DOCSLIB.ORG

Chemistry 102 Summary June 18Th Ideal Gas Law: PV =

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chemistry 102 Summary June 18Th Ideal Gas Law: PV = Chemistry 102 Summary June 18th Ideal Gas Law: PV = nRT - P = pressure (atm) - V = volume ( L) - n = number of moles (mol) - R = ideal gas constant (0.08206 Latm/molK) - T = temperature (K), where K = ˚C + 273 - The ideal gas law is the result of the discovery of three seminal laws. Development of ideal gas law: (a) Boyle’s Law: Pressure and Volume (at constant temperature and number of moles) are inversely related. - As pressure increases the volume decreases. - Mathematically PV = constant or V = constant (1/P) - Boyle’s law doesn’t hold at high pressure only at very low pressures. Question: Sketch a plot of P versus Volume? What about Volume versus 1/P? Question: Why are pressure and volume related in an inverse fashion? Consider this room - imagine the doors, windows and cracks were sealed. What would happen if the walls started to move in? Answer: (b) Charles’ Law: Volume of a gas is directly proportional to temperature at constant pressure and number of moles. - As temperature increases the volume increases. - Mathematically V = constant (T) - Temperature is in K = ˚C + 273 - Absolute zero refers to 0 K. 0 K is the lowest possible temperature and is a theoretical value that has never been reached experimentally. Question: Sketch a plot of V vs T in terms of K and in ˚C? Why are they different? Question: Why are volume and temperature directly related? Consider a balloon. Balloon: Can be thought of as a constant pressure system. A balloon expands or contracts in order for the internal pressure exerted by the gas inside the balloon to exactly equal the external atmospheric pressure. Demonstration: What will happen if liquid N2 (T = 77.2 K or -196 ˚C) is poured over a balloon? Result: Balloon collapses. - Temperature is related to the average velocity of the gas molecules. - As temperature increases, the average speed of the gas molecules increases. - When liquid N2 is poured over the balloon the temperature of the air inside of the balloon decreases, therefore the average velocity of the gas molecules also decreases. - This phenomenon leads to less forceful and less frequent collisions with the walls of the container. - This in turn leads to a decrease in pressure inside the balloon, remember the balloon is a constant pressure system, as a result there is a mismatch between the external and internal pressure and to compensate the balloon contracts. The reason for this decrease in volume is to increase the pressure inside the balloon (in other words to re-establish a match of external and internal pressures in the balloon). (c) Avogadro’s Law: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of a gas present. Stated in an alternative manner, equal volumes of gas contain equal moles of gas at constant temperature and pressure. - Mathematically: V = constant (n) Example: for any gas, 2L of a gas contains twice as many moles of gas as 1 L of a gas. Question: Why does Avogadro’s law hold? Consider two balloons, one is twice the size of the other, why? Answer: Remember, the pressure inside both balloons is the same. The larger balloon has more moles of gas. In order for the internal pressure to equal the external pressure, the balloon with more gas molecules must have a larger volume (larger surface area) in order for the collisions per unit area to be the same. Question (Chapter 5 #96): At STP (refers to conditions of standard pressure, 1.0 atm and temperature, 273K), 1.0 L Br2 reacts completely with 3.0 L of F2 , producing 2.0 L of a product. What is the formula of the product? (All substances are gases) Answer: - All of the work of Boyle, Charles and Avogadro is summarized into the ideal gas law: PV = nRT. Ideal Gas Law Problems 1) What will be the effect on the volume of one mole of an ideal gas if the pressure is doubled and the temperature is halved? 2) Lung capacity for a typical person is 2.0 L. If air at 20.˚C and 1.0 atm fills the lungs, how many molecules of air are present? 3) 0.30 g of a gas occupied a volume of 82.0 mL at 3.00 atm pressure at 27˚C. Calculate the molar mass of the gas. 4) Calculate the density of SF6 at STP. Dalton’s Law of Partial Pressures: For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone: PTOT = P1 + P2 + P3……… 1) The stopcock between a 3.0 L bulb containing oxygen at 295 torr and a 2.00 L bulb containing nitrogen at 530 torr is opened. What is the total pressure of the gas in the mixture? (Assume T remains constant) 2) A sample of N2 gas is collected over water at 20.˚C and a total pressure of 1.00 atm. The volume of gas collected is 250.0 mL. What mass of N2 is collected? (At 20.˚C the vapor pressure of water is 17.5 torr) .
Load more

Recommended publications
  • Chapter 3. Second and Third Law of Thermodynamics
    Chapter 3. Second and third law of thermodynamics Important Concepts Review Entropy; Gibbs Free Energy • Entropy (S) – definitions Law of Corresponding States (ch 1 notes) • Entropy changes in reversible and Reduced pressure, temperatures, volumes irreversible processes • Entropy of mixing of ideal gases • 2nd law of thermodynamics • 3rd law of thermodynamics Math • Free energy Numerical integration by computer • Maxwell relations (Trapezoidal integration • Dependence of free energy on P, V, T https://en.wikipedia.org/wiki/Trapezoidal_rule) • Thermodynamic functions of mixtures Properties of partial differential equations • Partial molar quantities and chemical Rules for inequalities potential Major Concept Review • Adiabats vs. isotherms p1V1 p2V2 • Sign convention for work and heat w done on c=C /R vm system, q supplied to system : + p1V1 p2V2 =Cp/CV w done by system, q removed from system : c c V1T1 V2T2 - • Joule-Thomson expansion (DH=0); • State variables depend on final & initial state; not Joule-Thomson coefficient, inversion path. temperature • Reversible change occurs in series of equilibrium V states T TT V P p • Adiabatic q = 0; Isothermal DT = 0 H CP • Equations of state for enthalpy, H and internal • Formation reaction; enthalpies of energy, U reaction, Hess’s Law; other changes D rxn H iD f Hi i T D rxn H Drxn Href DrxnCpdT Tref • Calorimetry Spontaneous and Nonspontaneous Changes First Law: when one form of energy is converted to another, the total energy in universe is conserved. • Does not give any other restriction on a process • But many processes have a natural direction Examples • gas expands into a vacuum; not the reverse • can burn paper; can't unburn paper • heat never flows spontaneously from cold to hot These changes are called nonspontaneous changes.
    [Show full text]
  • Estimation of Internal Pressure of Liquids and Liquid Mixtures
    Available online at www.ilcpa.pl International Letters of Chemistry, Physics and Astronomy 5 (2012) 1-7 ISSN 2299-3843 Estimation of internal pressure of liquids and liquid mixtures N. Santhi 1, P. Sabarathinam 2, G. Alamelumangai 1, J. Madhumitha 1, M. Emayavaramban 1 1Department of Chemistry, Government Arts College, C.Mutlur, Chidambaram-608102, India 2Retd. Registrar & Head of the Department of Technology, Annamalai University, Annamalainagar-608002, India E-mail address: [email protected] ABSTRACT By combining the van der Waals’ equation of state and the Free Length Theory of Jacobson, a new theoretical model is developed for the prediction of internal pressure of pure liquids and liquid mixtures. It requires only the molar volume data in addition to the ratio of heat capacities and critical temperature. The proposed model is simple, reliably accurate and capable of predicting internal pressure of pure liquids with an average absolute deviation of 4.24% in the predicted internal pressure values compared to those given in literature. The average absolute deviation in the predicted internal pressure values through the proposed model for the five binary liquid mixtures tested varies from 0.29% to 1.9% when compared to those of literature values. Keywords: van der Waals, pressure of liquids, theory of Jacobson, capacity of heat liquids, equation of Srivastava and Berkowitz 1. INTRODUTION The importance of internal pressure in understanding the properties of liquids and the full potential of internal pressure as a structural probe did become apparent with the pioneering work of Hildebrand 1, 2 and the first review of the subject by Richards 3 appeared in 1925.
    [Show full text]
  • The Carnot Cycle, Reversibility and Entropy
    entropy Article The Carnot Cycle, Reversibility and Entropy David Sands Department of Physics and Mathematics, University of Hull, Hull HU6 7RX, UK; [email protected] Abstract: The Carnot cycle and the attendant notions of reversibility and entropy are examined. It is shown how the modern view of these concepts still corresponds to the ideas Clausius laid down in the nineteenth century. As such, they reflect the outmoded idea, current at the time, that heat is motion. It is shown how this view of heat led Clausius to develop the entropy of a body based on the work that could be performed in a reversible process rather than the work that is actually performed in an irreversible process. In consequence, Clausius built into entropy a conflict with energy conservation, which is concerned with actual changes in energy. In this paper, reversibility and irreversibility are investigated by means of a macroscopic formulation of internal mechanisms of damping based on rate equations for the distribution of energy within a gas. It is shown that work processes involving a step change in external pressure, however small, are intrinsically irreversible. However, under idealised conditions of zero damping the gas inside a piston expands and traces out a trajectory through the space of equilibrium states. Therefore, the entropy change due to heat flow from the reservoir matches the entropy change of the equilibrium states. This trajectory can be traced out in reverse as the piston reverses direction, but if the external conditions are adjusted appropriately, the gas can be made to trace out a Carnot cycle in P-V space.
    [Show full text]
  • Pressure Vessels
    PRESSURE VESSELS David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 August 23, 2001 Introduction A good deal of the Mechanics of Materials can be introduced entirely within the confines of uniaxially stressed structural elements, and this was the goal of the previous modules. But of course the real world is three-dimensional, and we need to extend these concepts accordingly. We now take the next step, and consider those structures in which the loading is still simple, but where the stresses and strains now require a second dimension for their description. Both for their value in demonstrating two-dimensional effects and also for their practical use in mechanical design, we turn to a slightly more complicated structural type: the thin-walled pressure vessel. Structures such as pipes or bottles capable of holding internal pressure have been very important in the history of science and technology. Although the ancient Romans had developed municipal engineering to a high order in many ways, the very need for their impressive system of large aqueducts for carrying water was due to their not yet having pipes that could maintain internal pressure. Water can flow uphill when driven by the hydraulic pressure of the reservoir at a higher elevation, but without a pressure-containing pipe an aqueduct must be constructed so the water can run downhill all the way from the reservoir to the destination. Airplane cabins are another familiar example of pressure-containing structures. They illus- trate very dramatically the importance of proper design, since the atmosphere in the cabin has enough energy associated with its relative pressurization compared to the thin air outside that catastrophic crack growth is a real possibility.
    [Show full text]
  • CHAPTER 17 Internal Pressure and Internal Energy of Saturated and Compressed Phases Ainstitute of Physics of the Dagestan Scient
    CHAPTER 17 Internal Pressure and Internal Energy of Saturated and Compressed Phases ILMUTDIN M. ABDULAGATOV,a,b JOSEPH W. MAGEE,c NIKOLAI G. POLIKHRONIDI,a RABIYAT G. BATYROVAa aInstitute of Physics of the Dagestan Scientific Center of the Russian Academy of Sciences, Makhachkala, Dagestan, Russia. E-mail: [email protected] bDagestan State University, Makhachkala, Dagestan, Russia cNational Institute of Standards and Technology, Boulder, Colorado 80305 USA. E- mail: [email protected] Abstract Following a critical review of the field, a comprehensive analysis is provided of the internal pressure of fluids and fluid mixtures and its determination in a wide range of temperatures and pressures. Further, the physical meaning is discussed of the internal pressure along with its microscopic interpretation by means of calorimetric experiments. A new relation is explored between the internal pressure and the isochoric heat capacity jump along the coexistence curve near the critical point. Various methods (direct and indirect) of internal pressure determination are discussed. Relationships are studied between the internal pressure and key thermodynamic properties, namely expansion coefficient, isothermal compressibility, speed of sound, enthalpy increments, and viscosity. Loci of isothermal, isobaric, and isochoric internal pressure maxima and minima were examined in addition to the locus of zero internal pressure. Details were discussed of the new method of direct internal pressure determination by a calorimetric experiment that involves simultaneous measurement of the thermal pressure coefficient (∂P / ∂T )V , i.e. internal pressure Pint = (∂U / ∂V )T and heat capacity cV = (∂U / ∂T )V . The dependence of internal pressure on external pressure, temperature and density for pure fluids, and on concentration for binary mixtures is considered on the basis of reference (NIST REFPROP) and crossover EOS.
    [Show full text]
  • Ideal Gas Temperature.)
    FUNDAMENTALS OF CLASSICAL AND STATISTICAL THERMODYNAMICS SPRING 2005 1 1. Basic Concepts of Thermodynamics The basic concepts of thermodynamics such as system, energy, property, state, process, cycle, pressure, and temperature are explained. Thermodynamics can be defined as the science of energy. Energy can be viewed as the ability to cause changes. Thermodynamics is concerned with the transfer of heat and the appearance or disappearance of work attending various chemical and physical processes. • The natural phenomena that occur about us; • Controlled chemical reactions; • The performance of engines • Hypothetical processes such as chemical reactions that do not occur but can be imagined. HISTORY: Thermodynamics emerged as a science with the construction of the first successful atmospheric steam engines in England by Thomas Savery in 1697 and Thomas Newcomen in 1712. These engines were very slow and inefficient, but they opened the way for the development of a new science. The first and second laws of thermodynamics emerged 2 simultaneously in the 1850s primarily out of the works of William Rankine, Rudolph Clausius, and Lord Kelvin (formerly William Thomson). The term thermodynamics was first used in a publication by Lord Kelvin in 1849. The first thermodynamic textbook was written in 1859 by William Rankine, a professor at the University of Glasgow. 3 Classical vs. Statistical Thermodynamics Substances consist of large number of particles called molecules. The properties of the substance naturally depend on the behavior of these particles. For example, the pressure of a gas in a container is the result of momentum transfer between the molecules and the walls of the container.
    [Show full text]
  • Lecture452 2 12.Pdf
    University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2012 Lecture 2. 6/20/12 A. Differentials and State Functions • Thermodynamics allows us to calculate energy transformations occurring in systems composed of large numbers of particles, systems so complex as to make rigorous mechanical calculations impractical. • The limitation is that thermodynamics does not allow us to calculate trajectories. We can only calculate energy changes that occur when a system passes from one equilibrium state to another. • In thermodynamics, we do not calculate the internal energy U. We calculate the change in internal energy ∆U, taken as the difference between the internal energy of the initial equilibrium state and the internal energy of the final equilibrium state: ∆=UUfinal − U initial • The internal energy U belongs to a class of functions called state functions. State function changes ∆F are only dependent on the initial state of the system, described by Pinitial, Vinitial, Tinitial, ninitial, and the final state of the system, described by Pfinal, Vfinal, Tfinal, and nfinal. State function changes do not depend upon the details of the specific path followed (i.e. the trajectory). • Quantities that are path-dependent are not state functions. • Thermodynamic state functions are functions of several state variables including P, V, T, and n. changes in the state variable n is are not considered at present. We will concentrate at first on single component/single phase systems with no loss or gain of material. Of the three remaining state variables P, V, T only two are independent because of the constraint imposed by the equation of state.
    [Show full text]
  • 3. the First Law of Thermodynamics and Related Definitions
    09/30/08 1 3. THE FIRST LAW OF THERMODYNAMICS AND RELATED DEFINITIONS 3.1 General statement of the law Simply stated, the First Law states that the energy of the universe is constant. This is an empirical conservation principle (conservation of energy) and defines the term "energy." We will also see that "internal energy" is defined by the First Law. [As is always the case in atmospheric science, we will ignore the Einstein mass-energy equivalence relation.] Thus, the First Law states the following: 1. Heat is a form of energy. 2. Energy is conserved. The ways in which energy is transformed is of interest to us. The First Law is the second fundamental principle in (atmospheric) thermodynamics, and is used extensively. (The first was the equation of state.) One form of the First Law defines the relationship among work, internal energy, and heat input. In this chapter (and in subsequent chapters), we will explore many applications derived from the First Law and Equation of State. 3.2 Work of expansion If a system (parcel) is not in mechanical (pressure) equilibrium with its surroundings, it will expand or contract. Consider the example of a piston/cylinder system, in which the cylinder is filled with a gas. The cylinder undergoes an expansion or compression as shown below. Also shown in Fig. 3.1 is a p-V thermodynamic diagram, in which the physical state of the gas is represented by two thermodynamic variables: p,V in this case. [We will consider this and other types of thermodynamic diagrams in more detail later.
    [Show full text]
  • Problem Set #5 Assigned September 20, 2013 – Due Friday, September 27, 2013 Please Show All Work for Credit to “Warm Up” O
    Problem Set #5 Assigned September 20, 2013 – Due Friday, September 27, 2013 Please show all work for credit To “warm up” or practice try the Atkins Exercises, which are generally simple one step problems Thermal expansion and isothermal compressibility 1. Engel - P3.20 (Thermal expansion derivation for an ideal and real gas) 2. Atkins – 2.32(b) (expansion coefficient) 3. Atkins – 2.33(b) (compressiblity) Joule-Thomson Coefficient 4. Atkins - 2.20 (Enthalpy change of compressed gas) 5. Atkins - 2.46 (Joule-Thompson coefficient of tetrafluoroethane from table data) Enthalpy and Phase Changes 6. Atkins - 2.6(b) (Methanol condensation) Thermochemistry 7. Atkins - 2.25 (b) (Enthalpy of formation of NOCl(g) ) * Need Table 2.8 8. Atkins – 2.19(b) (diborame formation) 9. Atkins - 2.18 (Silane oxidation) 10. Atkins – 2.42 (anerobic oxidation) 11. Engel - P4.21 (calorimeter calibration) 12. Engel - P4.24 (Photosynthetic glucose production, H) 13. Engel – P4.37 (N2 fixation, glycine production) Extra, do not hand in Good model problems for exam 1. Engel - P3.14 (Internal Energy derivatives derivation) 2. Engel - P3.21 (Joule coefficient for ideal and van der Waals gas) 3. Engel – P3.26 (dCv/dV) T calc 4. Engel - P3.11 (isothermal compressibilty coefficient for van der Waals gas) 5. Atkins 2.16(b) (Liquid vaporization) Tests of your understanding 6. Atkins – 2.30(b) ( J-T coefficient calculation) 7. Atkins - 2.34(b) (Joule-Thompson experiment with CO2) – de-emphasize 8. Atkins – 2.12 (glucose combustion) 9. Atkins - 2.43 (Alkyl radicals) 10. Engel - P3.19 (use Joule coefficient for H calc, ideal and Van der Waals gas) 11.
    [Show full text]
  • Chem 340 - Lecture Notes 4 – Fall 2013 – State Function Manipulations
    Chem 340 - Lecture Notes 4 – Fall 2013 – State function manipulations Properties of State Functions State variables are interrelated by equation of state, so they are not independent, express relationship mathematically as a partial derivative, and only need two of T,V, P Example: Consider ideal gas: PV = nRT so P = f(V,T) = nRT/V, let n=1 2 Can now do derivatives: (P/V)T = -RT/V and : (P/T)P = R/V Full differential show variation with respect to one variable at a time, sum for both: (equations all taken from Engel, © Pearson) shows total change in P if have some change in V and in T Example, on hill and want to know how far down (dz) you will go if move some amount in x and another in y. contour map can tell, or if knew function could compute dzx from dz/dx for motion in x and dzy from dz/dy for motion in y total change in z is just sum: dz = (dz/dx)ydx + (dz/dy)xdy Note: for dz, small change (big ones need higher derivative) Can of course keep going with 2nd and 3rd derivatives or mixed ones For state functions the order of taking the derivative is not important, or The corollary works, reversed derivative equal determine if property is state function as above, state function has an exact differential: f = ∫df = ff - fi good examples are U and H, but, q and w are not state functions 1 Some handy calculus things: If z = f(x,y) can rearrange to x = g(y,x) or y = h(x,z) [e.g.P=nRT/V, V=nRT/P, T=PV/nR] Inversion: cyclic rule: So we can evaluate (P/V)T or (P/T)V for real system, use cyclic rule and inverse: divide both sides by (T/P)V get 1/(T/P)V=(P/T)V similarly (P/V)T=1/(V/P)T so get ratio of two volume changes cancel (V/T)P = V const.
    [Show full text]
  • Lecture 8: Surface Tension, Internal Pressure and Energy of a Spherical Particle Or Droplet
    Lecture 8: Surface tension, internal pressure and energy of a spherical particle or droplet Today’s topics • Understand what is surface tension or surface energy, and how this balances with the internal pressure of a droplet to determine the droplet size. • Why smaller droplets are not stable and tend to fuse into larger ones? So far, we have considered only bulk quantities of any given substance when describing its thermodynamic properties. The role of surfaces/interfaces is ignored. However, when the substance shrink in size down to a small droplet, particle, or precipitate, the effects of surface/interface is no longer negligible, since the number atoms on Surface/Interface is comparable to number of atoms inside bulk. Surface effects (surface energy) play critical role many kinetics process of materials, such as the particle ripening and nucleation, as we will learn the lectures later. Typically, for many liquids and solid, surface energy (surface tension) is in the order of ~ 1 J/m2 (or N/m). For example, for water under ambient conditions, the surface energy is 0.072 J/m2 (or surface tension of 0.072 N/m). Think about a large oil droplet suspending in a cup of water: shake the cup, the oil droplet will disperse as many small ones, but these small droplets will eventually fuse together, forming back to a large one if let the cup stabilize for a while. This is because the increased surface energy due to the smaller droplets (particles), fusing back to one large particle decreases the total energy, favorable in thermodynamic. Essentially every phase transformation begins with the formation of a tiny spherical particle called nucleus.
    [Show full text]
  • Full-Scale External and Internal Pressure Measurements for a Low
    A Resource for the State of Florida HURRICANE LOSS REDUCTION FOR HOUSING IN FLORIDA: Full­scale External and Internal Pressure Measurements for a Low­rise Building A Research Project Funded by The State of Florida Division of Emergency Management Submitted by: Dr. Girma T. Bitsuamlak, PEng, Assistant Professor Amanuel S. Tecle, Graduate Research Assistant In Partnership with: The International Hurricane Research Center Florida International University September 2009 EXCUTIVE SUMMARY In this project, a wind induced internal and external pressure in typical low-rise building models is investigated primarily by using a full-scale wind testing facility generically named Wall of Wind (WoW). Effect of different dominant openings (representing open door and window conditions or breaching of a building envelope by wind-borne debris), vents (gable end, goose neck, turbine, and soffit) and background leakage under different wind angle of attack is carried out. Prior to performing the full-scale analysis, a three tier approach comprising (i) a less expensive computer simulation and (ii) small-scale WoW (1:8 replica of the full-scale WoW) followed by (iii) a confirmatory test using the full-scale WoW is adopted to assess effect of blockage and proximity to the WoW flow simulator. Computer model of various size are first simulated to assess the blockage effect and additional simulations are done to assess the proximity effect by placing a model at different distance from the wall of wind. For the computer simulation, a commercially available software FLUENT (version 6.2) is utilized. In order to verify and ascertain the results of the computer simulations, a less expensive small scale physical experiment was carried out by designing three small WoW model cubes (i.e., scale 1:8 with 5ft, 7ft, and 9.5ft side lengths).
    [Show full text]