Mineral Chemistry Past Paper (May 2021) PDF

UNIVERSITY OF MINES & TECHNOLOGY, (UMaT), TARKWA MINERALS ENGINEERING DEPARTMENT MINERAL CHEMISTRY (MR 172) Compiled by Eric A Agorhom (PhD) AAusIMM, MWAIM May 2021  Course Aims and Objectives The main aim of this course is; To prepare student...

UNIVERSITY OF MINES & TECHNOLOGY, (UMaT), TARKWA MINERALS ENGINEERING DEPARTMENT MINERAL CHEMISTRY (MR 172) Compiled by Eric A Agorhom (PhD) AAusIMM, MWAIM May 2021  Course Aims and Objectives The main aim of this course is; To prepare students to become competent minerals engineers by exposing them with the chemistry underpinning extractive metallurgy and mineral processing Course objectives include: To educate students on physical and surface chemistry To introduce students to various branches of chemistry involved in minerals engineering To encourage students to make good use of the knowledge acquired during this lectures in their profession as mineral engineers  Expected Outcome of the Course At the end of the course, students are expected to: Gain good knowledge of physical chemistry, interfacial and colloid science Apply the principles learnt during course delivery in practical work both as a student and a professional engineer  Course Presentation and Assessment This course will be delivered through lectures with supporting lecture notes and practical work at the laboratory to aid students’ understanding of the course Assignments will be given after each chapter to test students’ understanding. These assignments should be presented to the lecturer before the commencement of a new chapter Students will be assessed through: ✓ Continuous Assessment 40% ✓ Final exams 60%  The continuous assessment will comprise class attendance, assignments, class test, announced and unannounced quizzes  Course Content 1. Chapter 1 – Atomic theory 2. Chapter 2 – Periodicity 3. Chapter 3 – Chemical bonding 4. Chapter 4 – Chemical equilibrium 5. Chapter 5 – States of matter 6. Interfacial Science 7. Colloid science 8. Reference  CHAPTER ONE ATOMIC THEORY  Introduction - Atom The concept of an atom was born in Greece around 450 B. C. It was attributed to Democritus, a Greek philosopher, who argued that matter and motion are discontinuous and could not be divided infinitely. An ultimate fundamental indivisible particle will emerge, which cannot be divided further. He called this particle an atom, from the greek word atomos, which means “uncuttable” 7  John Dalton In 1803, John Dalton, a modest English School Teacher, following Democritus philosophy, offered experimental evidence of the said particles. In the seventeenth century, Robert Boyle had concluded from experiments that a gas was made up of tiny particles. Dalton expanded on Boyle’s conclusion and proposed that all matter was composed of particles His contribution was the first significant step towards the development of atomic theory Dalton built his postulates based on the laws of chemical combination. 8  Laws of Chemical Combination Law of Conservation of Mass: Mass is neither created nor destroyed in chemical reactions. Law of Definite Proportions (constant composition): In a given compound, the constituent elements are always combined in the same proportions by mass, regardless of the origin or mode of preparation of the compound. Law of Multiple Proportions: When two elements combine with each other to form more than one compound, the weights of one element that combine with a fixed weight of the other are in a 9 ratio of small whole numbers. 10 11  Laws of Chemical Combination According to the law of definite composition, carbon and oxygen always react in the same mass ratio to produce carbon dioxide. Dalton proposed that one atom of carbon combines with two atoms of oxygen to produce a molecule of CO2. Carbon dioxide, CO2 Similarly, he proposed that two atoms of hydrogen combine with one atom of oxygen to give a molecule of H2O Water, H2O 12  Laws of Chemical Combination Finally, Dalton reasoned that two atoms of hydrogen in water could substitute for each of the oxygen atoms in carbon dioxide. This would results in a molecule with one carbon atom and four hydrogen atoms, which was then known as marsh gas, but now called methane (CH4) Methane, CH4 Through this experimentation, Dalton found that the combining ratio of carbon to hydrogen in methane was 1 to 4, which agreed with his prediction. 12  Dalton’s Postulate An element is composed of tiny, indivisible, indestructible particles called atoms. All atoms of an element are identical and have the same properties. Atoms of different elements combine to form compounds. Compounds contain atoms in small whole number ratios. Atoms combine in more than one ratio to form different compounds Dalton’s first two postulates were incorrect. 13  About 50 years after Dalton’s proposal, there was disturbing evidence that the atom was divisible after all. The evidence came from sealed glass tubes containing a gas. When electricity was applied, the tube began to glow and emit a ray. When different gases were introduced, these tubes glowed in different colors. This eventually led to the discovery of a negatively charged particle called an electron and a positively charged particle called a proton. The electron had a relative charge of -1, and the proton had an opposite but equal charge of +1. 14  Thompson’s Model of the Atom In 1904, J. J. Thompson proposed a subatomic model of the atom. The model pictured a positively charged atom containing negatively charged electrons. Thomson visualized electrons in homogeneous (evenly distributed) spheres of positive charge (see Figure 1). Thomson proposal became popularly known as the plum-pudding model of atom 15 Thompson’s Model of the Atom 16  Thompson’s Model of the Atom Originally, Thompson was only able to determine the relative charge-to-mass ratio of the electron and the proton. However in 1911, after 5 years of tedious observation, the American physicist Robert Millikan determined the actual charge on the electron This allowed Thompson to calculate the actual mass of the electron and the proton as 9.11 X 10-28 g and 1.67 X 10 -24 g 17  Rutherford’s Alpha Particle Experiment Ernest Rutherford (1897 – 1937) studied subatomic particles and earned his doctorate working for J.J. Thomson at Cambridge. Rutherford was interested in the observation that some elements, including radium, emit streams of particles called alpha particles (α-particles). Studying how α-particles behave in the presence of electrically charged plates and magnets, he identified these particles as helium atoms that have lost all their electrons (in 1906). He experimented with alpha rays by firing them at thin gold foils. As expected, the particles passed straight through the foil or, on occasion, deflected slightly (see Figure 2) 18 Rutherford’s Alpha Particle Experiment 19  Rutherford’s Alpha Particle Experiment This observation seemed reasonable since the plum- pudding model of the atom pictured homogeneous spheres. If the “plum-pudding” model of the atom was correct, α-particles should pass through undeflected. However, some of the alpha particles were deflected backwards. 20 Rutherford’s Experiment 21  Rutherford’s Experiment - Interpretation Most of the alpha particles passed through the foil because an atom is largely empty space. At the center of an atom is the atomic nucleus, which contains the atom’s protons. The α-particles that bounced backwards did so after striking the dense nucleus. 22  Rutherford’s Model of the Atom In 1911, Rutherford proposed a new model of atom. He suggested that negatively charged electrons were distributed about a positively charged nucleus. He calculated that an atom has a diameter of about 1 X 10-8 cm and that the nucleus has a diameter of about 1 X 10-13 cm. 23  Sub-Atomic Particles Based on the heaviness of the nucleus, Rutherford predicted that it must contain neutral particles in addition to protons. Neutrons, n0, were discovered about 30 years later. A neutron is about the size of a proton without any charge. 24  Bohr’s Model of the Atom In 1991, a brilliant young Danish physicist, Neils Bohr (1885 – 1962), completed his doctorate and left for England to begin postdoctoral work under J. J. Thompson. After a new months, he left Cambridge to join Rutherford at Manchester where the atomic nucleus had been discovered. It took him only 2 years to raise our understanding of the atom to yet another level. In 1913, Bohr proposed that electrons orbit around the atomic nucleus just as the planets circle around the sun. 25  Bohr’s Model of the Atom Electrons orbit around the nucleus just as planets orbit the sun. Electrons orbit at fixed distances from the nucleus with a definite energy. The electrons were said to travel in a fixed-energy orbit referred to as an energy level. Electrons could be found only in specific energy levels and nowhere else. 26  Limitations of Bohr’s Model The model does not explain the cause of radiations when electrons change their orbit. The model explains the spectra observed for hydrogen and hydrogen like ions well (eg. He+, Li2+, Be3+ etc). Other spectra lines obtained when other elements are analyzed could not be accounted for. 27  Recent Models Werner Heisenberg, a German scientist argued that it is not possible to accurately determine both the position and energy of an electron. This theory is called the uncertainty principle. This idea combined with the quantized energy levels principle gave rise to the quantum mechanical model. While the quantum model defined energy of an electron in terms of a fixed energy orbit about the nucleus. The quantum mechanical model describes the energy of an electron in terms of the probability of being 28 within a specified region around the nucleus.  Modern View of an Atom The atom consists of a tiny nucleus with a diameter of about 10-13 cm and electrons that move about the nucleus at an average distance of about 10-8 cm away. The nucleus contains protons, which have a positive charge equal in magnitude to the electron’s negative charge, and neutrons, which have virtually the same mass as a proton but no charge Nucleus ~ 10-13 cm Cross-sectional view of an atom 29  Introduction Aristotle on the other hand around 350 B.C. argued that, matter and motion are continuous. Matter could be divided an infinite number of times and even the smallest particle could be further divided. Aristotle’s influence as a great philosopher made people doubt the existence of an atom. 30 CHAPTER TWO PERIODICITY 31 Electronic Configuration and Quantum Numbers Quantum numbers are used to describe completely the movement of each electron within an atom. Quantum numbers are the details required to locate an electron in an atom In order to specify the energy, size ,shape and orientation of the electron orbital, quantum numbers are required Quantum numbers are also used to determine other characteristics of atoms, such as ionization energy and the atomic radius. Each electron in an atom has a unique set of quantum numbers; according to the Pauli Exclusion Principle, no two electrons can share the same combination of 32 Electronic Configuration and Quantum Numbers four quantum numbers Electronic Configuration and Quantum Numbers There are four principal quantum numbers: 1. The Principal Quantum Number (n) 2. The Azimuthal/Angular Quantum Number (l) 3. The Magnetic Quantum Number (m) 4. Spin Quantum Number (ms) These quantum numbers describe the size, shape and orientation in space of the orbital on an atom 33  The Periodic Table Organization of Elements- J.W. Döbereiner Chemists had been looking for a method to classify the elements. In 1829, the German chemist J.W. Döbereiner observed that several elements could be classified into groups of three, or triads. Triad followed a trend whereby the value of the middle element in the triad would be exactly or near exactly predicted by taking the arithmetic mean of values for that property (atomic weight and density) of the other two elements All three elements in a triad showed very similar chemical properties and an orderly trend in physical properties (density, ,melting point and atomic mass). 34 The triads 35  The Periodic Table Newlands J.A.R. Newlands, in 1865, suggested that the 62 known elements can be arranged into groups of seven according to increasing atomic mass. His theory was the law of octaves. He proposed that every eighth element would repeat the properties of the first in the group. His theory was not widely accepted for about 20 years even though it was mostly correct. 36  The Periodic Table Mendeleev In the 1860’s the Russian Chemist Dmitri Mendeleev proposed that the properties of the chemical elements repeat at regular intervals when arranged in order of increasing atomic mass. Today, Mendeleeve is regarded as the architect of the modern periodic table. He had the insight and courage to predict the existence and properties of three elements before their discovery (WHAT ARE THEY??) 37  The Periodic Table Moseley In 1913, H.G.J. Moseley (1887 – 1915), a postdoctoral student, bombarded atomic nuclei with high-energy radiation By studying the X rays that were subsequently emitted, Moseley discovered that the nuclear charge increased by 1 for each element in the periodic table He concluded that arranging elements according to increasing nuclear charge (atomic number) rather than atomic mass, more clearly explained their repeating properties. That is, arranging elements according to atomic number better explained the trends found in the periodic table. 38  The Periodic Law It states that the properties of elements recur in a repeating pattern when arranged according to increasing atomic number. With the introduction of the concept of electron energy levels by Niels Bohr, the periodic table took its current arrangement. 39 The Periodic Law 40 Classification of Elements by Groups and Periods A vertical column on the periodic table is a group or family of elements. A horizontal row on the periodic table is a period or series of elements. There are 18 groups and 7 periods on the periodic table. 41  Classification of Elements by Common Names Several families have common trivial names. Group 1 are the alkali metals Group 2 are the alkaline earth metals Group 17 are the halogens Group 18 are the noble gases 42 Classification of Elements by Blocks and Sublevels 43  Other Classifications of Elements There are several groupings of elements. The representative elements or main-group elements, are in the A groups (groups 1, 2,and 13 – 18). Chemical behavior of these elements is easily predictable. Example: Magnesium always react with oxygen to form MgO. The transition elements are in the B groups (groups 3 – 12). Chemical behavior not easily predictable. Example: In limited oxygen, iron reacts to form FeO, but in excess oxygen, the product is Fe2O3. The inner transition elements are found below the periodic table. The first row (Ce–Lu plus La, Sc, and Y) are also referred to as the rare earth elements. The inner transition elements are divided into the lanthanide series and the actinide series. They are mostly radioactive. 44  PERIODIC TRENDS – ATOMIC SIZE Atomic radius is the distance from the nucleus to the outermost electrons. Since this distance is very small, its always express in nanometers Moving up the group of elements from bottom to top, the radii of the atoms decrease. This is because there are fewer energy levels electrons surrounding the nucleus. As the number of energy levels decreases, the distance from the nucleus to the outermost electrons decreases. Therefore, atomic radius decreases up a group Moving from left to right within a period of elements, the radii of atoms decrease. This is because atomic number and proton number increases. This results in increasing nuclear charge. This has the effect of pulling the electrons closer to the nucleus and reducing the size of the atom. Thus, atomic radius decreases across the period. 45  Ionization Energy Is the amount of energy required to remove an electron in the gaseous state. X(g) X+(g) + e- The closer the electron to the nucleus, the more energy is required to remove the electron. In general, the ionization energy increases as you go from the bottom to the top in a group. In general, the ionization energy increases as you go from left to right across a period of elements. 46 47  Electron Affinity Is the energy change associated with the addition of electron to a gaseous atom X(g) + e- X(g) It increases generally across the period, from left to right. However, there are several exceptions to this rule in each period Down a group, electron affinity decreases, since electron is added at increasing distances from the nucleus. However, in going down most groups the changes in electron affinity are relatively small and numerous exceptions occur. 48  Atomic Radius and Metallic Character Metallic character is the degree of metal character of an element. Metallic character decreases left to right across a period and from bottom to top in a group. It is similar to the trend for atomic radius. 49 Atomic Radius and Metallic Character 50 Minerals Engineering Department University of Mines and Technology 51  Chemical Bonding In 1916 the first theories on chemical bonding was formulated by G. N. Lewis Noble gases were observed to be the most stable, with the exception of helium, they all had eight electrons in their outer shell. Lewis theorized that atoms bonded together to form stable noble gas electron-structure (the octet rule) The octet rule states that atoms bond in such a way that each atom attains eight electrons in its outer shell 52  Chemical Bonding Atoms have core (found closer to the nucleus) and valence (found more distant subshells) electrons To satisfy the octet rule, electron pairs are transferred completely or shared between atoms 53  Ionic Bonds (Electrovalency) This is a type of bonding in which there is a complete transfer of electrons from an atom with low ionization energy to an atom with high electron affinity The attraction between the atoms is electrostatic in nature and exist between cations and anions Main groups metals (groups 1 & 2) achieve a noble gas configuration by losing their valence electrons. 54  Ionic Bonds (Electrovalency) Main group metals are always isoelectronic (have the same number of electrons) with noble gases Nonmetal atoms (groups 16 & 17) on the other hand gain valence electrons and become negatively charged to satisfy the octet rule 55  Ionic Bonds Formed between atoms of different electronegativity. The less electronegative atom completely donates one or more electron to the more electronegative atom. The resultant ions are held together by electrostatic attraction Mostly the bonding between oxygen and Mg, Si, Al, Na, K. Thus, the primary bonding type in silicate and oxide minerals (halite- NaCl, fluorite- CaF2, calcite- CaCO3, etc.) 56  Covalent Bonding The covalent bond is formed when two atoms (of similar electronegativity) share one or more pairs of electrons, each atom contributing one electron of each pair This sort of combination is known as COVALENCY Examples are HF, NH3, CH4, H2O 57  Electronegativity and Bond Polarity Is the ability of an atom in a molecule to draw onto itself a shared pair of electron. Although we defined covalent bonding as electron sharing, the electrons in a covalent bond are not always shared equally by the two bonded atoms. Unless the bond connects two atoms of the same element, there will always be one atom that attracts the electrons in the bond more strongly than the other atom does, as shown in Figure 10. 58  Electronegativity and Bond Polarity Figure 10 Polar versus Nonpolar Covalent Bonds. (a) The electrons in the covalent bond are equally shared by both hydrogen atoms. This is a nonpolar covalent bond. (b) The fluorine atom attracts the electrons in the bond more than the hydrogen atom does, leading to an imbalance in the electron distribution. This is a polar covalent bond. 59  Electronegativity and Bond Polarity When such an imbalance occurs, there is a resulting buildup of some negative charge (called a partial negative charge and designated δ−) on one side of the bond and some positive charge (designated δ+) on the other side of the bond. A covalent bond that has an unequal sharing of electrons, as in part (b) of Figure 10, is called a polar covalent bond. A covalent bond that has an equal sharing of electrons (part (a) of Figure 10) is called a nonpolar covalent bond. 60  Electronegativity and Bond Polarity Any covalent bond between atoms of different elements is a polar bond, but the degree of polarity varies widely. Some bonds between different elements are only minimally polar, while others are strongly polar. Ionic bonds can be considered the ultimate in polarity, with electrons being transferred rather than shared. To judge the relative polarity of a covalent bond, chemists use electronegativity, which is a relative measure of how strongly an atom attracts electrons when it forms a covalent bond - Linus Pauling Electronegativity Model 61  Electronegativity and Bond Polarity The polarity of a covalent bond can be judged by determining the difference in the electronegativities of the two atoms making the bond. The greater the difference in electronegativities, the greater the imbalance of electron sharing in the bond. Although there are no hard and fast rules, the general rule is if the difference in electronegativities is less than about 0.4, the bond is considered nonpolar; if the difference is greater than 0.4, the bond is considered polar. 62  Electronegativity and Bond Polarity If the difference in electronegativities is large enough (generally greater than about 1.8), the resulting compound is considered ionic rather than covalent. An electronegativity difference of zero, of course, indicates a nonpolar covalent bond. 63 Electronegativity and Bond Polarity 64  Electronegativity and Bond Polarity Linus Pauling Electronegativity Model 65  EXAMPLE - Electronegativity and Bond Polarity Describe the electronegativity difference between each pair of atoms and the resulting polarity (or bond type). 1. C and H 2. H and H 3. Na and Cl 4. O and H 66  EXAMPLE - Electronegativity and Bond Polarity 1. Carbon has an electronegativity of 2.5, while the value for hydrogen is 2.1. The difference is 0.4, which is rather small. The C–H bond is therefore considered nonpolar. 2. Both hydrogen atoms have the same electronegativity value—2.1. The difference is zero, so the bond is nonpolar. 3. Sodium’s electronegativity is 0.9, while chlorine’s is 3.0. The difference is 2.1, which is rather high, and so sodium and chlorine form an ionic compound. 4. With 2.1 for hydrogen and 3.5 for oxygen, the electronegativity difference is 1.4. We would expect a very polar bond, but not so polar that the O–H bond is considered ionic 67  EXERCISE - Electronegativity and Bond Polarity Describe the electronegativity difference between each pair of atoms and the resulting polarity (or bond type). 1. C and O 2. N and H 3. N and N 4. C and F 68  Coordinate Covalent Bonds Here the shared pair of electrons is donated by only one of the species (atoms or molecules) involved in the bonding (e.g. formation of NH4+) The resulted bond is purely covalent bond This sort of bond formation is known as co-ordinate covalency The atom which donates a pair of electron is known as ‘donor’ atom and the atom which accepts the pair of electrons is known as ‘acceptor’ atom NB: The donor atom should have a lone pair of electrons. 70 Coordinate Covalent Bonds - The Reaction Between Ammonia and Hydrogen Chloride The reaction is NH3(g) + HCl(g) → NH4Cl(s) Ammonium ions, NH4+, are formed by the transfer of a hydrogen ion (a proton) from the hydrogen chloride molecule to the lone pair of electrons on the ammonia molecule When the ammonium ion, NH4+, is formed, the fourth hydrogen is attached by a dative covalent bond, because only the hydrogen's nucleus is transferred from the chlorine to the nitrogen. The hydrogen's electron is left behind on the chlorine to form a negative chloride ion. Once the ammonium ion has been formed it is impossible to tell any difference between the dative covalent and the ordinary covalent bonds. Although the electrons are shown differently in the diagram, there is no difference between them in reality. 71 Coordinate Covalent Bonds - The Reaction Between Ammonia and Hydrogen Chloride 72 Coordinate Covalent Bonds - DISSOLVING HCl(g) IN WATER TO MAKE HYDROCHLORIC ACID 73 Coordinate Covalent Bonds - CARBON MONOXIDE 74 Coordinate Covalent Bonds - NITRIC ACID 75  Metallic Bonding Metallic bonds are strong bonds in metal crystals. Each metal atom in a metal crystal contributes electrons from its outermost shell to form a “sea of delocalized electrons”. When a metal atom looses electron it becomes positively charged. So, it is quite likely that a metal crystal consists of positively charged metal atoms embedded in a sea of shared electrons Each atom shares electrons freely with other atoms, and some of the electrons are free to move from atom to atom They have low to moderate hardness, very malleable and ductile, soluble in acids, good thermal and electrical conductors 76  Metallic Bonding Metallic Bonding: The Electron Sea Model: Positive atomic nuclei (orange circles) surrounded by a sea of delocalized electrons (yellow circles). Minerals Engineering Department University of Mines and Technology 77 CHEMICAL KINETICS AND EQUILIBRIUM 78  Chemical Equilibrium Previously, we have assumed that a chemical reaction continues until the reactants are used up and the reaction stops. However, in reality, most reactions continue to occur as an ongoing, reversible process. That is, a reaction occurs in the forward direction to give products, and simultaneously a reverse reaction occur in the opposite direction to give the original reactants. precipitating Soluble substance Insoluble particles dissolving 79  Chemical Equilibrium Since some particles are precipitating while others are dissolving, the ongoing process is said to be dynamic. So most chemical reactions involve a dynamic, reversible change. As reactants undergo a reaction to form products, the products react with each other to give the original reactions. When the rate of forward and backward reactions are the same, a state of equilibrium is attained 80  Collision Theory Molecules must collide in order to react The collision must provide at least the minimum energy necessary to produce the activated complex The orientation of the colliding particles must favor the formation of the activated complex, in which the new bond or bonds are able to form as the old bond or bonds break Three factors considered in collision theory are; Collision frequency Collision energy Collision geometry 82 83  Effect of Concentration, Temperature and Catalyst The previous factors are more conceptual in nature, but in practice, the rate of chemical reaction can be increased by: Increasing reactant concentration Reaction temperature Using a Catalyst 84  Energy Profiles of Reactions For a chemical reaction to occur, the reactants must collide with sufficient energy to react This energy is required to achieve the transition state required to form the products (a) Without sufficient energy, the reaction does not occur (b). 85  Reaction Profiles The energy required for reactants to achieve the transition state is the activation energy, Eact. The energy difference between reactants and products is the heat of reaction, H. The H for an endothermic reaction is positive. 86  Exothermic Reactions An exothermic reaction releases heat as the reaction proceeds. NO(g) + O3(g) ⇋ 2 NO2(g) + O2(g) + heat The H for an exothermic reaction is negative. 87  Effect of a Catalyst A catalyst is a substance that allows a reaction to proceed faster by lowering the activation energy. The reaction profile shows the effect of a catalyst on the reaction 2 H2(g) + O2(g) 2 H2O(g) + heat A catalyst does not change H for a reaction. A catalyst speeds up both the forward and reverse reactions. 88  Law of Chemical Equilibrium Consider the following general reaction: aA + bB ⇋ cC + dD The law of chemical equilibrium states that the molar concentrations of the products (raised to the powers c and d), divided by the molar concentrations of the reactants (raised to the powers a and b), equals a constant. 89  Equilibrium Constant Keq Mathematically, we express the law of chemical equilibrium as follows: [C]c[D]d Keq = [A]a[B]b The constant, Keq, is the general equilibrium constant. The value of Keq varies with temperature. So a given value of Keq is valid only for a specific temperature. 90  Writing Equilibrium Constants Let’s write the equilibrium constant expression for the reaction 2A ⇋ B. Recall, Keq is product(s) over reactant(s), each raised to its coefficient in the balanced reaction. Recall that square brackets represent the molar concentration of a species. [B] Keq = [A]2 The equilibrium constant expression is: 91 Equilibrium Expressions Involving Pressures For gases PV=nRT or 𝐧 P= RT=CRT 𝐕 𝒏 Where C= 𝑽 represents the molar concentration of the gas Generally, for the hypothetical reaction, aA + bB ⇋ cC + dD KP=KC.RT∆n Δn = (c + d) – (a + b) 92  Heterogeneous Equilibria A heterogeneous equilibrium is a reaction where one of the substances is in a different physical state. C(s) + H2O(g) ⇋ CO(g) + H2(g) The concentrations of liquids and solids do not change, and they are therefore omitted from equilibrium constant expressions: [CO][H2] Keq = [H2O] 93  Heterogeneous Equilibria - Example Many equilibria involve more than one phase and are called heterogeneous equilibria. For example, the thermal decomposition of calcium carbonate in the commercial preparation of lime occurs by a reaction involving both solid and gas phases: CaCO3(s) ⇌ CaO (s) + CO2 (g) Application of the law of mass action leads to the equilibrium expression [𝑪𝑶𝟐][𝑪𝒂𝑶] K= [CaCO3 ] 94  Heterogeneous Equilibria - Example However, experimental results show that the position of a heterogeneous equilibrium does not depend on the amounts of pure solids or liquids present. This result makes sense when the meaning of an activity for a pure solid or liquid is understood. Thus for the decomposition of CaCO3 considered above, we do not insert [CaCO3] or [CaO] into the equilibrium expression but rather into the activity of each. Examples include: 2H2O(l) ⇌2H2 (g) +O2 (g) 2H2O(g) ⇌2H2 (g) +O2 (g) 95  Homogeneous Equilibria A homogeneous equilibrium is a reaction where all of the products and reactants are in the same physical state. What is the equilibrium constant expression for the homogeneous equilibrium: 2 SO2(g) + O2(g) ⇋ 2 SO3(g) [SO3]2 Keq = [SO2]2[O2] 96  Equilibrium Constant Expressions So when we write equilibrium constant expressions, we only include the concentrations of substances in the gas or aqueous state. What is the equilibrium constant expression for the following reaction? NH4NO3(s) ⇋ N2O(g) + 2 H2O(g) Keq = [N2O][H2O]2 97  Experimental Determination of Keq We can calculate the numerical value of Keq if we know the concentrations of all the species in the reaction. H2(g) + I2(g) ⇋ 2 HI(g) If the concentrations at equilibrium are [H2] = 0.212 M, [I2] = 0.212 M, and [HI] = 1.576 M, what is Keq? [HI]2 = (1.576)2 Keq = [H ][I ] (0.212)(0.212) = 55.3 2 2 98  Extent of Reaction The inherent tendency for a reaction to occur is indicated by the magnitude of the equilibrium constant. If the equilibrium constant is far greater than 1 (K ≫ 1), then at equilibrium the reaction system will consist of mostly products ⇒ the equilibrium lies to the right; i.e. reactions with very large K go essentially to completion. If the equilibrium constant is far less than 1 (K≪ 1), then at equilibrium the system will consist mostly of reactants, ⇒ the equilibrium position is far to the left. The given reaction does not occur to any significant extent. 99  Shifts in Gaseous Equilibria Le Chatelier’s principle states that when a reversible reaction at equilibrium is stressed by a change in concentration, temperature, or pressure, the equilibrium shifts to relieve the stress. Let’s look at the equilibrium between colorless N2O4 and brown NO2: N2O4(g) ⇋ 2 NO2(g) If we increase the amount of N2O4, the reaction shifts to the right to produce more NO2. If we increase the amount of NO2, the reaction shifts to the left to produce more N2O4. 100  Effect of Temperature The reaction is endothermic: N2O4(g) + heat ⇋ 2 NO2(g) If we lower the temperature, the reaction shifts to produce more colorless N2O4. If we raise the temperature, the reaction shifts to produce more brown NO2. 101  Effect of Pressure In a gaseous equilibrium, increasing the pressure will shift the reaction to the side with fewer gas molecules. In the reaction N2O4(g) ⇋ 2 NO2(g), increasing the pressure will shift the reaction to the left, producing more N2O4. 102  Question Charcoal reacts with steam according to the reaction C (s) + H2O (g) + heat ⇌ CO (g) + H2 (g) Predict the direction of equilibrium shift for each of the following stresses. (a) Increase [H2O] (b) Decrease [H2O] (c) Increase [CO] (d) Decrease [H2] (e) Increase temperature (f) Increase pressure (g) Add a catalyst (h) Add charcoal 103  Reaction Quotient The reaction quotient (Q) measures the relative amounts of products and reactants present during a reaction at a particular point in time When reactants and products of a given chemical reaction are mixed, it is useful to know whether the mixture is at equilibrium, and if it is not, in which direction the system will shift to reach equilibrium. If the concentration of one of the reactants or products is zero, the system will shift in the direction that produces the missing 104  Reaction Quotient However, if all the initial concentrations are non-zero, it is more difficult to determine the direction of the move toward equilibrium. In such cases, we use the reaction quotient Q to determine the shift. Q is obtained by applying the law of mass action, but using initial concentrations instead of equilibrium concentrations. The Q value can be compared to the Equilibrium Constant, K to determine the direction of the reaction that is taking place. To determine Q, the concentrations of the reactants and products 105  Reaction Quotient A comparison of Q with K indicates which way the reaction shifts and which side of the reaction is favoured: 1. If Q > K, then the reaction favours the reactants. This indicates more products are present than there would be at equilibrium. LEFT SHIFT 2. Q < K, then the reaction favours the products – more reactants than there would be at equilibrium. RIGHT SHIFT 3. Q = K, then the reaction is already at equilibrium. 106  Solving Equilibrium Problem The following steps are taken when solving equilibrium problems. Write the balanced equation for the reaction. Write the equilibrium expression using the law of mass action List the initial concentrations Calculate Q and determine the direction of the shift to equilibrium Define the change needed to reach equilibrium, and define the equilibrium concentrations by applying the change to the initial concentrations Substitute the equilibrium concentrations into the equilibrium expression, and solve for the unknown Check your calculated equilibrium concentrations by making sure they give the correct value. 107  Solving Equilibrium Problem What is the Q value for this reaction? Which direction will the reaction shift? CO(g) + H2O(g) = CO2(g) + H2(g) Kc = 1.0 [CO2(g)] = 2.0 M [H2(g)] = 2.0 M [CO(g)] = 1.0 M [H2O(g)] = 1.0 M 108  Ionization Equilibrium Constant, Ki The equilibrium constant for the ionization of a weak acid or base is the ionization equilibrium constant, Ki. What is Ki constant for the ionization of hydrofluoric acid? HF(aq) ⇋ H+(aq) + F– (aq) [H+][F-] Ki = [HF] 109  Ionization of a Weak Base We can also write a Ki expression for the ionization of ammonium hydroxide: NH4OH(aq) ⇋ NH 4+(aq) + OH– (aq) [NH +][OH-] 4 Ki = [NH4OH] 110  Experimental Determination of Ki We can calculate the numerical value of Ki if we know the concentrations of all the species in the reaction. HC2H3O2(aq) ⇋ H+(aq) + C2H3O2– (aq) If the concentrations at equilibrium are [HC2H3O2] = 0.100 M, [H+] = 0.00134 M, and [C2H3O2–] = 0.00134 M, what is Ki? [H+][C2H3O –] (0.00134)(0.00134) 2 -5 Ki = = = 1.80 × 10 [HC2H3O2] (0.100) 111  Solubility Product Equilibria Insoluble salts are really very slightly soluble. If we add Ag2SO4 to water, some of the slightly soluble Ag2SO4 dissolves: Ag2SO4(s) ⇋ 2 Ag+(aq) + SO 42-(aq) We can write the solubility product equilibrium constant, Ksp, for the reaction: Ksp = [Ag+]2 [SO42-] Recall, we don’t include pure solids or liquids in equilibrium constant expressions. 112  Solubility Equilibria Shifts Let’s look at the following solubility equilibrium: AgCl(s) ⇋ Ag+(aq) + Cl-(aq) Ksp = [Ag+][Cl-] What happens if we add more AgCl? Nothing, since AgCl does not appear in Ksp. What happens if we add some soluble NaCl? We increase [Cl-], and the equilibrium shifts to the left producing more solid AgCl. 113  Ionic Product and Precipitation We use the concept of ionic product to decide whether we will obtain a precipitate (of a sparingly soluble salt) when two solutions of quite soluble salts are mixed. Three possibilities may arise under such conditions, viz., Q = KSP: ⇒ Saturated solution, we have an equilibrium situation. Q > KSP: ⇒ Supersaturated solution, we obtain a precipitation Q < KSP: ⇒ Unsaturated solution, we obtain no precipitation. 114  Solubility Product and pH of Solution The pH of a solution can affect a salt’s solubility quite significantly. For example, magnesium hydroxide dissolves according to the equilibrium Mg(OH)2 (s) ⇌ Mg2+ (aq) + 2OH- (aq) Addition of OH- ions (an increase in pH) will, by the common ion effect, force the equilibrium to the left, decreasing the solubility of Mg(OH)2. On the other hand, an addition of H+ ions (a decrease in pH) increases the solubility, because OH- ions are removed from solution by reacting with the added H+ ions. 115  TUTORIAL Will Barium Sulfate precipitate if 10.0 mL of 0.0020 M Na2SO4 is added to 100 mL of 3.2*10-4 M BaCl2. Take solubility product to be 1.08*10-10. [ANS: 5.2*10-8] The solubility product of Calcium Fluoride (CaF2) is 3.45*10-11. If 2.0 ml of a 0.10 M solution of NaF is added to 128 ml of a 2.0*10-5 M solution of Ca(NO3)2. Will CaF2 precipitate? [ANS: 4.7*10-11] A sample of ground water that has percolated through a layer of gypsum (CaSO4) with Ksp = 4.9*10-5 is found to have be 8.4*10-5 M in Ca2+ and 7.2*10-5 M in SO42-. What is the equilibrium state of this solution with respect to gypsum. [ANS: 6.0*10-4] 116 States of Matter 117  Properties of Gases Gases have an indefinite shape Gases can expand Gases can be compressed Gases have low densities Gases mix completely with other gases in the same container 118  Atmospheric Pressure Gas pressure is the result of gas molecules striking the inside of their container. The pressure depends on how often and how hard these molecules strike the walls of the container: If molecules collide more often, the gas pressure increases If molecules collide with more energy, the pressure increases As the temperature increases, the molecules move faster and collide more frequently and with more energy. 119  Atmospheric Pressure Italian scientist Evangelista Torricelli (1608-1647) published the first scientific explanation of vacuum. He proposed that a “sea of air” surrounds the Earth and exerts pressure on everything it contacts. Vacuum, has no gas molecules and gas pressure is zero. Atmospheric pressure is the result of air molecules in the environment. 120  Variables Affecting Gas Pressure Increase or decrease in the volume of the container. Increase or decrease in the temperature of gases. Increase or decrease in the number of molecules in the container The main variables are volume, temperature and number of molecules 121  Boyle’s law It states that at constant temperature, the volume of a fixed mass of gas is inversely proportional to the pressure. 𝟏 𝑽𝖺 𝑷 𝑷𝑽 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 122  Boyle’s law Highly accurate measurements on various gases at a constant temperature have shown that the product PV is not quite constant but changes with pressure. At pressures much higher than atmospheric pressure, the changes in PV become very significant. A gas that obeys Boyle’s law is called an ideal gas. It is commonly used to predict the new volume of a gas when the pressure is changed (at constant temperature), or vice versa 123 Boyle’s law 124  Charles’ law Charles’ law states that, at constant pressure, the volume of a gas is directly proportional to the temperature. 𝑽𝖺𝑻 𝑽 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝑻 Absolute zero has a special significance, as much evidence suggests that this temperature cannot be attained. At temperatures below this point, the extrapolated volumes, from a plot of V = b.T, would be negative. Temperatures of approximately 10-6 K have been produced in laboratories, but 0 K has never been reached. 125 Charles’ law 126  Avogardo’s Law The volume of a gas is directly proportional to its number of moles gas at constant temperature and pressure. 𝑽𝖺𝒏 𝑽=𝒂𝒏 V = volume of the gas n = number of moles a = proportionality constant 127  Ideal Gas Behaviour The ideal gas law is obtained by combining the three laws considered previously Boyle’s law: V = k / P (@ constant T and n) Charles’s law: V = b. T (@ constant P and n) Avogadro’s law: V = a. n (@ constant T and P) 𝒏. 𝑻 𝑽=𝑹 𝑷 Where R is the combined proportionality constant called the universal gas constant. When the pressure is expressed in atmospheres and the volume in liters, R has the value 0.08206 L atm mol-1 K-1. 128  Ideal Gas Behaviour The ideal gas law is an equation of state for a gas, where the state of the gas is described by its condition at a given time. A particular state of a gas is described by its pressure, volume, temperature, and number of moles. Knowledge of any three of these properties is enough to completely define the state of the gas, since the fourth property can be determined from the ideal gas law. 129  Ideal Gas Behaviour It is important to recognize that the ideal gas law is an empirical equation; based on experimental measurements of the properties of gases. Gases that obey this law are said to behave ideally. Most gases obey this law closely enough at pressures below 1 atm. 130  Ideal Gas Behaviour Example: A sample of hydrogen gas (H2) has a volume of 8.56 L at a temperature of 0 0C and a pressure of 1.5 atm. Calculate the moles of H2 present in this sample. R = 0.08206 L atm mol-1 K-1. (Ans = 0.57 mol ) 131  Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of the pressures each gas would exert if it were alone. PTOTAL = P1 + P2 + P3... The pressures P1, P2, P3... etc., are called partial pressures. 132  Dalton’s Law of Partial Pressures Assuming ideal behaviour for each gas, the partial pressure gas can be calculated from the ideal gas law: 𝒏𝟏𝑹𝑻 𝑷 = ,𝑷 𝒏𝟐𝑹𝑻 𝒏𝟑𝑹𝑻 𝟏 𝑽 𝟐 = 𝑽 , 𝑷𝟑 = 𝑽 𝑷𝑻𝑶𝑻𝑨𝑳 = 𝑷𝟏 + 𝑷𝟐 + 𝑷𝟑 𝒏𝟏𝑹𝑻 𝒏𝟐𝑹𝑻 𝒏𝟑𝑹𝑻 = + + 𝑽 𝑽 𝑽 𝑹𝑻 = 𝒏𝟏 + 𝒏𝟐 + 𝒏𝟑 𝑽 𝑹𝑻 = 𝒏𝑻𝑶𝑻𝑨𝑳 𝑽 133  Dalton’s Law of Partial Pressures Thus for a mixture of ideal gases, it is the total number of moles of particles that is important, not the identity or composition of the individual gas particles. The fact that the pressure exerted by an ideal gas is not affected by the identity (structure) of the gas particles reveals two things about ideal gases: The volume of the individual gas particles must not be important; and The forces among the particles must not be important. 134  Real Gases An ideal gas is a hypothetical concept. No gas exactly follows the ideal gas law, although many gases come very close at low pressures and/or high temperatures. 𝒂𝒏𝟐 𝑷+ 𝑽 − 𝒏𝒃 = 𝒏𝑹𝑻 𝑽𝟐 135  Intermolecular Forces Most Liquids are molecular in nature. Intermolecular forces within molecules give rise to covalent bonding which influences the shape, bond energies and chemical behaviour. In gases, interactions between molecules causes deviations from ideal behaviour. Like wise intermolecular forces influences the behaviour of liquid and solids and it defines their properties. 136 Properties of Liquids, Solids and Gases 137  Intermolecular Bonds Concept A polar molecule has positive and negative charges concentrated in different regions due to unequal sharing of electrons in bonds. This uneven distribution of electrons in a molecule is called a dipole. Intermolecular attractions result from temporary or permanent dipoles in molecules. There are three intermolecular forces: Dispersion forces Dipole forces Hydrogen bonds 138  Intermolecular Bonds Concept Dispersion forces: are the result of a temporary dipole. Electrons are constantly shifting, and a region may become temporarily electron poor and slightly positive, while another region becomes slightly negative. This creates a temporary dipole, and two molecules with temporary dipoles are attracted to each other. Dipole forces: is a result of permanent dipoles. The oppositely charged ends of polar molecules are attracted to each other; this is the dipole force. They are stronger than dispersion forces. 139  Intermolecular Bonds Concept Hydrogen bonds are a special type of dipole attraction. Hydrogen bonds are present when a molecule has an N—H, O—H, or F—H bond. Hydrogen bonds are especially important in water and living organisms. 140  Properties of Liquids Unlike gases, liquids do not respond dramatically to temperature and pressure changes. We can make five general observations about liquids: Liquids have a variable shape, but a fixed volume. Liquids take the shape of their container. Liquids usually flow readily. However, not all liquids flow at the same rate. Liquids do not compress or expand significantly. The volume of a liquid varies very little as the temperature and pressure change. 141  Properties of Liquids We can make five general observations about liquids: Liquids have a high density compared to gases. Liquids are about 1000 times more dense than gases. Liquids that are soluble mix homogeneously. Liquids diffuse more slowly than gases, but eventually form a homogeneous mixture. 142  Intermolecular Bonds Concept An intermolecular bond is an attraction between molecules, whereas an intramolecular bond is between atoms in a molecule. Some properties of liquids, such as vapor pressure, viscosity, and surface tension, are determined by the strength of attraction between molecules. Intermolecular bonds are much weaker than intramolecular bonds. 143  Properties of Liquids There are four physical properties of liquids that we can relate to the intermolecular attractions present in molecules: Vapor pressure Boiling point Viscosity Surface tension 144  Vapour Pressure At the surface of a liquid, some molecules gain enough energy to escape the intermolecular attractions of neighboring molecules and enter the vapor state. This is evaporation. The reverse process is called condensation. When the rates of evaporation and condensation are equal, the pressure exerted by the gas molecules above a liquid is called the vapor pressure. The stronger the intermolecular forces between the molecules in the liquid, the less molecules that escape into the gas phase. As the attractive force between molecules increases, vapor pressure decreases. 145  Boiling Point The normal boiling point of a substance is the temperature at which the vapor pressure is equal to the standard atmospheric pressure. The stronger the intermolecular attractions, the higher the boiling point of the liquid. A liquid with a high boiling point has a low vapor pressure. 146  Viscosity The viscosity of a liquid is a liquid’s resistance to flow. Viscosity is related to the ease with which individual molecules of a liquid move with respect to one another. Viscosity decreases with temperature due to the greater average kinetic energy available to overcome attractive intermolecular interactions. 147 Interfacial Science 148  Key Concepts and Terms Phase is a region of space throughout which all physical properties (eg colour, density, viscosity) of a material is essentially uniform. Surface or Interface is a region of infinite thickness between two homogenous bulk phases where the properties change, rather markedly, as one moves from one bulk phase to another Surface or Interfacial Energy measures the energy change associated with the work done to increase an interface by a unit area. Surface energy or interfacial energy is a basic property of the interface. 149  Surface Tension For liquids, surface free energy and surface tension can be used interchangeably because, they are fluids and the bulk and surface molecules achieve equilibrium easily when a new surface is created For liquids, the surface tension, resembles the properties of an elastic skin under tension Surface tension as a force, represented by the symbol (γ) Is defined as the force along a line of unit length, where the force is parallel to the surface but perpendicular to the line. 150  Surface Tension Thermodynamic definition of surface tension is the work done per unit area to increase the surface. This work is stored as potential energy 𝑭𝒐𝒓𝒄𝒆(𝑭) Surface Tension (γ) = 𝑨𝒓𝒆𝒂(𝑨) 151  Surface Tension Measurement Some common methods for liquids’ surface tension measurement are: Wilhelmy plate method Pendent drop method Sessile drop method 152  Surface Tension Measurement Wilhelmy Plate Method Sessile Drop Setup 153 Surface Tension Measurement Wilhelmy Plate Method 154 Contact Angle measurements – different surfaces 155  Surface Energy of Solids In solids however, the work required to form a new surface (e.g. by splitting a body into two parts) is different from the work required to stretch it because bulk and surface cannot equilibrate rapidly. This is due to the fixed positions of atoms in the solid’s lattice. There are different methods for the determination of the surface energy of solids such as: ✓ Contact angle measurement ✓ Polymer melt ✓ Inverse gas chromatography ✓ Force microscopy of surfaces ✓ Spectroscopic methods 156  Young’s Equation Derivation: Tangential force balance (mechanics); Free energy minimization (thermodynamics). γ𝐿𝑉 γ𝑆𝑉 𝞱 γ𝑆𝐿 𝜸𝑺𝑽 = 𝝲 𝑳𝑽𝒄𝒐𝒔𝞱 + 𝑦𝑺𝑳 157  Wettability Wettability is a measure of the ease at which liquids spread on solid surfaces Contact angle measurement, which measures how liquids wet solid surfaces is the simplest and least expensive method θ90°- means that wetting of the surface is unfavourable An ideal solid surface is one that is flat, rigid, perfectly smooth, chemically homogeneous, and has zero contact angle hysteresis. 158  Wettability Unlike ideal surfaces, real surfaces do not have perfect smoothness, rigidity, or chemical homogeneity Thus, the contact angle provides an inverse measure of wettability 159  Cohesion and Adhesion Wettability can also be understood as a balance between cohesion and adhesion. Cohesion is the tendency for similar molecules to attract each other, while adhesion is the degree to which dissimilar molecules attract each other. 160  Wettability Application Oil recovery (relies on capillarity) Lubrication (requires liquid to spread on surface to reduce the co-efficient of friction) Printing (NB: lubrication and printing requires adhesion) Super hydrophobic solids (like non-sticking sauce pan, etc) Flotation of minerals, reverse flotation for water treatment 161 COLLOIDS 162  Colloids A colloid, or disperse phase, is a dispersion of small particles of one material in another. In this context, ‘small’ means something less than about 500 nm in diameter (about the wavelength of visible light). In general, colloidal particles are aggregates of numerous atoms or molecules, but are too small to be seen with an ordinary optical microscope. They pass through most filter papers, but can be detected by light- scattering and sedimentation Minerals Engineering Department University of Mines and Technology 163  Colloids According to Thomas Graham (1861), colloid is a two phase heterogeneous system in which one phase is dispersed in a fine state of subdivision having diameter of 10-4 to 10-7 cm in another medium termed the continuous or dispersion medium In a colloidal solution there exist a discontinuous phase called the dispersed phase and continuous dispersion medium, and also a stabilizing agent which does not allow the dispersed phase to coalesce and settle 164  Colloids A colloidal system consist of two separate phases: a dispersed phase (or internal phase) and a continuous phase (or dispersion medium) A colloidal system may be solid, liquid or gaseous. 165  Classification of Colloids The name given to a colloid depends on the two phases involved: A sol is a dispersion of a solid in a liquid or of a solid in a solid An aerosol is a dispersion of a liquid in a gas (eg. fog and many sprays) or a solid in a gas (eg. smoke): the particles are often large enough to be seen with a microscope An emulsion is a dispersion of a liquid in a liquid (such as milk) A further classification of colloids is as lyophilic, or solvent attracting, and lyophobic, solvent repelling If the solvent is water, the terms hydrophilic and hydrophobic Minerals Engineering Department University of Mines and Technology 166  Classification based on their affinity to a Solvent Lyophilic sol Lyophobic sol Lyophilic -solvent Stable Unstable loving Viscosity is much higher than that Viscosity is same as that of the Lyophobic- solvent of the medium medium They are reversible sols They are irreversible repelling Surface tension is much lower than Surface tension is same as that of If the solvent is water, that of the medium the medium the terms hydrophilic Not visible under ultramicroscope Visible under ultramicroscope and hydrophobic Prepared by direct dissolving Prepared by indirect methods Starch gelatin, gum are lyophilic Colloidal metals, metallic sulphides colloids are lyophobic colloids Minerals Engineering Department University of Mines and Technology 167  Common Colloids System Disperse Phase Continuous Phase Product Sol Solid Liquid Ink, blood Gel Liquid Solid Jelly, Jam Emulsion Liquid Liquid Mayonnaise, milk Solid Emulsion Liquid Solid Butter, Margarine Whipped cream, Foam Gas Liquid Soap lather Cake, bread, ice Solid Foam Gas Solid cream Preparation of common colloids (Discussion) Minerals Engineering Department University of Mines and Technology 168  Properties of Colloids Brownian Motion Diffusion Osmosis Sedimentation and Creaming Light Scattering Minerals Engineering Department University of Mines and Technology 169  Colloid Stability Colloid particles are electrically charged, so they repel each other and become stable. When the charge is neutralised, the particles approach each other to form aggregates and settle down. The precipitation of colloidal solution is called coagulation or flocculation. Minerals Engineering Department University of Mines and Technology 170  Colloid Stability One of the important aspects of the study of colloidal dispersions is understanding their stability so that we can manipulate the state of dispersions for particular applications. Tendency to aggregate or in terms of their tendency to sediment under the action of gravity. Charge stabilisation is one means by which this can be achieved by changing the chemical environment using salt concentration or pH. Minerals Engineering Department University of Mines and Technology 171  Colloid Stability Stabilising colloids Adding oppositely charged Schulze-Hardy law states that, the coagulating power of an ion increases with increasing valency of the coagulating ion. Coagulating power increases in the series Na+ < Ba+2 < Al3+ or Cl-