to the 3-bromo.
sY-0uDLNYmk-016|If you look at the reaction over time though, as I go out to four hours, what's happening is the 3-bromo is building up in concentration.
sY-0uDLNYmk-017|So over time, the 3-bromo is more stable, so it's more thermodynamically stable.
sY-0uDLNYmk-020|The thermodynamically favored means there should be a larger difference in energy between the reactants and the products.
sY-0uDLNYmk-022|So in this case, the correct answer is B.
xcJkUZ4fzEE-000|Let's do a calculation involving isotopes.
xcJkUZ4fzEE-003|Here we're going to take a sample of pure carbon and look at the mass spectrum.
xcJkUZ4fzEE-004|Now remember, pure carbon means we take a sample of pure carbon from the ground and we run it through the mass spectrometer.
xcJkUZ4fzEE-005|The question is, what is this peak at mass 13?
xcJkUZ4fzEE-006|What's the molar mass of the sample?
xcJkUZ4fzEE-007|And how many protons and neutrons are in carbon-12?
xcJkUZ4fzEE-008|We can go through these initially.
xcJkUZ4fzEE-009|The sample is naturally occurring carbon.
xcJkUZ4fzEE-010|So it's 1% carbon-13 and 99% carbon-12.
xcJkUZ4fzEE-011|And that's reflected in the mass spectrum, a peak about 100 times as big at 12 as you have at 13.
xcJkUZ4fzEE-012|So that explains the mass spectrum, the naturally occurring isotope carbon-13.
xcJkUZ4fzEE-013|Now, the molar mass is the weighted average of those two isotopes.
xcJkUZ4fzEE-014|The ratio, in every 100 atoms, there are 99 carbon 12's and one carbon-13.
xcJkUZ4fzEE-024|And it determines the identity of the atom.
xcJkUZ4fzEE-025|Remember, if you know the number of protons, you know the identity of the element-- not the mass, the number of protons.
xcJkUZ4fzEE-026|It has mass 12.
xcJkUZ4fzEE-027|So those other 6 mass units, 6 for the proton, mass 12, there's 6 more mass units.
xcJkUZ4fzEE-028|Those must be the neutrons.
xcJkUZ4fzEE-029|So there's 6 neutrons in carbon-12 nucleus.
8qqpmXD8cjU-000|Let's look at some weak acids and weak bases in solution and see if we can predict which will have the highest pH.
8qqpmXD8cjU-001|So here I have three solutions.
8qqpmXD8cjU-002|They'll all be at 0.1 molar.
8qqpmXD8cjU-003|Which has the highest pH?
8qqpmXD8cjU-012|A weak base, weak base equilibrium constant-- 10 to the minus 8.
8qqpmXD8cjU-013|So this reacts as a weak base.
8qqpmXD8cjU-014|This will be a slightly basic solution.
8qqpmXD8cjU-015|Another of ours is sodium acetate.
8qqpmXD8cjU-019|Here's the acetate ion reacting with water as a base.
8qqpmXD8cjU-020|We had a Kb 10 to the minus 10.
8qqpmXD8cjU-021|So a Kb 10 to the minus 10, this base considerably stronger than this base.
8qqpmXD8cjU-022|The last one we have, NH4Cl, that forms NH4 plus ions in solution-- and Cl minus.
8qqpmXD8cjU-023|And we've seen that.
8qqpmXD8cjU-025|So this last one is an acid.
8qqpmXD8cjU-030|And of these two, NH3 is the stronger base.
8qqpmXD8cjU-031|So the highest pH, the highest OH minus concentration, comes from the strongest base.
8qqpmXD8cjU-032|And in this case that is NH3.
Xt-yom79grM-000|Let's look at the equilibrium between liquid water and gaseous water at 25 degrees C.
Xt-yom79grM-001|And what can we say about the standard state free energy difference and K for that physical process?
Xt-yom79grM-014|That's where water comes up to the boiling point.
Xt-yom79grM-015|1 atmosphere of pressure is the pressure that defines the boiling point.
Xt-yom79grM-016|So, I have 1 atmosphere of pressure.
Xt-yom79grM-017|That's too high for 25 degrees C.