BCHEM 259 Physical Chemistry I Solutions I-1 PDF

BCHEM 259 - Physical Chemistry I Lecturer: Elliot S. Menkah, Ph.D. Teaching Assistant: Silas Ameshiku (First Class) Department of Chemistry, FoPCS, KNUST 2023/2024 Academic Year  BCHEM 259 - Physical Chemistry I - Course Content Solutions: Molecular and ionic solutions and their prope...

BCHEM 259 - Physical Chemistry I Lecturer: Elliot S. Menkah, Ph.D. Teaching Assistant: Silas Ameshiku (First Class) Department of Chemistry, FoPCS, KNUST 2023/2024 Academic Year  BCHEM 259 - Physical Chemistry I - Course Content Solutions: Molecular and ionic solutions and their properties, ideal and real solutions, colligative properties of solutions, phase equilibria Principles of solubility and complex formation, Systems of Variable Composition - Chemical Equilibrium Electrochemistry: electrochemical concepts and analytical applications. Catalysis: Homogenous and Heterogenous Catalysis. Reading Ref: 1. Physical Chemistry, 8th Edition, Peter Artkins and Julio de Paula 2. Physical Chemistry, Thomas Engel and Philip Reid  BCHEM 259 - Physical Chemistry I - Course Content Solutions: Assessment Make-Up (1.0) Molecular and ionic solutions and their properties, ideal and real solutions, Principles of solubility and complex formation, Continuous assessment - 0.3: colligative properties of solutions, phase equilibria Systems of Variable Composition - Chemical Equilibrium Tests, Exercises, Attendance - 0.1 Electrochemistry: electrochemical concepts and analytical applications. Mid-semester Exams - 0.2, Catalysis: Homogenous and Heterogenous Catalysis. End of Semester Examination: 0.7 Reading Ref: Examinations is Computer Based 1. Physical Chemistry, 8th Edition, Peter Artkins and Julio de Paula 2. Physical Chemistry, Thomas Engel and Philip Reid 3. Essentials of Physical Chemistry, Arun Bahl & Bs. Bahl 4. Physical Chemistry Essentials, Andreas Hofmann Solutions - Molecular and Ionic concepts Ionic Compounds Lattice Structures NaCl Solutions - Molecular and Ionic concepts Molecular or Covalent Compounds Molecular or Covalent Compounds Clumps of molecules Universal Solvent H2O Has ability to dissolve a lot of other molecules Solutions - Ionic Solutes in water Like dissolves like: Substances with similar polarities will easily dissolve each other. NaCl(s) Na+(aq) + Cl-(aq) When there’re more ions than water molecules, the ions re-combine and precipitation occurs Solutions - Molecular Solutes in water Some molecules contain polar covalent bonds resulting from dipoles. Will dissolve in water because of existing polarity or charge separation. Hydrogen Bond Solutions - Molecular Solutes in water Some molecules contain polar covalent bonds resulting from dipoles. Will dissolve in water because of existing polarity or charge separation. + Methanol (CH3OH) Solutions - Molecular Solutes in water Non-polar solvents will not easily dissolve in water(H2O). Absence of dipole leaves no positive or negative attractive ends + Dipoles are cancelled Solutions - Solubility Refers to the amount of solute dissolved in a solvent to form a homogeneous solution at a given temperature. Unit = mol/l, g/l , M, N Solubility is similar to Concentration 1 specific value Infinite values Solubility tell you how much u can dissolve at a Concentration tells you the amount of solute that given temperature. dissolves in the solution per the given volume and this can vary or span a number of values Solutions - Solubility - Saturated & Unsaturated Solutions lution Disso Conc < Solubility unsaturated Conc = Solubility saturated Equilibrium Conc > Solubility Supersaturated Prec ipitat ion Solutions(Non-Electrolyte Solutions) - General A solution is a mixture of two or more species; this consists of one or more minority substances, the solute(s), dispersed in a majority substance, present in greater amounts, the solvent. The term mixture can also be used more generally to describe a system with more than one substance, often under conditions that include approximately equal amounts, where no one substance can be considered the solvent. Heterogeneous solutions are solutions with non-uniform composition and properties throughout the solution; a solution of oil and water, water and chalk powder and solution of water and sand, etc. (e.g. colloids - milk) Homogeneous mixture has uniform composition and properties 12 (e.g. vinegar, salt solution) Solutions 13 Solutions- Electrolyte Solutions Eg. NaCl in H2O There are electrolyte(ionic) solutions and non-electrolyte solutions. Electrolyte solutions are solutions that have charged particles that could interact electrostatically. The electrostatic interaction is an added complication of the relatively long-range attractive and repulsive forces between ions of opposite and like charges found in ionic or electrolyte solutions. 14 Solutions- Non-Electrolyte Solutions There are electrolyte(ionic) Eg. Sugar in H2O solutions and non-electrolyte solutions. Non-Electrolyte solutions are solutions that have no charged particles and do not interact electrostatically. 15 Solutions Concentration (amount of substance in solution) is the normal variable used to define the composition, or the relative amounts of solvent and solute in a solution. The concentration of a species A can be defined as molarity (moldm-3). NB: V is total volume of solution. Other composition variables are the: Mole fraction, xA. Molality, M (molkg-1). Solutions For a system, containing multiple solutes A, B and C; Thus, sum of the partial mole fraction is unity Where there are NO obvious solvents, such systems constitutes the concepts of phases -> phases diagrams. Solutions – Chemical Potential & Gibbs Free Energy ❖ One of the most important thermodynamic variables that matters in the case, with respect to Partial molar quantities and can be calculated for, in a closed system*, is the Gibbs free energy, G. ❖ The Gibbs Free energy tells if mixing will occur. ❖ Partial molar Gibbs free energy or Chemical potential, μi , is the Gibbs free energy per mole of the species in the mixture. ❖ Molar quantity is an intensive property of an extensive property ❖ E.g. μ = dG/dn (molar free energy is the chemical potential) Solutions – Chemical Potential & Gibbs Free Energy The more chemical potential a species has, the more free energy it possesses. The more free energy they possess, the more unstable they are, the faster they move and the more pressure they possess. Higher chemical potential , higher activity and higher partial pressure. The change in chemical activity of any species can be derived under standard conditions in a mixture, however the activity relationship becomes difficult to predict in non-ideal mixtures of liquids. Assumptions of perfect gases fail for complex interactions. Solutions – Chemical Potential & Gibbs Free Energy ❖ Given a multi component system of A, B and C species, respective partial molar Gibbs free energy, G, is expressed ❖ μA = dG/dnA μB = dG/dnB The total Gibbs free energy per mole of the mixture is given by: … for all the species, i, in a given system. The chemical potential of a pure substance is generally not the same as the chemical potential of that substance in a mixture and this is due to differences in the molecular arrangement, which produce differences in the molecular interactions, in the two systems. Solutions – Chemical Potential & Gibbs Free Energy The difference in chemical potential for any species i at any temperature, T, are given by its activity; the standard chemical potential of the species, or the chemical potential when the activity is unity. … for a perfect/ideal gas where pi is the partial pressure of the gas, i, and pƟ is the standard pressure of 1 atmosphere. Solutions – Chemical Potential & Gibbs Free Energy At Equilibrium, change in Gibbs free energy for the reaction is zero; G of reactants and products are equal. For a physical transition, for example vaporization: Chemical potential of A in the gas phase and A in the liquid phase must be equal: ❖ For a transition to occur, the overall G for the reaction should be –ve ❖ The free energy can also be calculated from the individual chemical potentials as  Solutions – Vapor Pressure If a quantity of a pure liquid is placed in an evacuated container that has a volume greater than that of the liquid, a portion of the liquid will evaporate so as to fill the remaining volume of the container with vapor; Equilibrium gets established after some time. Provided that some liquid remains after the equilibrium is established, the pressure of the vapor in the container is a function only of the temperature of the system. The pressure developed is the vapor pressure of the liquid, which is a characteristic property of a liquid ; it increases rapidly with temperature. Image Ref: https://en.wikipedia.org/wiki/Vapor_pressure The temperature at which the vapor pressure is equal to 1 atm is the normal boiling point of the liquid, T Solutions – Vapor Pressure - …cont’d Some solids are sufficiently volatile to produce a measurable vapor pressure even at ordinary temperatures ; if it should happen that the vapor pressure of the solid reaches 1 atm at a temperature below the melting point of the solid, the solid sublimes. This temperature is called the normal sublimation point, Ts. The boiling point and sublimation point depend upon the pressure imposed upon the substance. Even at low temperatures a fraction of the molecules in the liquid have, energies in excess of the cohesive energy of the liquid. The result is a rapid increase in the vapor pressure with increase in temperature. The same is true of volatile solids Solutions – Vapor Pressure Clausius-Clapeyron Equation P1 = Initial vapor pressure ( atm / torr) P2 = Final vapor pressure T1 = Initial Temperature (kelvin) T2 = Final Temperature ΔHvap = Heat of vapourization (Jmol-1) R = Gas constant (8.3145 Jmol-1K-1) Solutions – Vapor Pressure Clausius-Clapeyron Equation Solutions – Vapor Pressure - Sample Question At 20 oC, the heat of vaporization, ΔHvap, of water (H2O) is 44 Jmol-1 and the corresponding vapour pressure is 2.33 kPa. What would be the vapor pressure, in kPa, of the water when the temperature rises to 40 oC ? R = 8.3145 Jmol-1K-1 Kelvin constant = 273.5 Give answer to three (3) decimal places Solutions – Vapor Pressure - Sample Question At 20 oC, the heat of vaporization, ΔHvap, of water (H2O) is 44 Jmol-1 and the corresponding vapour pressure is 2.33 kPa. What would be the vapor pressure, in kPa, of the water when the temperature rises to 40 oC ? R = 8.3145 Jmol-1K-1 Kelvin constant = 273.5 Give answer to three (3) decimal places Solutions – Vapor Pressure - Sample Question At 20 oC, the heat of vaporization, ΔHvap, of water (H2O) is 44 Jmol-1 and the corresponding vapour pressure is 2.33 kPa. What would be the vapor pressure, in kPa, of the water when the temperature rises to 40 oC ? R = 8.3145 Jmol-1K-1 Kelvin constant = 273.5 Give answer to three (3) decimal places P2 = 7360.598 Pa Solutions – Vapor Pressure The argument implies that at a specified temperature a liquid with a large cohesive energy (that is, a large molar heat of vaporization Qvap) will have a smaller vapor pressure than one with a small cohesive energy. At 20 °C the heat of vaporization of water is 44 kJ/mol, while that of carbon tetrachloride is 32 kJ/mol ; correspondingly, the vapor pressures at this temperature are 2.33 kPa for water and 12.13 kPa for carbon tetrachloride. Solutions – Ideal Solutions and Raoult’s Law An ideal solution of a mixture of two liquids, A and B, is one in which the interactions between similar pairs of molecules, A and A or B and B in a solution are similar in magnitude to those between the dissimilar molecules A and B. Benzene Toluene Raoult’s Law pi = partial vapor pressure xi = mole fraction pi* = vapor pressure of liquid Chlorobenzene and Bromobenzene species i (A or B) Chloroethane and Bromoethane N-hexane and n-heptane Solutions – Ideal Solutions and Raoult’s Law pi = partial vapor pressure Sum of vapour pressure xi = mole fraction of vapour mixture pi* = vapor pressure of liquid species i (A or B) The partial vapor pressure is directly proportional to the vapour pressure of the corresponding pure substance. The mole fraction, xi, is the proportionality constant. The mole fraction of any species in a liquid system is the equivalent variable to the partial pressure of a species in a gas. Increasing activity means increasing the mole fraction in solution (or the number of moles) Raoult’s Law is a limiting law: Real solutions obey the law as the solution becomes dilute Solutions – Ideal Solutions and Raoult’s Law Sum of vapour pressure of vapour mixture The partial vapour pressure of a liquid (in solution) is equal to the vapour pressure of the pure component multiplied by its mole fraction in solution. ▪ Since the mole fraction of compound A is always less than 1, the partial pressure is always lower than the actual pressure of the pure solvent ▪ The difference bring about an effect is called vapor pressure depression in solution. ▪ Boiling occurs when the vapour pressure equals atmospheric pressure, hence there is boiling point elevation for liquid solutions. ▪ Properties of liquids that depend on solute molecules are called colligative properties. Solutions – Ideal Solutions and Raoult’s Law(Derivation) Solution is in equilibrium with the gas phase Gas-phase composition determined by dynamic balance between evaporation from the solution and condensation from the gas phase. Rates of evaporation, Revap and condensation Rcond of the solvent from the surface of a pure liquid solvent are given by the expressions above Solutions – Ideal Solutions and Raoult’s Law(Derivation) Rates of evaporation, Revap and condensation Rcond of the solvent from the surface of a pure liquid solvent are given by the expressions: For ideal solutions, equilibrium vapor pressure is; rate of evaporation is reduced by the factor xsolvent. A = surface area of the liquid kevap and kcond = rate constants evap and cond For pure solvents, equilibrium vapor pressure is; Solutions – Ideal Solutions Chemical Potential of a Component in the Gas and Solution Phase Liquid and vapour being in equilibrium: Combing Chemical potential of the pure liquid and Raoult’s Law expression μ = chemical pot of pure component i in gas phase at standard pressure Po of 1 bar. Chemical Potential of pure liquid becomes: Gibbs energy of a mixture of gases Solutions – Ideal Solutions Chemical Potential of a Component in the Gas and Solution Phase Liquid and vapour being in equilibrium: 28.1 28.2 How is equation 28.2 related to equation 28.1? Solutions – Ideal Solutions Chemical Potential of a Component in the Gas and Solution Phase - Exercise An ideal solution is made from 5.00 mol of benzene and 0.25 mol of toluene at 25 oC: Is the mixing spontaneous? Solutions – No-Ideal Solutions - Henry’s Law It states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. Basically, it’s partial vapor pressure is directly proportional to its mole fraction. Henry’s Law KB = Henry’s Law constant. pB is still proportional to mole fraction of, xB. Solutions – No-Ideal Solutions - Henry’s Law Molar Gibbs free energy —-> Where ax = xA Adding a solute, B, decreases xA and this results in the chemical potential, μ, of an impure solvent being always less than that of a pure one. Implies that this that an impure solvent is more stable than a pure one, as it has a lower molar Gibbs free energy. By adding the solute, the tendency for a solvent to vapourize or freeze is decreased and this is the origin of colligative properties the solvent.