General Chemistry I Dr. PHAN TẠI HUÂN Faculty of Food Science and Technology Nong Lam University Module 3: The Three States of Matter Gas state (Equation of state: ideal gas and real gas). Liquid state (Attractive forces between molecules, fluid viscosity). Solid state (Amorphous and crystalline solids, crystal structure). 2 1
Comparison of solids, liquids, and gases 3 Gases An overview Chemists use 4 basic measurements when working with gases: The pressure of the gas, P (in atmospheres). The temperature of the gas, T (in kelvins). The quantity of the gas, n (in moles). The volumes of gas, V (in liters). 4 2
Gases An overview Pressure is defined as force per unit area. All fluids (liquids and gases) exert pressure at all points within them in all directions. Gas Pressure is defined as the measure, per unit area, of force exerted by gas molecules on the walls of their container Unit of pressure is pascal (Pa) which is equivalent to kg/(m.s2) 1 atmosphere (atm) = 760 mm Hg = 760 torr = 1.01 x 10 5 Pa. 5 Simple Barometer and Manometer 6 3
Gas Pressure The pressure relative to absolute vacuum is called the absolute pressure. The difference between the absolute pressure and the local atmospheric pressure is called the gage (gauge) pressure. Pressures below atmospheric pressure are called vacuum pressures. The absolute, gage, and vacuum pressures are related by: P gage = P abs P atm (for pressures above P atm ). P vac = P atm P abs (for pressure below P atm ). 7 Standard temperature and pressure In order to standardize the quantities of gases measured and conveyed, arbitrary reference conditions called Standard Temperature and Pressure (STP) have been chosen and internationally accepted. The standard molar volume of an ideal gas is taken to be 22.4 liters per mole at STP. 8 4
Gas laws Gases behave ideally under reasonably high temperatures and low pressures. The gas laws are helpful in quantitatively relating pressure, volume, temperature, and molar units. Boyle s Law Charles s Law The Combined Gas Law Avogadro s Law The Ideal Gas Law Dalton s Law of Partial Pressures Graham s Law 9 Boyle s law (1662) : The volume pressure relationship 10 5
Boyle s law 11 Boyle s law At constant temperature the volume, V, occupied by a definite mass of a gas is inversely proportional to the applied pressure, P. 12 6
Exercise A sample of gas occupies 12 L under a pressure of 1.2 atm. What would its volume be if the pressure were increased to 2.4 atm (the temperature did not change)? Ans: 13 Charles s law: the volume - temperautre relationship (ca. 1800) 14 7
Charles s law 15 Charles s law At constant pressure, the volume occupied by a definite mass of a gas is directly proportional to its absolute temperature. K = C + 273.15. 16 8
Exercise A sample of nitrogen occupies 117 ml at 100. C. At what temperature in C would it occupy 234 ml if the pressure did not change? Ans: 17 The combined gas law The gas laws (Charles' and Boyle's law) can be combined to form the combined gas law. 18 9
Exercise A sample of neon occupies 105 liters at 27 C under a pressure of 985 torr. What volume would it occupy at standard temperature and pressure (STP)? Ans: 19 Avogadro s law (1811) At the same temperature and pressure, equal volumes of all gases contain the same number of molecules. At constant temperature and pressure, the volume, V, occupied by a gas sample is directly proportional to the number of moles, n, of gas. 20 10
The ideal gas law R, the universal gas constant 21 Exercise How many moles of O 2 are present in a 0.5 L sample at 25 C and 1.09 atm? Ans: 22 11
Exercise Design an air bag for a car. The bag should be filled with gas with a pressure higher than atmospheric pressure, say 828 mm Hg, at temperature of 22 C. The bag has a volumee of 45.5 L. What quantity of sodium azide, NaN 3, should we use to generate the required quatity of gas? 2 NaN 3 (s) => 2 Na (s) + 3 N 2 (g) Ans: 23 Dalton's law of partial pressures 24 12
Dalton's law of partial pressures The total pressure exerted by a mixture of ideal gases is the sum of the partial pressures of those gases. P Total = P A + P B + P C +... (constant V, T) The partial pressure of an individual gas A in a mixture of gases: P A = P Total X A X A n = n A Total = Total Number _ of _ moles _ of _ gas _ A _ number _ of _ moles _ of _ gases _ in _ the _ mixture 25 Exercise A sealed vessel contains 0.50 mol of neon gas, 0.20 mol hydrogen gas, and 0.3 mol oxygen gas. The total pressure of the the gas mixture is 8.0atm. What is the partial pressure of oxygen? Ans: 26 13
Water vapor At 25 C, water is ordinarily a liquid. However, even at 25 C, water evaporates. In a closed container at 25 C, water evaporates enough to get a 24-torr water vapor pressure in its container. The pressure of the gaseous water is called its vapor pressure at that temperature. At different temperatures, it evaporates to different extents to give different vapor pressures. The water vapor mixes with any other gas(es) present, and the mixture is governed by Dalton s law of partial pressures. 27 Gas collected over water 28 14
Exercise How many moles of oxygen are contained in a 1.00-L vessel over water at 25 C and a barometric pressure of 1.00 atm? Ans: 29 Graham s Law Diffusion of gases can be described as the process by which a gas spreads to occupy the available and accessible space, thereby creating a uniform pressure throughout the space the gas occupies. A gas having a higher partial pressure will travel or diffuse toward regions of gases having a lower partial pressure,until an equilibrium is reached. The effusion rate of a gas is inversely related to the square root of the molecular weight of the gas. 30 15
Graham s Law : Diffusion and effusion of a gas 31 Exercise Calculate the ratio of effusion of the gases oxygen and hydrogen. Assume that the two gases are in the same container having a tiny hole in it. Ans: 32 16
Kinetic theory of gases 1. Gases consist of discrete molecules. The individual molecules are very small and are very far apart relative to their own sizes. 2. The gas molecules are in continuous, random, straightline motion with varying velocities. 3. The collisions between gas molecules and with the walls of the container are elastic; the total energy is conserved during a collision; that is, there is no net energy gain or loss. 4. Gas particles neither attract nor repel one another. 33 Kinetic theory of gases The kinetic energy (KE) of an individual gas molecule : KE = 1 2 mv 2 (where m is the mass of the molecule and v is the velocity) To calculate an average kinetic energy, we therefore need an expression for the average velocity, alternately written as u rms (the root-mean-square velocity). u = 3RT M The kinetic energy per mole of a gas: KE = 3 2 RT 34 17
Maxwell-Boltzman distribution The average kinetic energy of gaseous molecules is directly proportional to the absolute temperature of the sample. 35 Real gases: deviations from ideality The van der Waals equation, like the ideal gas equation, is known as an equation of state. 36 18
van der Waals constants 37 Exercise Calculate the pressure exerted by 1.00 mole of methane, CH4, in a 500.-mL vessel at 25.0 C assuming (a) ideal behavior and (b) nonideal behavior. Ans: 38 19
Comparison of solids, liquids, and gases 39 Comparison of solids, liquids, and gases The molecules of most gases are so widely separated at ordinary temperatures and pressures that they do not interact with one another significantly. The physical properties of gases are reasonably well described by the simple relationships. # In liquids and solids, the so-called condensed phases, the particles are close together so they interact strongly. Although the properties of liquids and solids can be described, they cannot be adequately explained by simple mathematical relationships. 40 20
The liquid state Liquids are considered to be relatively incompressible. Unlike gas molecules, liquid molecules are tightly packed. Liquids have a fixed volume, whereas gases do not. Liquids do not have a definite shape. The properties of liquids can be attributed to the presence of various types of intermolecular forces. 41 Intermolecular forces Intermolecular forces are weak attractive forces that contribute to many of the physical properties exhibited by liquids 1) Hydrogen bonding. 2) Dipole-dipole interactions. 3) London forces or dispersion forces (van der Waals). 42 21
Properties of the liquid state Viscosity Surface tension Capilary action Evaporation Vapor Pressure Boiling Points Heat Transfer Involving Liquids 43 Viscosity Viscosity is the resistance to flow of a liquid. For a liquid to flow, the molecules must be able to slide past one another. In general, the stronger the intermolecular forces of attraction, the more viscous the liquid is. 44 22
Viscosity The viscosity of a liquid can be measured with a viscometer 45 Viscosity Viscosity decreases with increasing temperature, as long as no changes in composition occur. Substances that have a great ability to form hydrogen bonds usually have high viscosities. (The viscosity of water at 25 C is 0.89 centipoise.) The poise is the unit used to express viscosity. 46 23
Viscosity Increasing the size and surface area of molecules generally results in increased viscosity, due to the increased dispersion forces. 47 Surface tension Molecules below the surface of a liquid are influenced by intermolecular attractions from all directions. Those on the surface are attracted only toward the interior. These attractions pull the surface layer toward the center. The most stable situation is one in which the surface area is minimal. 48 24
Surface tension Surface tension is a measure of the inward forces that must be overcome to expand the surface area of a liquid. The toughness of the skin``. 49 Capilary action Cohesive forces: intermolecular forces of attraction within a substance, which cause the molecules of the substance to resist separation. Adhesive forces: intermolecular forces of attraction between two different substances. Capillary action occurs when one end of a capillary tube, a glass tube with a small bore (inside diameter), is immersed in a liquid. If adhesive forces exceed cohesive forces, the liquid creeps up the sides of the tube until a balance is reached between adhesive forces and the weight of liquid. 50 25
Capilary action Water adheres to glass, or is said to wet glass. The surface of the water, its meniscus, has a concave shape. Mercury does not wet glass because its cohesive forces are much stronger than its attraction to glass. Thus, its meniscus is convex. 51 Evaporation Evaporation, or vaporization, is the process by which molecules on the surface of a liquid break away and go into the gas phase. 52 26
Evaporation Kinetic energies of molecules in liquids depend on temperature in the same way as they do in gases. Only the higher-energy molecules can escape from the liquid phase. 53 Evaporation vs condensation A molecule in the vapor may strike the liquid surface and be captured there. This process, the reverse of evaporation, is called condensation. In the closed container, the system composed of the liquid and gas molecules of the same substance eventually achieves a dynamic equilibrium in which the rate of evaporation equals the rate of condensation. 54 27
Vapor Pressure The partial pressure of vapor molecules above the surface of a liquid at equilibrium at a given temperature is the vapor pressure of the liquid at that temperature. 55 Vapor Pressure Because the rate of evaporation increases with increasing temperature, vapor pressures of liquids always increase as temperature increases. 56 28
Vapor Pressure Stronger cohesive forces tend to hold molecules in the liquid state. 57 Boiling point When a liquid is heated to a sufficiently high temperature under a given applied pressure, bubbles of vapor begin to form below the surface. If the vapor pressure inside the bubbles is less than the applied pressure on the surface of the liquid, the bubbles collapse as soon as they form. If the temperature is raised sufficiently, the vapor pressure is high enough that the bubbles can persist, rise to the surface, and burst, releasing the vapor into the air. This process is called boiling evaporation. The boiling point of a liquid is the temperature at which its vapor pressure equals the external pressure. 58 29
Exercise When a sealed flask of water is connected to a vacuum pump, the water in the flask is observered to boil at a temperature much lower than the normal boiling point of 100 C. Why does this occur? What does the vacuum pump do to allow the water to boil at such a low temperature? 59 Heat transfer involving liquids The specific heat (J/g C) or molar heat capacity ( J/mol C) of a liquid (or solid, or gas) is the amount of heat that must be added to the stated mass of liquid (or solid, or gas) to raise its temperature by one degree Celsius. Q= m.c. (t 2 t 1 ) = C. t where q is the heat required, m is mass, C is the specific heat, and t is the change in temperature. For example, the specific heats of water (L), ice (S) and steam (G) are 4.18 J/g C, 2.09 J/g C and 2.03 J/g C, respectively. 60 30
Heat transfer involving liquids Calculate the amount of heat, in joules, required to convert 100 grams of water at 25 C to 35 C. (the specific heat of water is 4.18 J/g C) Ans: 61 Heat transfer involving liquids Heat of vaporization ( H vap ) of a liquid substance is the quantity of heat required to vaporize one gram of that substance at its boiling point. The unit used is J/g (can also be expressed on a per mol basis; kj/mol). Heat of condensation of a substance is the quantity of heat that should be removed to condense one gram of that substance at its condensation point. The unit used is J/g (can also be expressed on a per mol basis; kj/mol). The heat of condensation of a liquid is equal in magnitude to the heat of vaporization. 62 31
Heats of vaporization, boiling points, and vapor pressures of some common liquids 63 Calculate the amount of heat, in joules, required to convert 180 grams of water at 10 C to steam at 105 C. Ans: Exercise 64 32
The Clausius Clapeyron Equation When the temperature of a liquid is changed from T 1 to T 2, the vapor pressure of the liquid changes from P 1 to P 2. These changes are related to the molar heat of vaporization, H vap, for the liquid by the Clausius Clapeyron equation. The units of R must be consistent with those of H vap. (R=8.314 J/mol.K). 65 The Clausius Clapeyron Equation The normal boiling point of ethanol, C 2 H 5 OH, is 78.3 C, and its molar heat of vaporization is 39.3 kj/mol. What would be the vapor pressure, in torr, of ethanol at 50.0 C? Ans: 66 33
The solid state Solids have definite shapes and volumes. Solids are not very compressible, are dense, and diffuse only very slowly into other solids. Solids are generally characterized by compact, ordered arrangements of particles that vibrate about fixed positions in their structures. 67 Melting point The melting point (freezing point) of a substance is the temperature at which its solid and liquid phases coexist in equilibrium. The melting point of a solid is the same as the freezing point of its liquid. It is the temperature at which the rate of melting of a solid is the same as the rate of freezing of its liquid under a given applied pressure. 68 34
Heat transfer involving solids The molar heat (or enthalpy) of fusion ( H fus ; kj/mol) is the amount of heat required to melt one mole of a solid at its melting point. Heats of fusion can also be expressed on a per gram basis. The heat (or enthalpy) of solidification (or crystallization) of a liquid is equal in magnitude to the heat of fusion. It represents removal of a sufficient amount of heat from a given amount (1 mol or 1 g) of liquid to solidify the liquid at its freezing point. 69 Heat transfer involving solids 70 35
Exercise Calculate the amount of heat that must be absorbed by 50 grams of ice at -12.0 C to convert it to water at 20.0 C Ans: 71 72 36
Sublimation and the vapor pressure of solids Some solids such as I 2 and CO 2 (s) vaporize at atmospheric pressure without passing through the liquid state. This process is known as sublimation. The reverse process, by which a vapor solidifies without passing through the liquid phase, is called deposition. Solids exhibit vapor pressures just as liquids do, but they generally have much lower vapor pressures. Solids with high vapor pressures sublime easily. 73 Pressure Phase change: Phase diagram Temperature 74 37
Phase diagram of H 2 O 75 Phase diagram of CO 2 76 38
Crystalline and Amorphous Solidss Solid-state chemistry is one of the most active areas of science, especially in the development of new materials. We classify solids into two major group: crystalline and noncrystalline (amorphous). 77 Crystalline and Amorphous Solidss Amorphous solids have no well-defined, ordered structure. Particles in amorphous solids are irregularly arranged, so intermolecular forces among their particles vary in strength within a sample. Melting occurs at different temperatures for various portions of the same sample as the intermolecular forces are overcome. e.g glass, rubber, some kinds of plastics, and amorphous sulfur. 78 39
Crystalline Solidss The molecules, atoms, or ions of crystalline solids are arranged in a regular structural array, called a crystal lattice. Crystal lattices are built of unit cells, which are the smallest repeating units with all of the symetry characteristics of the general structure. 79 80 40
Unit cell 81 82 41
Crystal structure We classify crystalline solids into categories according to the types of particles in the crystal and the bonding or interactions among them. The four categories are: 1) Metallic solid 2) Ionic solid 3) Molecular solid 4) Network solid (Covalent solid) 83 Metallic solid A metallic solid consists of positive atomic cores surrounded by electrons. Almost all metals are solids at room temperature. The free electrons in metallic solids account for their superior electrical conductivity (e.g., iron, gold, silver). Most metallic solids are composed of metal atoms packed together in crystal lattices based on a cube-shaped unit cell. These cubic unit cells can be one of three structural types: simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc). 84 42
Metallic solid 85 Band theory of metals 86 43
Band theory of metals 87 Ionic solid An ionic solid consists of cations and anions which are held together by the electrostatic attraction between them. These attractive forces are very strong and thus ionic solids have high melting points. Sodium chloride (NaCl), and cesium chloride (CsC1) are examples of ionic solids. 88 44
Molecular solid A molecular solid consists of atoms or molecules held together by intermolecular attractive forces. In molecular solids, the attractive forces include hydrogen bonds and dipoledipole forces (e.g. Ice [H 2 O (s)], Ice [CO 2 (s)] ). Because of the relatively weak intermolecular forces of attraction, molecules can be easily displaced. Thus, molecular solids are usually soft substances with low melting points 89 Network solid In a network solid, the atoms are held together by large networks of covalent bonds. For these reasons, network solids have very high melting points. 90 45
Summary After you have studied this module 3, you should be able to List the properties of gases and compare gases, liquids, and solids. Describe how pressure is measured. Use and understand the absolute (Kelvin) temperature scale. Describe the relationships among pressure, volume, temperature, and amount of gas (Boyle s Law, Charles s Law, Avogadro s Law, and the Combined Gas Law). Use Boyle s Law, Charles s Law, Avogadro s Law, and the Combined Gas Law, as appropriate, to calculate changes in pressure, volume, temperature, and amount of gas. 91 Summary Use the ideal gas equation to do pressure, volume, temperature, and mole calculations as related to gas samples. Describe how mixtures of gases behave and predict their properties (Dalton s Law of Partial Pressures). Describe molecular motion, diffusion, and effusion of gases Understand the kinetic molecular description of gases. Describe the molecular features that are responsible for nonideal behavior of real gases and explain when this nonideal behavior is important. 92 46
Summary Describe the properties of liquids and solids and how they differ from gases. Understand the kinetic molecular description of liquids and solids, and show how this description differs from that for gases. Use the terminology of phase changes. Understand various kinds of intermolecular attractions and how they are related to physical properties such as vapor pressure, viscosity, melting point, and boiling point. Describe evaporation, condensation, and boiling in molecular terms. Calculate the heat transfer involved in warming or cooling without change of phase. 93 Summary Calculate the heat transfer involved in phase changes. Describe melting, solidification, sublimation, and deposition in molecular terms. Interpret P versus T phase diagrams. Describe the regular structure of crystalline solids. Describe various types of solids. Relate the properties of different types of solids to the bonding or interactions among particles in these solids. Visualize some common simple arrangements of atoms in solids. 94 47