C.Gas Laws D.Combined Gas
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THE SOLUBILITY of GASES in LIQUIDS Introductory Information C
THE SOLUBILITY OF GASES IN LIQUIDS Introductory Information C. L. Young, R. Battino, and H. L. Clever INTRODUCTION The Solubility Data Project aims to make a comprehensive search of the literature for data on the solubility of gases, liquids and solids in liquids. Data of suitable accuracy are compiled into data sheets set out in a uniform format. The data for each system are evaluated and where data of sufficient accuracy are available values are recommended and in some cases a smoothing equation is given to represent the variation of solubility with pressure and/or temperature. A text giving an evaluation and recommended values and the compiled data sheets are published on consecutive pages. The following paper by E. Wilhelm gives a rigorous thermodynamic treatment on the solubility of gases in liquids. DEFINITION OF GAS SOLUBILITY The distinction between vapor-liquid equilibria and the solubility of gases in liquids is arbitrary. It is generally accepted that the equilibrium set up at 300K between a typical gas such as argon and a liquid such as water is gas-liquid solubility whereas the equilibrium set up between hexane and cyclohexane at 350K is an example of vapor-liquid equilibrium. However, the distinction between gas-liquid solubility and vapor-liquid equilibrium is often not so clear. The equilibria set up between methane and propane above the critical temperature of methane and below the criti cal temperature of propane may be classed as vapor-liquid equilibrium or as gas-liquid solubility depending on the particular range of pressure considered and the particular worker concerned. -
Air-Sea Gas Exchange
Air-Sea Gas Exchange OCN 623 – Chemical Oceanography 17 March 2015 Readings: Libes, Chapter 6 – pp. 158 -168 Wanninkhof et al. (2009) Advances in quantifying air-sea gas exchange and environmental forcing, Annual Reviews of Marine Science © 2015 David Ho and Frank Sansone Overview • Introduction • Theory/models of gas exchange • Mechanisms/lab studies of gas exchange • Field measurements • Parameterizations Why do we care about air-water gas exchange? . Globally, to understand cycling of biogeochemically important trace gases (e.g., CO2, DMS, CH4, N2O, CH3Br) . Regionally and locally . To understand indicators of water quality (e.g., dissolved O2) . To predict evasion rates of volatile pollutants (e.g., VOCs, PAHs, PCBs) Factors Influencing Air-water Transfer of Mass, Momentum, Heat From SOLAS Science Plan and Implementation Strategy Basic flux equation Concentration gradient Flux (mol cm-3) (mol cm-2 s-1) “driving force” Gas transfer velocity (cm s-1) “resistance” k: Gas transfer velocity, piston velocity, gas exchange coefficient Cw: Concentration in water near the surface Ca: Concentration in air near the surface α: Ostwald solubility coefficient (temp-compensated Bunsen coeff) Basic conceptual model Turbulent atmosphere C Atmosphere a Laminar Stagnant Cas Boundary Layer zFilm Cws (transport by Ocean molecular diffusion) Cw Turbulent bulk liquid F = k(Cw-αCa) Air/water side resistance Magnitude of typical Ostwald solubility coefficients He ≈ 0.01 Water-side resistance O2 ≈ 0.03 CO2 ≈ 0.7 DMS ≈ 10 Air- and water-side resistance CH3Br -
Chapter 6 - Engineering Equations of State II
Introductory Chemical Engineering Thermodynamics By J.R. Elliott and C.T. Lira Chapter 6 - Engineering Equations of State II. Generalized Fluid Properties The principle of two-parameter corresponding states 50 50 40 40 30 30 T=705K 20 20 ρ T=286K L 10 10 T=470 T=191K T=329K 0 0 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 -10 T=133K -10 ρV Density (g/cc) Density (g/cc) VdW Pressure (bars) in Methane VdW Pressure (bars) in Pentane Critical Definitions: Tc - critical temperature - the temperature above which no liquid can exist. Pc - critical pressure - the pressure above which no vapor can exist. ω - acentric factor - a third parameter which helps to specify the vapor pressure curve which, in turn, affects the rest of the thermodynamic variables. ∂ ∂ 2 P = P = 0 and 0 at Tc and Pc Note: at the critical point, ∂ρ ∂ρ 2 T T Chapter 6 - Engineering Equations of State Slide 1 II. Generalized Fluid Properties The van der Waals (1873) Equation Of State (vdW-EOS) Based on some semi-empirical reasoning about the ways that temperature and density affect the pressure, van der Waals (1873) developed the equation below, which he considered to be fairly crude. We will discuss the reasoning at the end of the chapter, but it is useful to see what the equations are and how we use them before deriving the details. The vdW-EOS is: bρ aρ 1 aρ Z =+1 −= − ()1− bρ RT()1− bρ RT van der Waals’ trick for characterizing the difference between subcritical and supercritical fluids was to recognize that, at the critical point, ∂P ∂ 2 P = 0 and = 0 at T , P ∂ρ ∂ρ 2 c c T T Since there are only two “undetermined parameters” in his EOS (a and b), he has reduced the problem to one of two equations and two unknowns. -
On the Van Der Waals Gas, Contact Geometry and the Toda Chain
entropy Article On the van der Waals Gas, Contact Geometry and the Toda Chain Diego Alarcón, P. Fernández de Córdoba ID , J. M. Isidro * ID and Carlos Orea Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, Spain; [email protected] (D.A.); [email protected] (P.F.d.C.); [email protected] (C.O.) * Correspondence: [email protected] Received: 7 June 2018; Accepted: 16 July 2018; Published: 26 July 2018 Abstract: A Toda–chain symmetry is shown to underlie the van der Waals gas and its close cousin, the ideal gas. Links to contact geometry are explored. Keywords: van der Waals gas; contact geometry; Toda chain 1. Introduction The contact geometry of the classical van der Waals gas [1] is described geometrically using a five-dimensional contact manifold M [2] that can be endowed with the local coordinates U (internal energy), S (entropy), V (volume), T (temperature) and p (pressure). This description corresponds to a choice of the fundamental equation, in the energy representation, in which U depends on the two extensive variables S and V. One defines the corresponding momenta T = ¶U/¶S and −p = ¶U/¶V. Then, the standard contact form on M reads [3,4] a = dU + TdS − pdV. (1) One can introduce Poisson brackets on the four-dimensional Poisson manifold P (a submanifold of M) spanned by the coordinates S, V and their conjugate variables T, −p, the nonvanishing brackets being fS, Tg = 1, fV, −pg = 1. (2) Given now an equation of state f (p, T,...) = 0, (3) one can make the replacements T = ¶U/¶S, −p = ¶U/¶V in order to obtain ¶U ¶U f − , ,.. -
AP Chemistry Chapter 5 Gases Ch
AP Chemistry Chapter 5 Gases Ch. 5 Gases Agenda 23 September 2017 Per 3 & 5 ○ 5.1 Pressure ○ 5.2 The Gas Laws ○ 5.3 The Ideal Gas Law ○ 5.4 Gas Stoichiometry ○ 5.5 Dalton’s Law of Partial Pressures ○ 5.6 The Kinetic Molecular Theory of Gases ○ 5.7 Effusion and Diffusion ○ 5.8 Real Gases ○ 5.9 Characteristics of Several Real Gases ○ 5.10 Chemistry in the Atmosphere 5.1 Units of Pressure 760 mm Hg = 760 Torr = 1 atm Pressure = Force = Newton = pascal (Pa) Area m2 5.2 Gas Laws of Boyle, Charles and Avogadro PV = k Slope = k V = k P y = k(1/P) + 0 5.2 Gas Laws of Boyle - use the actual data from Boyle’s Experiment Table 5.1 And Desmos to plot Volume vs. Pressure And then Pressure vs 1/V. And PV vs. V And PV vs. P Boyle’s Law 3 centuries later? Boyle’s law only holds precisely at very low pressures.Measurements at higher pressures reveal PV is not constant, but varies as pressure varies. Deviations slight at pressures close to 1 atm we assume gases obey Boyle’s law in our calcs. A gas that strictly obeys Boyle’s Law is called an Ideal gas. Extrapolate (extend the line beyond the experimental points) back to zero pressure to find “ideal” value for k, 22.41 L atm Look Extrapolatefamiliar? (extend the line beyond the experimental points) back to zero pressure to find “ideal” value for k, 22.41 L atm The volume of a gas at constant pressure increases linearly with the Charles’ Law temperature of the gas. -
Part Two Physical Processes in Oceanography
Part Two Physical Processes in Oceanography 8 8.1 Introduction Small-Scale Forty years ago, the detailed physical mechanisms re- Mixing Processes sponsible for the mixing of heat, salt, and other prop- erties in the ocean had hardly been considered. Using profiles obtained from water-bottle measurements, and J. S. Turner their variations in time and space, it was deduced that mixing must be taking place at rates much greater than could be accounted for by molecular diffusion. It was taken for granted that the ocean (because of its large scale) must be everywhere turbulent, and this was sup- ported by the observation that the major constituents are reasonably well mixed. It seemed a natural step to define eddy viscosities and eddy conductivities, or mix- ing coefficients, to relate the deduced fluxes of mo- mentum or heat (or salt) to the mean smoothed gra- dients of corresponding properties. Extensive tables of these mixing coefficients, KM for momentum, KH for heat, and Ks for salinity, and their variation with po- sition and other parameters, were published about that time [see, e.g., Sverdrup, Johnson, and Fleming (1942, p. 482)]. Much mathematical modeling of oceanic flows on various scales was (and still is) based on simple assumptions about the eddy viscosity, which is often taken to have a constant value, chosen to give the best agreement with the observations. This approach to the theory is well summarized in Proudman (1953), and more recent extensions of the method are described in the conference proceedings edited by Nihoul 1975). Though the preoccupation with finding numerical values of these parameters was not in retrospect always helpful, certain features of those results contained the seeds of many later developments in this subject. -
THE SOLUBILITY of GASES in LIQUIDS INTRODUCTION the Solubility Data Project Aims to Make a Comprehensive Search of the Lit- Erat
THE SOLUBILITY OF GASES IN LIQUIDS R. Battino, H. L. Clever and C. L. Young INTRODUCTION The Solubility Data Project aims to make a comprehensive search of the lit erature for data on the solubility of gases, liquids and solids in liquids. Data of suitable accuracy are compiled into data sheets set out in a uni form format. The data for each system are evaluated and where data of suf ficient accuracy are available values recommended and in some cases a smoothing equation suggested to represent the variation of solubility with pressure and/or temperature. A text giving an evaluation and recommended values and the compiled data sheets are pUblished on consecutive pages. DEFINITION OF GAS SOLUBILITY The distinction between vapor-liquid equilibria and the solUbility of gases in liquids is arbitrary. It is generally accepted that the equilibrium set up at 300K between a typical gas such as argon and a liquid such as water is gas liquid solubility whereas the equilibrium set up between hexane and cyclohexane at 350K is an example of vapor-liquid equilibrium. However, the distinction between gas-liquid solUbility and vapor-liquid equilibrium is often not so clear. The equilibria set up between methane and propane above the critical temperature of methane and below the critical temperature of propane may be classed as vapor-liquid equilibrium or as gas-liquid solu bility depending on the particular range of pressure considered and the par ticular worker concerned. The difficulty partly stems from our inability to rigorously distinguish between a gas, a vapor, and a liquid, which has been discussed in numerous textbooks. -
Modes of Mass Transfer Chapter Objectives
MODES OF MASS TRANSFER CHAPTER OBJECTIVES - After you have studied this chapter, you should be able to: 1. Explain the process of molecular diffusion and its dependence on molecular mobility. 2. Explain the process of capillary diffusion 3. Explain the process of dispersion in a fluid or in a porous solid. 4. Understand the process of convective mass transfer as due to bulk flow added to diffusion or dispersion. 5. Explain saturated flow and unsaturated capillary flow in a porous solid 6. Have an idea of the relative rates of the different modes of mass transfer. 7. Explain osmotic flow. KEY TERMS diffusion, diffusivity, and. diffusion coefficient dispersion and dispersion coefficient hydraulic conductivity capillarity osmotic flow mass and molar flux Fick's law Darcy's law 1. A Primer on Porous Media Flow Physical Interpretation of Hydraulic Conductivity K and Permeability k Figure 1. Idealization of a porous media as bundle of tubes of varying diameter and tortuosity. Capillarity and Unsaturated Flow in a Porous Media Figure 2.Capillary attraction between the tube walls and the fluid causes the fluid to rise. Osmotic Flow in a Porous Media Figure 3.Osmotic flow from a dilute to a concentrated solution through a semi-permeable membrane. 2. Molecular Diffusion • In a material with two or more mass species whose concentrations vary within the material, there is tendency for mass to move. Diffusive mass transfer is the transport of one mass component from a region of higher concentration to a region of lower concentration. Physical interpretation of diffusivity Figure 4. Concentration profiles at different times from an instantaneous source placed at zero distance. -
Diffusion at Work
or collective redistirbution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of The Oceanography Society. Send all correspondence to: [email protected] ofor Th e The to: [email protected] Oceanography approval Oceanography correspondence POall Box 1931, portionthe Send Society. Rockville, ofwith any permittedUSA. articleonly photocopy by Society, is MD 20849-1931, of machine, this reposting, means or collective or other redistirbution article has This been published in hands - on O ceanography Oceanography Diffusion at Work , Volume 20, Number 3, a quarterly journal of The Oceanography Society. Copyright 2007 by The Oceanography Society. All rights reserved. Permission is granted to copy this article for use in teaching and research. Republication, systemmatic reproduction, reproduction, Republication, systemmatic research. for this and teaching article copy to use in reserved.by The 2007 is rights ofAll granted journal Copyright Oceanography The Permission 20, NumberOceanography 3, a quarterly Society. Society. , Volume An Interactive Simulation B Y L ee K arp-B oss , E mmanuel B oss , and J ames L oftin PURPOSE OF ACTIVITY or small particles due to their random (Brownian) motion and The goal of this activity is to help students better understand the resultant net migration of material from regions of high the nonintuitive concept of diffusion and introduce them to a concentration to regions of low concentration. Stirring (where variety of diffusion-related processes in the ocean. As part of material gets stretched and folded) expands the area available this activity, students also practice data collection and statisti- for diffusion to occur, resulting in enhanced mixing compared cal analysis (e.g., average, variance, and probability distribution to that due to molecular diffusion alone. -
What Is the Difference Between Osmosis and Diffusion?
What is the difference between osmosis and diffusion? Students are often asked to explain the similarities and differences between osmosis and diffusion or to compare and contrast the two forms of transport. To answer the question, you need to know the definitions of osmosis and diffusion and really understand what they mean. Osmosis And Diffusion Definitions Osmosis: Osmosis is the movement of solvent particles across a semipermeable membrane from a dilute solution into a concentrated solution. The solvent moves to dilute the concentrated solution and equalize the concentration on both sides of the membrane. Diffusion: Diffusion is the movement of particles from an area of higher concentration to lower concentration. The overall effect is to equalize concentration throughout the medium. Osmosis And Diffusion Examples Examples of Osmosis: Examples of osmosis include red blood cells swelling up when exposed to fresh water and plant root hairs taking up water. To see an easy demonstration of osmosis, soak gummy candies in water. The gel of the candies acts as a semipermeable membrane. Examples of Diffusion: Examples of diffusion include perfume filling a whole room and the movement of small molecules across a cell membrane. One of the simplest demonstrations of diffusion is adding a drop of food coloring to water. Although other transport processes do occur, diffusion is the key player. Osmosis And Diffusion Similarities Osmosis and diffusion are related processes that display similarities. Both osmosis and diffusion equalize the concentration of two solutions. Both diffusion and osmosis are passive transport processes, which means they do not require any input of extra energy to occur. -
Unit 5 Interactive Notebook Gas Laws and Kinetic Molecular Theory Grant Union High School January 6, 2014 – January 29, 2014
Unit 5 Interactive Notebook Gas Laws and Kinetic Molecular Theory Grant Union High School January 6, 2014 – January 29, 2014 Student Mastery Scale of Learning Goals Date Page Std Learning Goal Homework Mastery 1/6/14 1/7/14 1/8/14 1/9/14 1/10/14 1/13/14 1/14/14 1/15/14 1 1/16/14 1/21/14 1/22/14 1/23/14 1/24/14 1/27/14 1/28/14 1/29/14 Unit 5 EXAM 2 California Standard Gas Laws 4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of gases. As a basis for understanding this concept: a. Students know the random motion of molecules and their collisions with a surface create the observable pressure on that surface. Fluids, gases or liquids, consist of molecules that freely move past each other in random directions. Intermolecular forces hold the atoms or molecules in liquids close to each other. Gases consist of tiny particles, either atoms or molecules, spaced far apart from each other and free to move at high speeds. Pressure is defined as force per unit area. The force in fluids comes from collisions of atoms or molecules with the walls of a container. Air pressure is created by the weight of the gas in the atmosphere striking surfaces. Gravity pulls air molecules toward Earth, the surface that they strike. Water pressure can be understood in the same fashion, but the pressures are much greater because of the greater density of water. -
Real Gases – As Opposed to a Perfect Or Ideal Gas – Exhibit Properties That Cannot Be Explained Entirely Using the Ideal Gas Law
Basic principle II Second class Dr. Arkan Jasim Hadi 1. Real gas Real gases – as opposed to a perfect or ideal gas – exhibit properties that cannot be explained entirely using the ideal gas law. To understand the behavior of real gases, the following must be taken into account: compressibility effects; variable specific heat capacity; van der Waals forces; non-equilibrium thermodynamic effects; Issues with molecular dissociation and elementary reactions with variable composition. Critical state and Reduced conditions Critical point: The point at highest temp. (Tc) and Pressure (Pc) at which a pure chemical species can exist in vapour/liquid equilibrium. The point critical is the point at which the liquid and vapour phases are not distinguishable; because of the liquid and vapour having same properties. Reduced properties of a fluid are a set of state variables normalized by the fluid's state properties at its critical point. These dimensionless thermodynamic coordinates, taken together with a substance's compressibility factor, provide the basis for the simplest form of the theorem of corresponding states The reduced pressure is defined as its actual pressure divided by its critical pressure : The reduced temperature of a fluid is its actual temperature, divided by its critical temperature: The reduced specific volume ") of a fluid is computed from the ideal gas law at the substance's critical pressure and temperature: This property is useful when the specific volume and either temperature or pressure are known, in which case the missing third property can be computed directly. 1 Basic principle II Second class Dr. Arkan Jasim Hadi In Kay's method, pseudocritical values for mixtures of gases are calculated on the assumption that each component in the mixture contributes to the pseudocritical value in the same proportion as the mol fraction of that component in the gas.