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Intro to Quantum Mechanics .txt | It won't accept five cent coins. |
Intro to Quantum Mechanics .txt | It won't accept dollar bills. |
Intro to Quantum Mechanics .txt | It only accepts a single coin known as the quarter. |
Intro to Quantum Mechanics .txt | Now, in the same analogous way, electrons and protons and neutrons and other subatomic particles accept energy bursts this feet amount called a photon. |
Intro to Quantum Mechanics .txt | Now, one other result from quantum mechanics is the following. |
Intro to Quantum Mechanics .txt | Electromagnetic waves, such as as light waves, have dual natures. |
Intro to Quantum Mechanics .txt | In other words, they can act as both a particle and as a wave. |
Intro to Quantum Mechanics .txt | And we'll talk more about that when we'll talk about the photoelectric effect. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So we already spoke about the root mean square velocity of any set of points. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, we're going to look specifically at the root mean square velocity for gases. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, in gases, root mean square velocity is given by the following formula, which can be derived using calculus. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, I will spare you the calculus and simply give you the formula. |
Average Kinetic Energy and Root Mean Square Velocity .txt | But if you're curious about where this formula comes from, leave A comment and I'll Show you. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So, VRMs is equal to the square root of three times R times T divided by M, where M is our molar mass of gas, t is our temperature in Kelvin, and R is the molar gas constant. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, my goal is I want to use this VRMs to find the average kinetic energy. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Because remember, kinetic energy of anything is given by one half times mass times V squared. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, to find the kinetic average, I basically plug in my Dr meh into my D, and that will give me the average, because remember, this guy is the average or the quadratic average of my sets of points. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So average kinetic energy is equal to one half times and times VR mass squared equals one half times mass. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, I take my formula for BRMs, for Dances, and plug into my equation. |
Average Kinetic Energy and Root Mean Square Velocity .txt | The radical will disappear, because the radical has an exponent of a half a half times two is one. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So I simply get one half times mass over molam mass times R and T. Now, remember, molar mass has units of mass divided by moles. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So the mass will cancel, and moles will go on top, and we'll get one half the mass will cancel. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So this M and this M will cancel. |
Average Kinetic Energy and Root Mean Square Velocity .txt | The moles will go on top, and we'll have R times T. So my file final representation of my kinetic or average kinetic energy is three times N times R times T divided by two, where N is our number of moles. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So Suppose we have 1 mol of any gas. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Well, since we have 1 Mol, our N will be one. |
Average Kinetic Energy and Root Mean Square Velocity .txt | And for 1 Mol, our formula becomes average kinetic energy of 1 mol of gas. |
Average Kinetic Energy and Root Mean Square Velocity .txt | That's equal to three times R times T divided by two. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So the only non constant in this equation is T. So we see kinetic energy depends strictly on temperature, or 1 mol of gas depends strictly on the temperature. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, suppose instead I want to find one molecule. |
Average Kinetic Energy and Root Mean Square Velocity .txt | What's the kinetic average of one molecule of gas? |
Average Kinetic Energy and Root Mean Square Velocity .txt | Not 1 mol. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Well, remember, a mole has an avocado's number of molecules. |
Average Kinetic Energy and Root Mean Square Velocity .txt | So I simply take my formula and divide it by N. So three times R times two divided by two N. The reason I singled out the R and the N is because this guy is known as a Boltzmann constant. |
Average Kinetic Energy and Root Mean Square Velocity .txt | In other words, scientists use some value k that equals r divided by n. So we replace this R divided by n with k called the Bolton constant, and our equation becomes three times k times t over two. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Which is the same thing as saying three times R times t divided by two times n.
So once again, for one molecule, a single molecule, to find the kinetic average of that molecule, we simply use this formula where k is at boltsman constant. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now, to find the average kinetic energy of a mole of molecules, we have to use this formula. |
Average Kinetic Energy and Root Mean Square Velocity .txt | Now note that at any given time, our molecule can have any kinetic energy. |
Average Kinetic Energy and Root Mean Square Velocity .txt | But on average, a mole of molecules will have this much energy. |
Average Kinetic Energy and Root Mean Square Velocity .txt | And on average, a molecule within this mole will have this much kinetic energy. |
Colloids .txt | Colloids are mixtures of two or more compounds found in different states. |
Colloids .txt | That means that they are nonhomogeneous solutions. |
Colloids .txt | Recall that a homogeneous solution is a solution in which the compounds that compose the mixture are in the same state while colloids are composed of compounds in different states. |
Colloids .txt | Now, they also contain larger solid particles. |
Colloids .txt | For example, blood, which is a colloid, is composed mostly of water and hemoglobin. |
Colloids .txt | Hemoglobin is the larger particle, the solute, while water is a solvent, okay? |
Colloids .txt | Now, the larger particles are also called colloidal particles. |
Colloids .txt | So hemoglobin is the colloidal particle. |
Colloids .txt | Now, other examples of colloids exist. |
Colloids .txt | Fog. |
Colloids .txt | Fog is composed of liquid particles found in the gas state. |
Colloids .txt | Smoke is composed of solid particles or carbon, found in the gas state. |
Colloids .txt | Wood cream is composed of gas particles found in the liquid state. |
Colloids .txt | And paint is composed of solid particles found in the liquid state. |
Colloids .txt | Now, carbon systems also experience something called a Tyndall effect. |
Colloids .txt | The tyle effect is a scattering of light due to the presence of large particles. |
Colloids .txt | Now, if you look at this system here, pretend that this is a cup and inside is a colloidal system, okay? |
Colloids .txt | And these are the colloidal particles or the large particles. |
Colloids .txt | Now, when light will enter it's going to bounce back and forth between these particles and it's going to lose energy. |
Colloids .txt | Eventually, when it comes out, it's going to come out with less energy because remember, light carries energy. |
Colloids .txt | Light is composed of photons. |
Colloids .txt | That means that the system, the colloidal system will be translucent so you won't be able to see through it very clearly. |
Colloids .txt | The solid portion of the colloid is called a continuous phase. |
Colloids .txt | The solid portion of the colloid is called dispersed phase. |
Colloids .txt | Now, when water is a solvent, classification occurs in two ways. |
Colloids .txt | Lyophilicaloids are those colloids that have strong attractions between continuous and dispersed phases. |
Colloids .txt | Examples include protein water, which is found in blood. |
Colloids .txt | Protein is a dispersed phase. |
Colloids .txt | Water is a continuous phase and they mix very well. |
Colloids .txt | Biophobic colloids are those colloids that lack attraction between continuous and dispersed phases. |
Colloids .txt | And examples include fat and water mixtures. |
Colloids .txt | We know that fat, the dispersed phase and water continuous days don't mix very well. |
Colloids .txt | Now, there are two ways to filter colloids. |
Colloids .txt | The first way is by heating and then filtration. |
Colloids .txt | If you heat a colloid, this will cause the salute to coagulate and then you could filter it by simple filtration. |
Colloids .txt | The second way is via dialysis. |
Colloids .txt | Dialysis is a separation using a semi permeable membrane. |
Colloids .txt | For example, you have a semi permeable membrane here. |
Colloids .txt | Red blood cells mixed with water. |
Colloids .txt | The red blood cells are the dispersed phase. |
Colloids .txt | The water is a continuous phase. |
Colloids .txt | Water will flow easily for one side is next. |
Colloids .txt | The red blood cells are too big to pass so they will be left behind on this side. |
Cell voltage example .txt | So we begin with a certain electrochemical cell that's composed of cadmium and zinc. |
Cell voltage example .txt | Now, we are given the cell voltage or the electromotive force around cells, and it's given to be zero point 36 volts. |
Cell voltage example .txt | Under standard conditions, that means 1 bar pressure and one molar concentration. |
Cell voltage example .txt | Now, this guy is also at 25 degrees Celsius. |
Cell voltage example .txt | So we are also given the cell voltage for one of the two half reactions, one of the two half cells. |
Cell voltage example .txt | And the zinc half reaction is given negative zero point 76 volts. |
Cell voltage example .txt | We want to find our goal is to find the cell voltage for the other half cell for the other half reaction. |
Cell voltage example .txt | So, in the first step, we begin our problem by writing their reduction reaction for the entire equation for the entire process. |
Cell voltage example .txt | So, solid zinc reacts with cadmium ions to produce aqueous zinc and solid cadmium. |
Cell voltage example .txt | So let's figure out which one is oxidized and which one is reduced. |
Cell voltage example .txt | This will help us place the metal that belongs to the anode and the metal that belongs to the cathode. |
Cell voltage example .txt | So, zinc solid goes from a neutral charge to a plus two charge. |
Cell voltage example .txt | That means it loses electrons. |
Cell voltage example .txt | So that means it is oxidized. |
Cell voltage example .txt | It's a reducing agent. |
Cell voltage example .txt | Now, this guy cadmium ion goes from an ion to a neutral charge, and that means this guy is reduced. |
Cell voltage example .txt | So it's the oxidizing agent. |