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CHEM 301 Physical Chemistry I

Rules of the Road. Attendance: encouraged, not mandatory Except for exams(see below)Responsible for any supplemental material covered in lecturesCell phones/pagers off during classStudents are expected to remain in class throughout periodDisabilitiesCertify through Office of Special Student ServicesHelpOffice: Room 133 Hours: Tues.

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CHEM 301 Physical Chemistry I

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    1. CHEM 301 Physical Chemistry I Dr. Robert E. Barletta rbarletta@jaguar1.usouthal.edu Phone: 460-7424 Tuesday and Thursday, 9:30 a.m. - 10::45 a.m. Room 107 Text: Physical Chemistry, 7th Edition, Peter Atkins and J. de Paula

    2. Rules of the Road Attendance: encouraged, not mandatory Except for exams(see below) Responsible for any supplemental material covered in lectures Cell phones/pagers off during class Students are expected to remain in class throughout period Disabilities Certify through Office of Special Student Services Help Office: Room 133 Hours: Tues. & Thurs. 11-noon Other - by appointment Homework: Problems assigned at the start of each chapter Due the day after the test on material To received credit for an assignment all work must be shown Exams - A non-programmable calculator only may be used 3 Hour Exams Exam : 1 After Chapter 4 covering Chapters 1, 24a, 2,3, and 4 Exam 2 After Chapter 8 covering Chapters 5-8 Exam 3 After Chapter 26 covering Chapters 9, 10, 24b, 25, and 26 1 Final comprehensive, Ch. 27 and portion to include ACS Thermodynamics test Make-up exams given only for documented excused absences Grading Homework - 5% Hour exams - 15% each Laboratory Grade - 25% Final Exam - 25%

    3. Physical Chemistry Application of physics to the study of chemistry Develops rigorous and detailed explanations of central, unifying concepts in chemistry Contains mathematical models that provide quantitative predictions. Mathematical underpinning to concepts applied in analytical, inorganic, organic, and biochemistry Includes essential concepts for studying advanced courses in chemistry Source: American Chemical Society

    4. Divisions of Physical Chemistry Main Problems Position of Chemical Equilibrium A + B <=> C + D Rate of Chemical Reactions - Kinetics Other special topics Approaches Top down (Traditional/Analytical/Historical Approach) Begin with things we observe in the world/laboratory Examine how those observables relate to the underlying structure of matter Bottom up (Synthetic/Molecular Approach) Consider the underlying structure of matter Derive observables

    5. Chapter 1: Properties of Gases Homework: Exercises (a only) : 1.4,6, 9, 11, 14, 16, 17, 18, 21 Problems: 1.1, 3, 12(a & b only), 20, 32

    6. Equations of State Gases are the simplest state of matter Completely fills any container it occupies Pure gases (single component) or mixtures of components Equation of state - equation that relates the variables defining its physical properties Equation of state for gas: p = f (T,V,n) Gases (pure) Properties - four, however, three specifies system Pressure, p, force per unit area, N/m2 = Pa (pascal) Standard pressure = př = 105 Pa = 1bar Measured by manometer (open or closed tube), p = pexternal + rgh g = gravitational acceleration = 9.81 m/s-2 Mechanical equilibrium - pressure on either side of movable wall will equalize Volume, V Amount of substance (number of moles), n Temperature, T, indicates direction of flow of energy (heat) between two bodies; change results in change of physical state of object Boundaries between objects Diathermic - heat flows between bodies. Change of state occurs when bodies of different temp. brought into contact Adiabatic - heat flows between bodies. No change of state occurs when bodies of different temp brought into contact

    7. Heat Flow and Thermal Equilibrium Thermal equilibrium - no change of state occurs when two objects are in contact through a diathermic boundary Zeroth Law of Thermodynamics - If A is in thermal equilibrium with B and B is in thermal equilibrium with C then A is in thermal equilibrium with C Justifies use of thermometer Temperature scales: Celsius scale, Q, · (°C) degree defined by ice point and B.P. of water Absolute scale, thermodynamic scale , (K not°K) T (K) = Q + 273.15

    8. Equation of State for Gases ( p = f(V,T,N) Ideal (Perfect) Gas Law Approximate equation of state for any gas Product of pressure and volume is proportional to product of amount and temperature PV = nRT R, gas constant, 8.31447 JK-1mol -1 R same for all gases, if not gas is not behaving ideally Increasingly exact as P ® 0 a limiting law For fixed n and V, as T ® 0, P ® 0 linearly Special cases (historical precident): Boyle’s Law (1661), Charles’Law [Gay-Lussac’s Law (1802-08)]; Avogodro’s principle (1811) Used to derive a range of relations in thermodynamics Practically important, e.g., at STP (T= 298.15, P = př =1bar), V/n (molar volume) = 24.789 L/mol For a fixed amount of gas (n, constant) plot of properties of gas give surface Isobar - pressure constant - line, V a T Isotherm - temperature constant, hyperbola, PV = constant Isochor - volume constant - line P a T

    9. Ideal (Perfect) Gas Law - Mixtures Dalton’s Law: Pressure exerted by a mixture of gases is sum of partial pressures of the gases Partial pressure is pressure component would exhibit if it were in a container of the same volume alone ptotal = pA + pB + pC + pD + ……. (A, B, C, D are individual gases in mixture) pJ V = nJRT This becomes : If xJ is the fraction of the molecule, J, in mixture {xJ = nJ / nTotal ), then S xJ =1 If xJ is the partial pressure of component J in the mixture, pJ = xJ p, where p is the total pressure Component J need not be ideal p = S pJ = S xJ p this is true of all gases, not just ideal gases

    10. Real Gases - General Observations Deviations from ideal gas law are particularly important at high pressures and low temperatures (rel. to condensation point of gas) Real gases differ from ideal gases in that there can be interactions between molecules in the gas state Repulsive forces important only when molecules are nearly in contact, i.e. very high pressures Gases at high pressures (spn small), gases less compressible Attractive forces operate at relatively long range (several molecular diameters) Gases at moderate pressures (spn few molecular dia.) are more compressible since attractive forces dominate At low pressures, neither repulsive or attractive forces dominate - ideal behavior

    11. Compression Factor, Z Compression factor, Z, is ratio of the actual molar volume of a gas to the molar volume of an ideal gas at the same T & P Z = Vm/ Vm°, where Vm = V/n Using ideal gas law, p Vm = RTZ The compression factor of a gas is a measure of its deviation from ideality Depends on pressure (influence of repulsive or attractive forces) z = 1, ideal behavior z < 1 attractive forces dominate, moderate pressures z > 1 repulsive forces dominate, high pressures

    12. Real Gases - Other Equations of State Virial Equation Consider carbon dioxide At high temperatures (>50°C) and high molar volumes (Vm > 0.3 L/mol), isotherm looks close to ideal Suggests that behavior of real gases can be approximated using a power series (virial) expansion in n/V (1/Vm) {Kammerlingh-Onnes, 1911} Virial expansions common in physical chemistry

    13. Virial Equation (continued) Coefficients experimentally determined (see Atkins, Table 1.3) 3rd coefficient less impt than 2nd, etc. B/Vm >> C/Vm2 For mixtures, coeff. depend on mole fractions B = x12B11 + 2 x1x2B12 + x22B22 x1x2B12 represents interaction between gases The compressibility factor, Z, is a function of p (see earlier figure) and T For ideal gas dZ/dp (slope of graph) = 0 Why? For real gas, dZ/dp can be determined using virial equation Substitute for Vm (Vm = Z Vm°); and Vm°=RT/p Slope = B’ + 2pC’+ …. As p ® 0, dZ/dP ® B’, not necessarily 0. Although eqn of state approaches ideal behavior as p ® 0, not all properties of gases do Since Z is also function of T there is a temperature at which Z ® 1 with zero slope - Boyle Temperature, TB At TB , B’ ® 0 and, since remaining terms in virial eqn are small, p Vm = RT for real gas

    14. Critical Constants Consider what happens when you compress a real gas at constant T (move to left from point A) Near A, P increases by Boyle’s Law From B to C deviate from Boyle’s Law, but p still increases At C, pressure stops increasing Liquid appears and two phases present (line CE) Gas present at any point is the vapor pressure of the liquid At E all gas has condensed and now you have liquid As you increase temperature for a real gas, the region where condensation occurs gets smaller and smaller At some temperature, Tc, only one phase exists across the entire range of compression This point corresponds to a certain temperature, Tc, pressure, Pc , and molar volume, Vc , for the system Tc, Pc , Vc are critical constants unique to gas Above critical point one phase exists (super critical fluid), much denser than typical gases

    15. Real Gases - Other Equations of State Virial equation is phenomenolgical, i.e., constants depend on the particular gas and must be determined experimentally Other equations of state based on models for real gases as well as cumulative data on gases Berthelot (1898) Better than van der Waals at pressures not much above 1 atm a is a constant van der Waals (1873) Dieterici (1899)

    16. van der Waals Equation Justification for van der Waals Equation Repulsion between molecules accounted for by assuming their impenetrable spheres Effective volume of container reduced by a number proportional to the number of molecules times a volume factor larger than the volume of one molecule Thus V becomes (V-nb) b depends on the particular gas He small, Xe large, bXe >bAr Attractive forces act to reduce the pressure Depends on both frequency and force of collisions and proportional to the square of the molar volume (n/V)2 Thus p becomes p + a (n/V)2 a depends on the particular gas He inert, CO2 less so, aCO2 >>aAr

    17. van der Waals Equation - Reliability Above Tc, fit is good Below Tc, deviations

    18. van der Waal’s Loops (cont.) CO2 Critical Temperature 304.2 K (31.05°C) Below Tc, oscillations occur van der Waals loops Unrealistic suggest that increase in p can increase V Replaced with straight lines of equal areas (Maxwell construction)

    19. van der Waals Equation - Reliability

    20. van der Waals Equation Effect of T and Vm Ideal gas isotherms obtained 2nd term becomes negligible at high enough T 1st term reduces to ideal gas law at high enough Vm At or below Tc Liquids and gases co-exist Two terms come into balance in magnitude and oscillations occur 1st is repulsive term, 2nd attractive At Tc, we should have an flat inflexion point, i.e., both 1st and 2nd derivatives of equation w.r.t Vm = 0

    21. Comparing Different Gases Different gases have different values of p, V and T at their critical point You can compare them at any value by creating a reduced variable by dividing by the corresponding critical value preduced = pr = p / pc; Vreduced = Vr = Vm / Vc; Treduced = Tr = T/ Tc This places all gases on the same scale and they behave in a regular fashion; gases at the same reduced volume and temperature exert the same reduced pressure. Law of Corresponding States Independent of equations of state having two variables

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