Chapter 4-Part 2_Final PDF

Chemistry 1 Chapter 4: Intermolecular Forces of Liquids and Solids Part 2: Crystal Structure (see chapter 11 in the text-book) 1 I. Ordered and disordered state in...

Chemistry 1 Chapter 4: Intermolecular Forces of Liquids and Solids Part 2: Crystal Structure (see chapter 11 in the text-book) 1 I. Ordered and disordered state in solids Outlines : II. Structure of crystalline solids II.1. Terminology II.2. Types of unit cells II.3. Cubic structure in metallic compounds II.3.1. Simple cubic cell (scc) II.3.2. The body-centered cubic cell (bcc) II.3.3. The face-centered cubic cell (fcc) III. Types of crystal structures III. 1. Ionic Crystals III. 2. Covalent Crystals III. 3. Molecular Crystals III. 4. Metallic Crystals IV. Phase changes IV. 1. Liquid-Vapor Equilibrium IV. 1.1. Vapor Pressure IV. 1.2. Molar Heat of Vaporization and Boiling Point IV. 2. Liquid-Solid Equilibrium IV. 3. Solid-Vapor Equilibrium V. Phase Diagrams 2 I. Ordered and disordered state in solids Solids can be divided into two categories: crystalline and amorphous. Crystalline solid Amorphous solid is a material whose atoms, ions or is a solid that lacks the long-range order in its structure molecules have regular long-range order. where atoms have a disrordered arrangement. Amorphous carbon Diamond Quartz glass 3  II. Structure of crystalline solids II.1. Terminology Unit cell: the smallest repeating entity of the atomic structure. The basic building block of the crystal structure. It defines the entire crystal structure with the atom positions within. Lattice: The positions of the components in a crystalline solid are usually represented by a lattice, which is a three-dimensional system of points describing the positions of the components (atoms, ions, or molecules) that make up the substance. Thus a particular lattice can be generated by repeating the unit cell in all three dimensions to form the extended structure. (a) A unit cell (b) its extension in three dimensions. Lattice point: Each sphere represents an atom, ion, or molecule and The black spheres represent either atoms, ions is called a lattice point. or molecules (lattice point). The coordination number is defined as the number of atoms (or ions) surrounding an atom (or ion) in a crystal lattice. 4  II.2. Types of unit cells Every crystalline solid can be described in terms of one of the seven types of unit cells shown below. The seven types of unit cells are characterized by 6 parameters: a,b and c are cell parameters. Angle α is defined by edges b and c, angle β by edges a and c, and angle γ by edges a and b Any of the unit cells, when repeated in space in all three dimensions, forms the lattice structure characteristic of a crystalline solid. The geometry of the cubic unit cell is particularly simple because all sides (or edges) and all angles are equal. Because of the simplicity of cubic unit cell we will consider this structure as an example to understand crystal structure. 5  How to calculate the number of atoms per (cubic) cell? Because every unit cell in a crystalline solid is adjacent to other unit cells, most of a cell’s atoms are shared by neighboring cells a- Each corner atom belongs to eight unit cells so it is accounted (1/8) b- an edge atom is shared by four unit cells it is accounted (1/4) c- a face-centered atom is shared by two unit cells it is accounted (1/2) https://www.youtube.com/watch?v=KNgRBqj9FS8 6 II.3. Cubic structure in metallic compounds The way the spheres are arranged in layers determines what type of unit cell we have. II.3.1. Simple cubic cell (scc) In simple cubic cell the three-dimensional structure can be generated by placing a layer above and below this layer in such a way that spheres in one layer are directly over the spheres in the layer below it. This procedure can be extended to generate many layers, as in the case of a crystal. The coordination number =6 ; Each sphere in this arrangement has a coordination number of 6 because it has six immediate neighbors (four spheres in its own layer, one sphere in the layer above, and one sphere in the layer below). Number of atoms per unit cell =1 ; Because each corner sphere is shared by eight unit cells and there are eight corners in a cube, there will be the equivalent of only one complete sphere. (a) Top view of one layer of spheres. (b) Definition of a simple cubic cell. (c) Because each sphere is shared by eight unit cells and there are eight corners in a cube, there is the equivalent of one complete sphere inside a simple cubic unit cell 7 II.3.2. The body-centered cubic cell (bcc) A body-centered cubic arrangement differs from a simple cube in that the second layer of spheres fits into the depressions of the first layer and the third layer into the depressions of the second layer. The coordination number of each sphere in this structure is 8 (each sphere is in contact with four spheres in the layer above and four spheres in the layer below). Number of atoms per unit cell =2 ; A body-centered cubic cell contains the equivalent of two complete spheres, one in the center and eight shared corner spheres (a) Top view. (b) Definition of a body-centered cubic unit cell. (c) There is the equivalent of two complete spheres inside a body- centered cubic unit cell. 8  II.3.3. The face-centered cubic cell (fcc) A metallic crystal can be pictured as containing spherical atoms packed together and bonded to each other equally in all directions. We can model such a structure by packing uniform, hard spheres in a manner that most efficiently uses the available space. Such an arrangement is called closest packing. The spheres are packed in layers, as shown below: A face-centered cubic unit cell, as shown below, adopts ABC layers arrangement and the resulting structure is called the cubic closest packed (ccp) structure (a) The first layer A is a close packed layer, where each x A sphere (i.e x) is in contact with six others. (b) Spheres in the second layer B fit into the B depressions between the first-layer spheres. (d) In the cubic close-packed structure, each third The ABC arrangement leads to Layer sphere fits into a depression that is directly C the cubic close-packed (ccp) over a depression in the first layer. structure, which corresponds to the face-centered cube (FCC). 9 Coordination number in The face-centered cubic cell (fcc) The coordination number = 12; each sphere is in contact with six spheres in its own layer, three spheres in the layer above, and three spheres in the layer below). Number of atoms per unit cell = 6x(1/2) + 8x(1/8) =4 3 atoms in contact with an atom in layer b Each atom is surrounded by 6 atoms of the same layer 3 atoms in contact with an atom in layer b CN= 3 + 3 + 6 =12 FCC unit cell Expanded model of FCC 10 Question: for each cubic structure express the cell parameter ‘a’ as a function of atomic radius r 11 III. Types of crystal structures Considering that crystalline structures can be formed by atoms, metals, ions or molecules, the arrangement of such particles in a crystalline solid is governed by net attractive intermolecular forces. The structures and properties of crystals, such as melting point, density, and hardness, are determined by the types of forces that hold the particles together. We can classify any crystal as one of four types: ionic, covalent, molecular, or metallic. Metallic solid 12 III. Types of crystal structures III. 1. Ionic Crystals Ionic crystals are composed of charged species : positively charged ions (cations) and negatively charged ions (anions) that are generally quite different in size. The studied solids will be assumed to be perfect, which means that ions will be assumed to be perfectly spherical. In ionic crystals, cations and anions are held together by strong electrostatic forces. Physical properties of ionic crystals: Most ionic crystals have high melting points, an indication of the strong electrostatic forces holding the ions together. These solids do not conduct electricity because the ions are fixed in their position. However, in the molten state (that is, when melted) or dissolved in water, the ions are free to move and the resulting liquid is electrically conducting. 13 III. 1. Ionic Crystals Example 1 : NaCl In NaCl crystal Cl- has FCC structure and Na+ occupy the middle of edges and the center of the cubic cell. Crystal structure that crystallises in the same way than NaCl: LiCl, MnO, PbS, etc 14 III. 1. Ionic Crystals Example 2 : CsCl Cl- In CsCl crystal, Cl- forms the simple cubic lattice (SCC) and Cs+ occupies the center of the cubic cell. Example of crystal structure that crystallises in the same way Cs+ than CsCl are : CsBr, CsI, TlCl 15 How to calculate the density of cubic cell ? mass of unit cell = number of atoms per unit cell (n) x mass of each atom 𝑑= volume of unit cell Volume of cubic cell = a3 Molar weight (g/mol) mass of atom = 𝑁𝐴 (𝑚𝑜𝑙 −1 ) 𝑛𝑥𝑀 𝑛𝑥𝑀 𝑑= = 3 𝑉𝑥𝑁𝐴 𝑎 𝑥𝑁𝐴 n: number of atoms, molecule or ion (also called motif) per unit cell cell M: molar mass of atoms, molecule or ion a= cell edge length NA: Avogadro number 16 How many Cl- and Na+ ions are in each NaCl unit cell? Answer : There are four Cl- and four Na+ ions in each NaCl unit cell. The edge length of the NaCl unit cell is 564 pm. What is the density of NaCl in g/cm3? 𝑛𝑥 𝑀 𝑑= 𝑎3 𝑥𝑁𝐴 4𝑥 (22.99+35.45) = (564x 10−10 )3𝑥6.022𝑥1023 d =2.16 g/cm3 17  III. 2. Covalent Crystals In covalent crystals, atoms are held together entirely by covalent bonds in an extensive (three-dimensional or 2D) network. Well-known examples are the two allotropes (different physical forms ) of carbon: diamond and graphite. In diamond each carbon atom is tetrahedrally bonded to four other atoms. The strong covalent bonds in three dimensions contribute to diamond’s unusual hardness and high melting point (3550°C). In graphite, carbon atoms are arranged in six-membered rings. The layers are held together by the weak van der Waals forces. The covalent bonds in graphite account for its hardness; however, because the layers can slide over one another, graphite is slippery to the touch and is effective as a lubricant. C tetrahedral Graphite layers The structure of diamond. Each carbon is tetrahedrally The structure of graphite. The distance bonded to four other carbon atoms. between successive layers is 335 pm 18 III. 3. Molecular Crystals A molecular crystal, the lattice points are occupied by molecules, and the attractive forces between them are van der Waals forces and/or hydrogen bonding. Examples : Sulfur dioxide (SO2) is a molecular crystal is solid, in which the predominant attractive force is dipole-dipole interaction. Other examples I2, P4, and S8 Molecules in molecular crystals are packed together as closely as their size and shape allow. Because van der Waals forces and hydrogen bonding are generally quite weak compared with covalent and ionic bonds, molecular crystals are more easily broken apart than ionic and covalent crystals. Indeed, most molecular crystals melt below 200°C. CO2 I2 19 Question : consider Cl2 and I2 molecular crystals, identify which crystal has higher melting point Answer The intermolecular forces responsible on the formation of Cl2 and I2 molecular crystals are dipersion forces. Since I2 is made up of larger number of electron, so it’s more polarizable, which means that it has stronger dispersion forces between molecules. Therefore I2 has higher melting point (113.7 °C) of than Cl2 (-101.5 °C) 20  III. 4. Metallic Crystals The structure of metallic crystals is the simplest because every lattice point in a crystal is occupied by an atom of the same metal. The bonding in metals is quite different from that in other types of crystals. In a metal, the bonding electrons are delocalized over the entire crystal. Metallic Metals (copper, silver, gold) crystallise in fcc bonds can be thought as a cloud of positively charged ions immersed in a cloud structure at room temperature of valence electrons. Metal ions Delocalized electrons The electrons are said delocalized. The mobility of the delocalized electrons makes metals good conductors of heat and electricity. The great cohesive force resulting from delocalization is responsible for a metal’s strength, which increases as the number of electrons available for bonding increases. For example, the melting point of sodium, with one valence electron, is 97.6°C, whereas that of aluminum, with three valence electrons, is 660°. 21 III. Types of crystal structures The forces responsible for the stability of a crystal can be ionic forces, covalent bonds, van der Waals forces, hydrogen bonds, or a combination of these forces. 22 X-ray diffraction X-ray diffraction refers to the scattering of X rays by the units of a crystalline solid. X-ray diffraction is extensively used in chemistry for the characterization of organic and inorganic compounds. The diffracted X-rays generate a pattern that allows to analyze solids and identify their structures, different phases, and their crystallinity. X-ray diffractograms of amorphous and crystalline phases 23 IV. Phase changes Phase changes, are the transformations from one phase to another, which happen when energy (usually in the form of heat) is added or removed from a substance. During a phase transformation, changes in molecular order occur; molecules in the solid phase have the greatest order, and those in the gas phase have the greatest randomness. 24 The various phase changes that a substance can undergo. 25  IV. 1. Liquid-Vapor Equilibrium At a given temperature, a certain number of the molecules in a liquid possess sufficient kinetic energy to escape from the surface. This process is called evaporation, or vaporization. IV. 1.1. Vapor Pressure When a liquid evaporates, its gaseous molecules exert a vapor pressure. Apparatus for measuring the vapor pressure of a liquid (a) Before evaporation : Initially the liquid is frozen so there are no molecules in the vapor phase (mercury levels are equal). (b) On heating, a liquid phase is formed and vaporization begins. At equilibrium, the number of molecules leaving the liquid is equal to the number of molecules returning to the liquid. The difference in the mercury levels (h) gives the equilibrium vapor pressure of the liquid at the specified temperature. mercury As soon as some molecules leave the liquid, a vapor phase is established. The vapor pressure is measurable only when a fair amount of vapor is present. 26 What happens at the molecular level during evaporation? (a) In the beginning, the traffic is only one way: Molecules are moving from the liquid to the empty space. Soon the molecules in the space above the liquid establish a vapor phase. (b) As the concentration of molecules in the vapor phase increases, some molecules condense, that is, they return to the liquid phase. Condensation, the change from the gas phase to the liquid phase, occurs because a molecule strikes the liquid surface and becomes trapped by intermolecular forces in the liquid (a) (b) The rate of evaporation is constant at any given temperature (T=constant), and the rate of condensation increases with increasing concentration of molecules in the vapor phase. A state of dynamic equilibrium, is reached when the rates of condensation and evaporation become equal. Evaporation and The equilibrium vapor pressure (Pv) is the maximum condensation vapor pressure of a liquid measured at a given rates are equal temperature when the condensation and evaporation beyond this time equilibrium is reached. Pv is constant at constant T. 27  Plots of vapor pressure versus temperature for three different liquids In general, the higher the temperature, the greater the kinetic energy, and hence more molecules leave the liquid. For this reason, the vapor pressure of a liquid always increases with temperature. Different substances have different vapor pressures , this depends on how molecules are attracted to each others in a liquid. The increase in vapor pressure with temperature for three liquids. The normal boiling points of the liquids (at 1 atm) are RT shown on the horizontal axis. The Normal Bp increases from diethyl ether to water to mercury because of the increase of the applied forces between entities. The strong metallic bonding in mercury results in a much lower vapor pressure of the liquid at room temperature (RT). Normal boiling points of the liquids (at 1 atm) 28  What affects the Boiling Point ? Pressure: When pressure is less than one atmosphere, the boiling point of the liquid is lower than its normal boiling point. When equal to one atmosphere, the boiling point of a liquid is called the normal boiling point. When greater than one atmosphere, the boiling point of the liquid is greater than its normal boiling point. The following graph shows the boiling point for water as a function of the pressure. The line on the graph shows the normal boiling point for water. 29  IV. 1.2. Molar Heat of Vaporization and Boiling Point How can we measure the strength of intermolecular forces in a liquid ? A measure of the strength of intermolecular forces in a liquid is the molar heat of vaporization (ΔHvap), defined as the energy (usually in kilojoules) required to vaporize 1 mole of a liquid. If the intermolecular attraction is strong, it takes a lot of energy to free the molecules from the liquid phase and the molar heat of vaporization ΔHvap will be high. As previously mentioned, the equilibrium vapor pressure (P) of a liquid increases with increasing temperature. The analysis of this behavior reveals that the quantitative relationship between the vapor pressure P of a liquid and the absolute temperature T is given by the Clausius Clapeyron equation: where ln is the natural logarithm, R is the gas constant (8.314 J/K.mol), and C is a constant. 30 The Clausius-Clapeyron equation has the form of the linear equation y =mx + b: By measuring the vapor pressure of a liquid at different temperatures (see figure Vapor pressure vs temperature) and plotting ln P versus 1/T, we determine the slope, which is equal to ( -ΔHvap /R). Plots of ln P versus 1/T for water and diethyl ether. ΔHvap is assumed to be independent of temperature. This is the method used to determine heats of vaporization 31  If we know the values of ∆Hvap and P1 of a liquid at one temperature (T1), we can use the Clausius-Clapeyron equation to calculate the vapor pressure of the liquid at a different temperature. At temperatures T1 and T2 the vapor pressures are P1 and P2. From the previous equation we can write 1 2 Subtracting Equation 1 from Equation 2 we obtain: Hence 32  IV. 2. Liquid-Solid Equilibrium The transformation of liquid to solid is called freezing, and the reverse process is called melting or fusion. melting Solid Liquid freezing The melting point of a solid (or the freezing point of a liquid) is the temperature at which solid and liquid phases coexist in equilibrium. The energy (usually in kilojoules) required to melt 1 mole of a solid is called the molar heat of fusion (∆Hfus). A comparison of data shows that for each substance ∆Hfus is smaller than ∆Hvap. This is consistent with the fact that molecules in a liquid are fairly closely packed together, so that some energy is needed to achieve the rearrangement from solid to liquid. On the other hand, when a liquid evaporates, its molecules are completely separated from one another and considerably more energy is required to overcome the attractive forces. 33 IV. 3. Solid-Vapor Equilibrium Solids undergo evaporation and therefore possess a vapor pressure. Consider the following dynamic equilibrium: Solid sublimation gas deposition The process in which molecules go directly from the solid into the vapor phase is called sublimation, and the reverse process (that is, from vapor directly to solid) is called deposition. The energy (usually in kilojoules) required to sublime 1 mole of a solid, called the molar heat of sublimation (∆Hsub), is given by the sum of the molar heats of fusion and vaporization: The enthalpy, or heat change, for the overall process is the same whether the substance changes directly from the solid to the vapor form or goes from solid to liquid and then to vapor. 34  V. Phase Diagrams The overall relationships among the solid, liquid, and vapor phases are best represented in a single graph known as a phase diagram. A phase diagram summarizes the conditions under which a substance exists as a solid, liquid, or gas. The phase diagram of water (a) Each solid line between two phases ( ) specifies the conditions of pressure and temperature under which the two phases can exist in equilibrium. (b) This phase diagram tells us that increasing the pressure on ice lowers its melting point and that increasing the pressure of liquid water raises its boiling point. The point at which all three phases can exist in equilibrium (0.006 atm and 0.01°C) is called the triple point. 35  Critical Temperature and Pressure (Tc and Pc) Point A : In principle, a gas can be made to liquefy by cooling a sample of gas we decrease the kinetic energy of its molecules, and eventually molecules aggregate to form small drops of liquid. Alternatively, we may apply pressure to the gas. Under compression, the average distance between molecules is reduced so that they are held together by mutual attraction. P B (Tc, Pc) T>Tc A substance has a critical temperature (Tc), above which its gas form cannot be made to liquefy, no matter how great the applied pressure. This is also T A the highest temperature at which a substance can exist as a liquid. T