CHEM 230 Lecture Notes - Lecture 5: Quadratic Equation, Equilibrium Constant, Partial Pressure

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purplebeaver856

21 Dec 2016

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The number in the negative dg actually tell you how far the products are going to go. There will always be some product and reactants left. Reaction doesn"t go to completion even if the products are favored. Doesn"t stay at all reactants; will make some products. When we talk about mixing, we"re talking about mixing reactants and products. Because of equilibrium which goes into mixing and entropy. Number tells us how reactant favor we really are or how little product we make. If we take a system and add more particles in (keep v and t constant), entropy goes up. The particles will spread out through the whole container. So they increased the volume they occupy and an increase in volume increases entropy. What you can have sometimes is if you have both products and reactants and they can mix into each other. Expansion into a bigger volume leads to a larger entropy.

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10. In this question, mean field theory will be used to derive the van der Waals equation. Consider a gas of interacting, indistinguishable particles. In principle, the potential energy from these interactions depends upon the positions of the particles so detailed structural information is needed to describe it. This is a difficult problem. However, we can take a much simpler, albeit approximate, approach by treating the interactions with a one-body energy term. The physical argument goes as follows. The interaction (potential) energies in principle will vary among microstates. However, we expect fluctuations to be small. Let's replace the exact potential U in the partition function with its average value (that is, the "mean field") eMF divided among the particles, and assume each particle has the same contribution regardless of its position. In other words, rather than considering the particles as interacting with each other (via a potential that depends upon particle positions) we treat them as interacting with the mean field (which is independent of particle positions and other particles). In this way, EMF becomes a one-body energy term that can be included in the usual non-interacting partition function as an additional energy contribution. That is, the interacting system is approximated by the non-interacting partition function with a one-body energy term approximating the particle interactions. With this mean-field approximation, the energy of our particles becomes E=E;deal + EMF , in which Eideal is the energy of a particle in an ideal gas. Since these energy contributions are independent, the particle partition function is q = qidealqMF . Normally, qideal would be the product of partition functions for translation, vibration, rota- tion, etc. but because the volume dependence will be important, let's write qidealc(T)V where c(T) includes all the constants and temperature dependencies arising from vibrations and rotations, and where the volume factor in the translational partition function has been explicitly accounted for. The remaining part of the translational partition function in included in c(T). In the present case though, we imagine the particles each occupy some volume b, so the "effective volume" of our system is V- Nb. In other words, take qideal cT)(V - Nb) We don't know the value of eMF but physical arguments suggest it must vary with the av- erage distance between particles, which in turn varies with density, N/V. So, let's suppose a linear dependence and write EMF =-aN/V with a some unknown constant. A minus sign is included here because it is anticipated EME will be negative (attractive interaction) so this will make a a positive number. This one energy is the same for each particle so 4 a) Derive the expression for the average pressure and show the system obeys the van der Waals equation of state. Note: as defined b is the volume per particle not per mole of particles as usually tabulated. Similarly, as defined a is per particle not per mole squared as usually tabulated. So, write Nb as nb, and aN2 as an2 if you want to use a and b as the usually tabulated molar values b) Show that the internal energy and heat capacity are given by an - - U ==ideal and Cv=CV,ideal, where Eideal and Cvideal are the internal energy and heat capacity for the ideal gas, respectively. Show that the first relation is consistent with (UaVTan2/V2, a relation derived from thermodynamics. Give a physical argument to explain why the van der Waals gas (an interacting system) could have the same Cv as the ideal gas (a non-interacting system)

This is the description from my organic chemistry lab.

Lab Observations and Data

We obtained 1.17g of cyclohexene oxide (clear liquid) and 3 mL of water into a 50 mL flask with a stir bar. When added a single drop of sulfuric acid, the clear liquid started to change to a very, very light yellow/brownish color. We obtained an ice bath on the side in case our mixture started to boil. After the solution stirred for about 25 minutes, we added sodium hydroxide. We inserted a pH paper and it turned a dark blue, meaning basic. Added another drop of sulfuric acid to make it a little less basic. Added the mixture to a separation funnel, shook it around and ended with separated layers. We separated the layers, thinking the bottom layer was the organic layer, when it was really the aqueous layer. So we ended up mixing the wrong layers back together. After some error, we isolated our new organic layer and added some drying agent. We then put that mixture with the drying agent, NaOH, into the rotovap. Our final product was a white powder and weighed 1.51 grams. We then set up a vacuum filtration while boiling water. We boiled our dried organic layer into the hexane. Added two drops of ethyl acetate to help the boiling process go faster. After vacuum filtering it, it weighed .394 grams. The melting point is 91 to 93 degrees Celsius. Our IR spectra matches the "trans" conformation. So for our TLC plate we observed blue dots to match the trans conformation.

The question is "calculate your percent yield" Which is actual yield/theoretical yield x 100. I just dont understand how I get those numbers.

Here is the lab manual description as well.

Procedure for the Preparation of 1,2-Cyclohexanediol Place a mixture of 1.18 g (0.012 mole) of cyclohexene oxide and 3 mL water into a 50 mL Erlenmeyer flask, equipped with a magnetic stir bar. To this mixture with vigorous stirring add one drop of 6 M sulfuric acid (33% H2SO4) Caution: After a short incubation time, the reaction mixture will become quite warm. This epoxide ring opening reaction is very exothermic. (Why?) If the reaction mixture begins to boil, place the flask in a bath of ice and water. Allow the reaction mixture to stir for the next 15 minutes and let it cool to room temperature. Afterwards, add a small amount of 10% sodium hydroxide drop-wise to neutralize the stirring solution. (No more than 3 or 4 drops of 10% NaOH should be necessary.) Place a drop of the reaction mixture on pH paper to check the pH. Extract the product from the reaction mixture into ethyl acetate or diethyl ether (2 x 15 mL). Dry the combined extracts over sodium sulfate. Decant the solution and remove the solvent to yield the crude product (~1 g). The product can be purified by recrystallization from a small amount (~ 5 mL) of hot toluene or hexanes. Collection of the purified product by suction filtration yields 1,2-cyclohexanediol. The cis isomer has a melting point of 97-101 Â°C whereas the trans isomer melts at 101-103 Â°C. Determine the product(s) or products the reaction. Include a percent yield calculation in your report along with the results of your TLC analysis

Science Tutor: Chemistry Name: Mixtures, Solutions, &Compounds: Chemical Equations Date Chemical Equations If a chemical symbol can be thought of as a letter and a chemical formula as a word in the language of chemistry, then a chemical equation is a statement or sentence. A chemical equation is a shorthand way of describing a chemical reaction between two or more substances. A "+ sign means "combines with." An arrow points away from the reactants and toward the products (See page 10), and an arrow means "yields." 2Na + Cl2 â 2NaCl means sodium combines with chlorine to yield sodiumn chloride (salt) Look closely at the equation above. Notice the "2" in front of NaCI on the right and Na on the left. That 2, called a coefficient, is necessary to make this equation balance. Remember Antoine Lavoisier? (Page 15) Matter is neither created nor destroyed in a chemical reaction. The same number of each kind of atom must be on both sides of a chemical equation. Because chlorine only exists as a molecule consisting of two chlorine atoms, it requires two atoms of sodium to yield two molecules of salt (NaCI). This illustrates another important law stated clearly by the French chemist Joseph-Louis Proust in 1799. Chemical compounds always combine in certain specific fixed proportions. Wherever sodium and chlorine combine, two atoms of sodium will be necessary to react with one molecule of gaseous chlorine. 1 . For the equation 2Mg + O2â 2MgO + energy: A. List the reactant or reactants 2Hato B. List the product or products C. How many atoms of magnesium does it take to combine with one molecule of oxygen? D. How many molecules of magnesium oxide are produced in this reaction? 2. Hydrogen can combine with oxygen to produce water. We could write the equation like this: H2 + O2 â H2O. But this equation is unbalanced! Rewrite this equation with the correct coefficients so that an atom of oxygen doesn't disappear! (Be careful. If you add a coefficient to one side you may have to adjust the other. Count all the atoms.) 3. Now that you have the idea, balance the following equations: A, Pho, â PbO + 02 C. Ca + H2O â Ca(OH)2 + H2 How is following a recipe to mix up a batch of biscuits (or any other food item) similar to Proust's law for chemical reactions? 4. OMark Twain Media, Inc., Publishers 17

CHEM 230 Lecture Notes - Lecture 5: Quadratic Equation, Equilibrium Constant, Partial Pressure

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