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خواص گازها مجموعه ای از مولکولها هستند به هر نسبتی قابل اختالط هستند جرم مشخصی دارند حجم قابل تغییر دارند تغییر شکل می دهند به سهولت پخش می شوند Gases: Their Properties and Behavior • Matter – Solids, Liquids and ….. – Relatively few substances that are gaseous at standard temperature. – Importance to history of chemistry and to basic concepts of reactions. Gases and Gas Pressure Gases and Gas Pressure Column of air 1.0m2 through Upper atmosphere 10,300kg of air P=pgh 1 atm = 760mm Hg 101,325 Pa Gases and Gas Pressure Barometer Gases and Gas Pressure Manometer Mercury Manometers Gas Laws • Boyle’s Law – The volume of a gas varies inversely with pressure. • PV = k with the same amount of gas if there are different amounts then PV/n = k • P = k/V Gas Laws • Boyle’s Law…. P=k/V Gas Laws • Charles’ Law – The volume of a gas varies directly with temperature. (at fixed pressure) • V/T = k or • V = kT • Actually discovered by Joseph Louis GayLussac in 1802. He gave credit to Jacques Charles’ work of 1787. Gas Laws • Charles’ Law • Gay-Lussac's Law Jacques Charles Joseph Louis Gay-Lussac V=kT Gas Laws • Avogadro’s Law – The volume of a gas depends on its molar amount (at fixed pressure and temperature). • V/n = k or • V = kn Gas Laws • Avogadro’s Law Ideal Gas Law • Ideal Gas Law was first written in 1834 by Emil Clapeyron • http://dbhs.wvusd.k12.ca. us/GasLaw/GasIdeal.html Ideal Gas Law • Is the combination of Boyle’s, Charles’ and Avogadro’s work. • PV = nRT • R = 8.3145 J/(K·mol) • Standard Temperature and Pressure (STP) • T = 0oC (273.15K) • P = 1 atm. • Note the changes to the standards (bottom of page 348). We will use the old standards for now. Attention! • R = 8.3145 J/(K·mol) • When P is in Pascals and V is in m3. • R = 0.08206 L·atm/K·mol The Kinetic-Molecular Theory of Gases • Ek = ½ • Ek = 3/2·RT/NA mv2 Maxwell Boltzmann The kinetic theory of gases was developed initially by James Clerk Maxwell and Ludwig Boltzmann. Maxwell's calculation (1859) of the distribution law of molecular velocities in thermal equilibrium can be considered as the starting point of statistical mechanics, the first time a macroscopic, thermodynamic concept such as temperature was quantitatively related to the microscopic dynamics. Boltzmann's later work really laid down the foundations for this discipline, with the first microscopic analysis of irreversibility and the approach to equilibrium (1872). The Kinetic-Molecular Theory of Gases • Assumptions • A gas consists of tiny particles in random motion. • The volume of the particles is insignificant compared to the volume of space occupied. • There is no interaction between particles (neither attractive nor repulsive forces exist). • The kinetic energy of each particle remains constant (all collisions are elastic). • The kinetic energy of the particles is proportional to the temperature (K). [All gases have the same average translational energy at T(K)] The Kinetic-Molecular Theory of Gases • گازها از ذراتی به نام مولکول ساخته شده اند • مولکولهای گازها در حال حرکت هستند و با یکدیگر و دیواره ظرف برخورد می کنند • میانگین انرژی جنبشی حرکتی گازها به دمای آن بستگی دارد • نیروی جاذبه بین مولکولهای گازها ناچیز و قابل صرف نظر کردن است اثبات قانون گاز کامل براساس نظریه جنبش مولکولی ؟ The Kinetic-Molecular Theory of Gases • Comments concerning the individual gas laws and the assumptions. • • • • Boyle’s law Charles’ law Avogadro’s law Dalton’s law P=k/V V = kT V = kn Pt = P1 + P2 + P3 …. • Last assumption is probably the most accurate and most meaningful here. We can use it to calculate the kinetic energy of a gas at T(K) and then find out how fast each particle is moving. رفتار مخلوط گازها • گازهایی که وقتی مخلوط شوند با یکدیگر واکنش شیمیایی می دهند .قانون ترکیب حجمی گیلوساک و آووگادرو • گازهایی که وقتی مخلوط شوند با یکدیگر واکنش شیمیایی نمی دهند .قانون فشارهای جزئی دالتون Stoichiometric Relationships with Gases • Any chemical reaction involving a gas, either reactant or product, will require a stoichiometric calculation of the balanced process. • Moles of gas (n) • Measurement of P and T. • Determination of V and finally mass. • The method in figure 9.11 is frequently used in laboratory experimentation….. 11-10 مثال 2C2 H 6 ( g ) 7O2 ( g ) 4CO2 ( g ) 6H 2O( g ) 2 LC2 H 6 7 LO2 7 LO2 52.5LO2 ? LO2 15.0 LC2 H 6 2LC2 H 6 2LC2 H 6 4LCO2 4 LCO2 30.0 LCO2 ? LCO2 15.0 LC2 H 6 2 LC2 H 6 )الف )ب 14-10 مثال 2 NaN3 (s) 2 Na(s) 3N 2 ( g ) 2molNaN3 3molN 2 1 mol NaN3 3 mol N 2 ? mol N 2 0.400 g NaN3 65.0 g NaN3 2 mol NaN3 ............... 0.00923 mol N 2 PV nRT V 0.230L Partial Pressure and Dalton’s Law • Ideal gas law can be applied to mixtures of gases in the same way as a pure gas. • Total PressurePt = P1 + P2 + P3…… – P1, P2, P3.. Represent the partial pressure of each individual gas in the mixture (as if it were alone in the volume of space). • Mole Fraction (X) – Introduced as another way to find the value of n for each individual gas in the mixture. nA XA n A nB ... nZ PA X A Pt The Kinetic-Molecular Theory of Gases 2000 1800 1600 1400 1200 1000 800 600 400 200 0 1960 1360 650 Hy He Wa dro liu ter m ge n Average Speed 520 Nit ro 490 415 Ox Ca y rbo ge ge nD n n iox id e 3RT Ek 2N Graham's Law of Effusion Which gas has a lower molecular weight? evacuated chamber mixed gases pinhole leak Graham's Law of Effusion • Uranium hexafluoride (UF6) is a gas that has been used as a method to enrich the amount of uranium-235 used in nuclear reactions. • Uranium has two principle isotopes, uranium235 and uranium-238. Graham's Law of Effusion If the effusion method is used to separate 235UF (MW = 349) from 238UF (MW = 352) 6 6 what will be the percentage enrichment per cycle? How many enrichment cycles will be needed to raise the uranium-235 content from the natural abundance 0.3% to 5%? Graham's Law of Effusion If the effusion method is used to separate 35UF (MW = 349) from 238UF (MW = 352) 6 6 what will be the percentage enrichment per cycle? Rate of effusion of 235UF6 Rate of effusion of 238UF 6 = = MW of 238UF 6 MW of 235UF 6 352 349 = 1.0043 Graham's Law of Effusion each enrichment cycle 1.0043 increase first cycle 1.0043 increase second cycle 1.0043 x 1.0043 increase nth cycle (1.0043)n increase Graham's Law of Effusion 0.3% natural abundance of U-235 0.3% x (1.0043)n (1.0043)n n ln (1.0043) 5.0% required purity of U-235 for nuclear applications 5.0% 5.0% / 0.3% = 16.7 ln (16.7) n = 657 cycles Ideal Gas Law • What is an Ideal Gas anyway? • Actually – none exist. Gas Ideal Ammonia Argon Carbon Dioxide Chlorine Fluorine Nitrogen Hydrogen Helium Molar Volume (L) 22.414 22.40 22.09 22.40 22.06 22.38 22.40 22.43 22.41 Ideal Gas Law Micheal Blader – Florida State U. Ideal Gas Law Micheal Blader – Florida State U. Ideal Gas Law • Non-Ideal gas adjustment - van der Waals equation. • (Pideal + a(n/V)2(Videal – bn) = nRT Intermolecular forces Molecular volume • a and b are constants for the specific gas. van der Waals constants Compound a (L2-atm/mol2) b (L/mol) He 0.0341 0.02370 Ne 0.211 0.0171 Ar 1.34 0.0322 Kr 2.32 0.0398 Xe 4.19 0.0510 H2 0.244 0.0266 N2 1.39 0.0391 O2 1.36 0.0318 Cl2 6.49 0.0562 H2O 5.46 0.0305 CH4 2.25 0.0428 CO2 3.59 0.0427 CCl4 20.4 0.1383 Application of Ideal Gas Law • Using the Ideal Gas Law, estimate the reduction of pressure in this tire if there is a change of temperature from 30oC to -30oC. Assume the tire to be mounted on a car with an initial pressure of 32 pounds per square inch (psi). • University of Minnesota Physics Dept. The Earth’s Atmosphere The Earth’s Atmosphere Ozone contribution from Mike Pluth Ozone Fact Bar Cl + O3 ClO + O2 ClO + O Cl + O2 O3 + O 2 O2 Web Sites • A nice site for gas explanations with Flash video. • http://www.chemistry.ohiostate.edu/betha/nealGasLaw/ • Search the web for “Ideal Gas Law” • 88,000 hits • Or “Ideal Gas Law Calculator” – 5000 تمرینهاي فصل 10 • 4-6-8-10-12-14-16-18-20-22-24-26-28-3032-34-36-38-40-50-52-54-58-60-62-64-6668 A Molecular Comparison of Liquids and Solids Intermolecular Forces انواع نیروهای بین مولکولی 1. 2. 3. 4. 5. Ion-Dipole Dipole-dipole Dipole-induced dipole Instantaneous dipole -induced dipole Hydrogen bonding Intermolecular Forces Intermolecular Forces Intermolecular Forces Intermolecular Forces London Dispersion Forces Intermolecular Forces London Dispersion Forces • Weakest of all intermolecular forces. • It is possible for two adjacent neutral molecules to affect each other. • The nucleus of one molecule (or atom) attracts the electrons of the adjacent molecule (or atom). • For an instant, the electron clouds become distorted. • In that instant a dipole is formed (called an instantaneous dipole). Intermolecular Forces London Dispersion Forces Intermolecular Forces London Dispersion Forces • One instantaneous dipole can induce another instantaneous dipole in an adjacent molecule (or atom). • The forces between instantaneous dipoles are called London dispersion forces. • Polarizability is the ease with which an electron cloud can be deformed. • The larger the molecule (the greater the number of electrons) the more polarizable. London Dispersion Forces -Temporary Induced Dipole-Dipole interactions –Very Weak always present in the condensed phase London Dispersion Forces Intermolecular Forces London Dispersion Forces • London dispersion forces increase as molecular weight increases. • London dispersion forces exist between all molecules. • London dispersion forces depend on the shape of the molecule. • The greater the surface area available for contact, the greater the dispersion forces. • London dispersion forces between spherical molecules are lower than between sausage-like molecules. London Forces in Hydrocarbons Intermolecular Forces London Dispersion Forces Intermolecular Forces Hydrogen Bonding • Special case of dipole-dipole forces. • By experiments: boiling points of compounds with H-F, H-O, and H-N bonds are abnormally high. • Intermolecular forces are abnormally strong. • H-bonding requires H bonded to an electronegative element (most important for compounds of F, O, and N). – Electrons in the H-X (X = electronegative element) lie much closer to X than H. – H has only one electron, so in the H-X bond, the + H presents an almost bare proton to the - X. – Therefore, H-bonds are strong. H-Bonding Occurs when Hydrogen is attached to a highly electronegative atom. + N-H… N- O-H… N- F-H… N- N-H… O- O-H… O- F-H… O- N-H… F- O-H… F- F-H… F- - Requires Unshared Electron Pairs of Highly Electronegative Elements Hydrogen Bonding in Water Molecules Clasters of Water Structure of Ice Observe the orientation of the Hydrogen Bonds كريستالهاي منجمدشده آب The messages from water 88 سالم (كاواچي ) رقص سنتي ژاپني “Goldberg Variations آهنگ باخ water can have highly organized local structures when it interacts with molecules capable of imposing these structures on the water. William Royer Jr. U. of Mass. Medical school Organized water molecules India, 2003 Stabilization by “bound water” molecules a b Water binding in hemoglobin The crystal structure of hemoglobin, shown (a) with bound water molecules (red spheres) and (b) without the water molecules B-DNA with a spine of water molecules ‘Bound water’ in biological systems • Intracellular water very close to any membrane or organelle (sometimes called vicinal water) • Organized very differently from bulk water • This structured water plays a significant role in governing the shape (and thus biological activity) of large folded biopolymers. Water chain in cytochrome f Proton hopping Water molecules form H-bonds with polar solutes 95 Electrostatic interaction with charged solutes • When NaCl is mixed with water, a shell of water surrounds each Na+ and Cl- ion. Ions change structure of liquid water • Ionic substances are soluble because the net attraction of the + and – ions for water is greater than the attraction of oppositely charged ions for each other. • Formation of the Hydration shell. 97 Structured water 2(H2O)4 More dense water (H2O)8 Less dense water 98 Types of ions • Structure-breaking ion 'chaotrope' (disorder-maker) (Na+) • structure-forming ion 'kosmotrope' (order-maker) (K+) • Kosmotropes shift the local equilibrium to the right. • Chaotropes shift it to the left. more dense (condensed) water less dense water Water preference Ion Surface charge density Intra-cellular Extra-cellular Ca2+ 2.11 0.1 mM 2.5 mM High density Na+ 1.00 10 mM 150 mM High density K+ 0.56 159 mM 4 mM Low density 99 Nonpolar gases are poorly soluble in water 100 Hydrocarbons in water • Hydrocarbons and nonpolar molecules are insoluble because water-water interactions are stronger than water-hydrocarbon interactions. So water molecules force nonpolar molecules together and surround them. • This phenomenon is called hydrophobic effect or hydrophobic interaction. 101 102 Intermolecular Forces Hydrogen Bonding • Hydrogen bonds are responsible for: – Ice Floating • • • • • • • • • Solids are usually more closely packed than liquids; therefore, solids are more dense than liquids. Ice is ordered with an open structure to optimize H-bonding. Therefore, ice is less dense than water. In water the H-O bond length is 1.0 Å. The O…H hydrogen bond length is 1.8 Å. Ice has waters arranged in an open, regular hexagon. Each + H points towards a lone pair on O. Ice floats, so it forms an insulating layer on top of lakes, rivers, etc. Therefore, aquatic life can survive in winter. Why Does Ice Float? D2O(s) H2O(s) The Boiling Points of the Covalent Hydrides of the Elements in Groups 4A, 5A, 6A, and 7A Intermolecular Forces Hydrogen Bonding Intermolecular Forces Hydrogen Bonding • Hydrogen bonds are responsible for: – Protein Structure • Protein folding is a consequence of H-bonding. • DNA Transport of Genetic Information Protein Secondary Structure Helix Protein Secondary Structure Pleated Sheet Summary Intermolecular Forces Proteins Intermolecular Forces Comparing Intermolecular Forces Force-distance relationship For the Fattraction proportional to 1/distance molecules in contact with each other Relative attractive force 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 Relative molecular distance 9 10 Force-distance relationship Relative attractive force 1 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 Relative molecular distance 9 10 Force-distance relationship Relative attractive force 1 2 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 Relative molecular distance 9 10 Force-distance relationship Relative attractive force 1 3 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 Relative molecular distance 9 10 Force-distance relationship Relative attractive force 1 4 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 6 7 8 Relative molecular distance 9 10 Force-distance relationship Relative attractive force 1 5 0.8 0.6 Less than 20% the strength at 5 molecular distances 0.4 0.2 0 0 1 2 3 4 5 6 7 8 Relative molecular distance 9 10 Increasing strengths of IMF The strength of IMF’s • • • • • • • H-bonding (fixed distance ~200 pm) Ion-ion (1/r) Ion-dipole (1/r2) Inverse 3 Dipole-dipole (1/r ) functions of distance to Ion-induced dipole (1/r4) various 6 Dipole-induced dipole (1/r ) powers Induced dipole-induced dipole (1/r6) How do the other functions behave compared to 1/r? Click here for an interactive Excel spreadsheet to explore Base Pairs in DNA: H-bonding AT pair Why not here? GC pair Lipid Bilayer: Induced Dipole – Induced Dipole Interaction for Hydrocarbon Chains phospholipid Some Properties of Liquids Viscosity • Viscosity is the resistance of a liquid to flow. • A liquid flows by sliding molecules over each other. • The stronger the intermolecular forces, the higher the viscosity. Surface Tension • Bulk molecules (those in the liquid) are equally attracted to their neighbors. Viscosity • Measure of a fluid’s resistance to flow • viscosity, flow • As IM forces , – viscosity – Glycerol vs. H2O example Some Properties of Liquids Surface Tension • Surface molecules are only attracted inwards towards the bulk molecules. – Therefore, surface molecules are packed more closely than bulk molecules. • Surface tension is the amount of energy required to increase the surface area of a liquid. • Cohesive forces bind molecules to each other. • Adhesive forces bind molecules to a surface. Bulk and Surface Interactions in Liquid Some Properties of Liquids Surface Tension Some Properties of Liquids Surface Tension • Meniscus is the shape of the liquid surface. – If adhesive forces are greater than cohesive forces, the liquid surface is attracted to its container more than the bulk molecules. Therefore, the meniscus is U-shaped (e.g. water in glass). – If cohesive forces are greater than adhesive forces, the meniscus is curved downwards. • Capillary Action: When a narrow glass tube is placed in water, the meniscus pulls the water up the tube. Meniscus of Water and of Mercury Adhesive and Cohesive Forces on Surface Capillary Action Phase Changes Energy Changes Accompanying Phase Changes Phase Changes Energy Changes Accompanying Phase Changes – Sublimation: Hsub > 0 (endothermic). – Vaporization: Hvap > 0 (endothermic). – Melting or Fusion: Hfus > 0 (endothermic). – Deposition: Hdep < 0 (exothermic). – Condensation: Hcon < 0 (exothermic). – Freezing: Hfre < 0 (exothermic). Phase Changes Heating Curves Clausius-Clapeyron log P H vap C 2.303RT H vap T2 T1 P1 log P2 2.303R T1T2 Phase Diagrams XRD تمرینهای پایان فصل • ،26 ،22 ،15 ،14 ،7 ،5 ،1 Solution • Homogeneous mixtures • Solute + Solvent Solution Types of Solutions • • • • • Gas-Gas Liquid-Gas Liquid-Liquid Liquid-Solid Solid-Solid Solution Process Solution Process Solution Process Solution Process • Rate of Dissolving – Solute + Solvent Solution • Saturation Point – Solute + Solvent Solution Rate of Dissolving • • • • Size of solute particles Temperature Concentration Stirring Saturated Solution Dynamic Equilibrium • Solute(s) Solute(aq) Solubility Factors • Nature of solute & solvent • Temperature • Pressure Energy Factors in Solubility • Enthalpy – Heat absorbed or evolved • Entropy – Measure of disorder – Most important for gas-gas Enthalpy in Solubility • Bond breaking vs Bond making + Enthalpy in Ionic Solutions • Relative strengths – Lattice energy: ion-ion attraction – Hydration: ion-dipole attraction Enthalpy in Solubility • Like dissolves like – Like bonding, small H – Entropy favors solution Effect of Temperature • Gas: – Less soluble at higher temperature • Liquid & Solid: – if H positive then more soluble – if H negative then less soluble Effect of Pressure • Gas: – More soluble at higher pressure • Liquid & Solid: – Very little effect Henry’s Law William Henry 1775-1836 • Solubility of a gas increases with pressure S = kH P S2 P2 S1 P1 Concentration Units • Mass Percent • Molarity • Mole fraction • Molality Mass Percent mass solute %mass 100% mass solution Molarity M moles solute Molarity Liters solution Molality moles solute Molality kg solvent Mole Fraction moles of A XA Total moles Conversion of Mass% to mole fraction • Calculate the masses of solvent and solute in 100g of solution. • Calculate moles of each from masses. • Calculate mole fraction Vapor Pressure Lowering Raoult’s Law Francois-Marie Raoult 1830-1901 PA o PA X A PTotal o PA X A o PB XB Colligative Properties of Ideal Solutions • Depend only on the concentration • Ionic solutions – Each ion can act as a separate particle. – van’t Hoff factor: i Colligative Properties • • • • Vapor pressure lowering Boiling point elevation Freezing point depression Osmotic pressure Colligative Properties • Boiling point elevation tb = iKbCm • Freezing point depression tf = iKfCm Calculations Tb molality Kb Tb moles kgsolvent Kb masssolute molar wt. Tb kgsolvent Kb Molar wt. of the unknown masssolute molar wt. Tb kgsolvent Kb Colligative Properties • Osmotic pressure • وانت هوف رابطه1887 در سال زیر را که شبیه به قانون گازها باشد را کشف کرد V=nRT • = MRT =iMRT H2O H2O Na+ Cl- H2O H2O H2O تمرین 12-12 • محلولی شامل 0/30گرم از یک پروتئین در آب فشار اسمزی معادل 0/0167اتمسفر در دمای 25/0درجه دارد جرم مولکولی پروتئین را محاسبه کنید؟ n RT V 4 M 4.39 10 تمرینهای پایان فصل • ،51 ،49 ،47 ،43 ،41 ،37 ،29 ،27 ،25 ،23 ،19 87 ،81 ،71،75 ،69 ،67 ،65، 63 ،55 ،53