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Chemistry 1302A/B Lecture 3: Chemistry 1302B lecture 4 (chapter 1.2 & 2.1)

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28 Jan 2017

School

Western University

Department

Course

Chemistry 1302A/B

Professor

Christina Booker

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Document Summary

Topic: application of ideal gas law & heat, work and energy (chapter 1. 2 and 2. 1) Kinetic energy of gas molecules is directly related to temperature. N: number of particles (increase particles will increase collision, thus increase pressure) V: volume (increase volume will decrease collision, thus decrease pressure) Molar mass is inversely proportional to kinetic energy; a small atom like hydrogen will have a higher mean squared speed compared to a heavier atom neon at the same temperature. Small particles move faster than large particles at same temperature. As molar mass increase, mean kinetic speed decrease. Larger distribution at smaller molar mass and narrower distribution at higher molar mass. Lighter gases effuse faster (starting amount of gases matters; if ratios are not equal, it might affects the outcome) A study of the energy change, or energy transfer, related to physical and chemical processes. Studies the changes in heat energy of chemical reaction.

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Related Questions

M 121 1 201 Ideal Gas Law (PV n Experiment to T ) Determine the Ideal Gas Constant R 1. Conduct basic measurements, measurement , mathematical calculations and conversions for of volume, pressure, and temperature: calculate percent error and account for sources of error in an e xperimental result name and by following safety proced ty experiments for a redox reaction by using equipment identifiable by form chemical calculations using mass, mole and volumes and idenify limitatios of measuring devices in order to state the uncertainty/significant figures in measurements and calculation results. 5. Demonstrate a proficiency in relating the chemistry of gases to everyday phenomenon. Introduction Molecules in gases have very little attraction for one another, because relative to their size, they are so far apart from each other. For this reason we can often assume that a gas behaves "idcally." meaning that the physical behavior of the gas is independent of the composition of the gas. If a gas behaves ideally, then its physical properties can be described by the Ideal Gas Equation: Let's consider why the variables in the ideal gas equation have the relationships expressed in Equation 1aã The ideal gas equation assumes that there are no attractive forces between gas molecules. One can picture two billiard balls bouncing off one another in a totally clastic collision. If these molecules are placed in a balloon the collisions will occur not only with each other but also with the wall of the balloon, causing the balloon to expand. This expansion can be measured as a volume (V). More molecules will cause more collisions and thus more expansion. Therefore the quantity of molecules or number of moles (n) is directly proportional to the volume, and thus volume and number of moles appear on opposite sides of the equation. Another factor to consider is the kinetic energy of these molecules. Kinetic energy is related to the temperature (T) of the molecules, in that the kinetic energy. If the collisions with the wall of the balloon are happening at a very high speed due to high kinetic energy, the collisions will be harder and more frequent and thus the wall of the balloon will be pushed out further (a larger volume) than if the kinetic energy were less. The result is that volume is also directly proportional to the temperature. This relationship is seen in Equation la with (T) on the right side of the equation and (V) on the left. higher the temperature the greater the considered. While the molecules inside the balloon are pushing the balloon out, there are also molecules in thea Finally the pressure of the outside environment (atmospheric pressure) needs to be 59

question 1 (C) only please:)

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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)