2019-05-12 CHEMISTRY a molecular approach NIVALDO J. TRO Westmount College TRAVIS D. FRIDGEN Memorial University of Newfoundland LAWTON E. SHAW Athabasca University PowerPoint Slides prepared by PHILIP J. DUTTON University of Windsor Chemistry, 2Ce SECOND CANADIAN EDITION Copyright © 2017 Pearson Canada Inc. slide 1-1 1 2019-05-12 Chapter 5 Gases 2 2019-05-12 Properties of Gases Gases - Do not have definite volumes or definite shapes - Expand to occupy the entire volume of the container - Assume shape of the container Other properties particular to gases: 1) The volume occupied by a gas changes significantly with pressure (unlike liquids and solids) 2) The volume of a gas changes with temperature. 3) Gases are miscible – easily mixed unless they chemically react with one another 4) Gases are typically less dense than liquids or solids – gas densities expressed in g/L rather than in g/mL as are liquids and solids 3 2019-05-12 Understanding Pressure (Sec. 5.1-5.2, p. 149-151) Pressure: the ratio of force (F) to surface area (A) kg·m/s2 or N kg m/s2 P = F ma = A A kg/m·s2 or N/m2 m2 Recall: F = ma Force, Area and Pressure same force, different area different force, same area 4 2019-05-12 Pressure Units (Sec. 5.2, p. 151-152) Millimeters of Mercury and Unit Conversion Dimensional Analysis and Unit Conversion Mathematically, do things the same way as always: » cm × cm = cm2 » cm + cm = cm » cm ÷ cm = 1 5 2019-05-12 The Manometer (Sec. 5.2, p. 152-153) Manometer: instrument used to measure the pressure of a gas sample in the laboratory Pgas = Patm - h Gas pressure is less than atmospheric pressure Pgas = Patm + h Gas pressure is less than atmospheric pressure 6 2019-05-12 The Gas Law’s (Sec. 5.3, p. 154-159) Four quantities required to describe a gas: 1.) amount of gas (in moles) 2.) pressure (in bar) 3.) volume (in L) 4.) temperature (in K) ** gas laws describe the relationships between pairs of these properties 7 2019-05-12 The Gas Laws (Sec. 5.3, p. 154-159) P1V1 = P2V2 Boyle’s Law V α 1/P Charles’s Law VαT V1 = V2 T1 T2 Gas Laws Avogadro’s Law Vα n V1 = V2 n1 n2 8 2019-05-12 The Ideal Gas Law (Sec. 5.4, p. 160-162) Charles’s Law VαT Boyle’s Law V α 1/P Constant T and n Constant P and n Ideal Gas Law PV = nRT Constant T and P Avogadro’s Law Vα n Ideal Gas Constant (R): = 0.08314 L·bar mol·K = 0.08314 L·bar·mol-1·K-1 9 2019-05-12 The Ideal Gas Law: Applications (Sec. 5.5, p. 162-165) Molar Volume at Standard Temperature and Pressure (STP) Standard Temperature and Pressure (STP) Standard Temperature: 273.15 K Standard Pressure: 1.00 bar Molar Volume: - the volume occupied by one mole of a substance V = nRT P L bar ) (273 K) mol K 1.00 bar (1.00 mol) (0.08314 V = V(273K) = 22.7 L V(298K) = 24.8 L (Note: conditions!!) 10 2019-05-12 The Ideal Gas Law: Applications Density of a Gas a) Under standard conditions (at STP): If, (Sec. 5.5, p. 162-165) m , V then, density = molar mass molar volume ** For gas: density α molar mass d= b) Under any conditions: Using PV = nRT , and knowing that Mm = m and rearranging to note that n = m n Mm Substituting, PV = m x RT and again knowing that d = m Mm V Then, rearranging: m = d = PMm V RT 11 2019-05-12 The Ideal Gas Law: Applications (Sec. 5.5, p. 162-165) Molar Mass of a Gas a) PV = nRT or PV = mRT Mm then rearranging Mm = mRT PV ** requires mass measurements, and typical measurements for ideal gas law b) Use previously established density equation and knowing density of gas and rearranging, then: d = PMm RT then Mm = dRT P 12 2019-05-12 Dalton’s Law: Mixtures of Gases (Sec. 5.6, p. 166-171) Partial Pressure: - pressure exerted by a particular gas in a mixture of gases Mole Fraction (χa) - the number of moles of a component in a mixture compared to the total of moles in the mixture χa = nnRT n RT ….. ; Pb = nbRT ; Pn = Pa = a Vtot V Vtot tot Pa Ptot = Pa + Pb + Pc … Ptot = (na + nb + nc+…) Ptot RT Vtot = (ntotal) RT Vtot = na ntot naRT/Vtot ntotRT/Vtot = na ntot Pa = χaPtot 13 2019-05-12 Dalton’s Law: Mixtures of Gases (Sec. 5.6, p. 166-171) Collecting Gases Over Water Zn (s) + HCl (aq) 25ºC 758.2 mmHg ZnCl2 (aq) + H2 (g) Ptotal = PH2 + PH2O 14 2019-05-12 Gases is Chemical Reactions: Stoichiometry (Sec. 5.7, p. 171-174) Gases and Balanced Chemical Equation - use given information about one gas, and stoichiometric factors of balanced chemical equation to determine desired information about another gas Molar Volume and Stoichiometry 2 H2(g) + O2(g) 2 H2O(l) If you are working at STP: 15 2019-05-12 Kinetic Molecular Theory: A Model for Gases (Sec. 5.8, p. 174-180) Kinetic Molecular Theory - theories – give underlying reasons for scientific behaviour - simplest model for behaviour of gases - gas sample modelled as collection of particles - gas particles move in constant straight-line motion - size of particles is negligibly small - particle collisions are elastic Postulates (assumptions) of the theory: 1. 2. 3. The size of each gas particle is negligibly small. The average kinetic energy of a particle is proportional to the temperature in kelvins. The collision of one particle with another (or with the walls of the container) is completely elastic. 16 2019-05-12 Kinetic Molecular Theory: A Model for Gases (Sec. 5.8, p. 174-180) - ideal gas law follows directly from kinetic molecular theory: - explanations p.175-176 Boyle’s Law at constant T: 1 V V collisions P V∝ T T collisions Pconst V Vconst P V∝ n n collisions Pconst V Vconst P collisions Pconst V P∝ Charles’s Law at constant P: Avogadro’s Law at constant T an P: Dalton’s Law (Ptot = Pa + Pb + Pc + …) at constant V and T: n 17 2019-05-12 Kinetic Molecular Theory: A Model for Gases Temperature and Molecular Velocities - all populations of gas particles at given temperature have same average kinetic energy (regardless of mass) kinetic energy of single particle (atom or molecule) of gas calculated as KE = - - (Sec. 5.8, p. 174-180) 1 2 mv2 m = mass v = velocity or speed this means, at any given moment, not all gas molecules are traveling at exactly the same velocity (ie. collisions between gas molecules may cause molecules in any sample to have range of speeds) only way for all particles to have same kinetic energy is if lighter particles travel faster (on average) than heavier ones Therefore, kinetic molecular theory says we define the root-mean square velocity as urms = u2 u2 = the average of the squares of the particle velocities 18 2019-05-12 Kinetic Molecular Theory: A Model for Gases (Sec. 5.8, p. 174-180) Temperature and Molecular Velocities - so, average kinetic energy of one mole of gas particles is now given with respect to the root-mean square velocity as where NA = Avogadro’s number now, the 2nd assumption of the kinetic molecular theory says average kinetic energy is proportional to the kelvin temperature - the constant of proportionality in this relationship is (3/2R) so - Note: R is the gas constant in units of 8.314 J mol-1 K-1 - combining these two equations and solving for u2, 19 2019-05-12 Kinetic Molecular Theory: A Model for Gases (Sec. 5.8, p. 174-180) Temperature and Molecular Velocities - Now, with m = in kg NA = Avogadro’s number so NAm = kg·mol-1, (molar mass in kg·mol-1) expressed as M, and - the root mean square velocity of a collection of gas particles is proportional to the square root of the temperature in kelvins - and is inversely proportional to the square root of the molar mass of the particles (Note: M has units of kg·mol-1) 20 2019-05-12 Kinetic Molecular Theory: A Model for Gases (Sec. 5.8, p. 174-180) - - the lower the molecular mass, the higher the root-mean square speed and the broader the distribution of speeds temperature is the same for all the gases (ie. same KEavg) Temperature and Molecular Velocities As the temperature increases for a particular gas - the root mean square velocity increases - the distributions broaden; that is, a smaller fraction of the molecules moves at any given speed - more speeds are represented by a significant fraction of the population 21 2019-05-12 Mean Free Path, Diffusion, and Effusion of Gases (Sec. 5.9, p. 180-181) Mean free path - the average distance that a molecule travels between collisions - Diffusion mean free path increases with decreasing pressure - the process by which gas molecules spread out in response to a concentration gradient (high to low concentration) despite the fact the particles undergo many collisions - heavier molecules diffuse more slowly than lighter ones 22 2019-05-12 Mean Free Path, Diffusion, and Effusion of Gases (Sec. 5.9, p. 180-181) Effusion and Graham’s Law of Effusion - the process by which a gas escapes from a container into a vacuum through a small hole - heavier molecules effuse more slowly than lighter ones - rate of effusion related to urms rate α 1 √M Graham’s Law of Effusion - ratio of effusion rates of two different gases rateA = rateB MB MA 23 2019-05-12 Real gases: The effects of Size and Intermolecular Forces (Sec. 5.7, p. 181-185) Until now, our assumptions: 1) all gases are behaving ideally - this is acceptable since under typical atmospheric pressures and temperatures, most gases do behave ideally - all gases acting nearly ideally at STP 2) the volume occupied by individual gas particles is negligible compared to the total volume occupied by the gas 3) there are no interactions between gas particles other than random elastic collisions (ie. forces between gas particles are not significant) ***these assumptions are all acceptable for most gases at STP 24 2019-05-12 Real gases: The effects of Size and Intermolecular Forces The Effect of the Finite Volume of Gas Particles Low pressure (Sec. 5.7, p. 181-185) High pressure Low Pressures - molar volume of argon is nearly identical to that of ideal gas High Pressures - molar volume of argon becomes greater than that of ideal gas Molar volume of Ideal gas and Argon at varying pressures Conclusion - finite volume of gas particles (ie. actual size) is important at higher pressure since volume of particles themselves occupies significant portion of total gas volume 25 2019-05-12 Real gases: The effects of Size and Intermolecular Forces (Sec. 5.7, p. 181-185) The Effect of the Finite Volume of Gas Particles - comparison of molar volume at various pressures of argon gas shows ideal gas law predicts a molar volume that is too small - small correction, made by Johannes van der Waals, accounts for volume of the gas particles themselves V = nRT P + nb Note: n = number of moles b = constant that depends on the gas V - nb = nRT P 26 2019-05-12 Real gases: The effects of Size and Intermolecular Forces (Sec. 5.7, p. 181-185) Intermolecular forces: - attractions between atoms or molecules that compose any substance - typically negligible in gases due to kinetic energy of molecules is great enough to overcome these forces of attraction a) High temp. affects on intermolecular forces - weak attractions between molecules, compared with relatively large kinetic energy between them, do not affect their collisions b) Lower temp. affects on intermolecular forces - collisions occur with less kinetic energy, with weak attractions affecting molecular collisions and even direction of motion Conclusion - effect of weak attractions between particles is a lower number of collisions with the surfaces thereby lowering the pressure compared to that of ideal gas 27 2019-05-12 Real gases: The effects of Size and Intermolecular Forces (Sec. 5.7, p. 181-185) Effect of Intermolecular Forces High temp. - pressure of xenon gas nearly identical to that of ideal gas Low temp. - pressure of xenon gas is less than that of ideal gas - significant interaction between xenon atoms result in few collisions with walls of container; lower pressure Pressure of 1.0 mol of Ideal gas and 1.0 mol of Xenon at varying pressures (constant volume) **graph shows that ideal gas law predicts pressure too large at low temps. - small correction, made by Johannes van der Waals, accounts for intermolecular forces between gas particles P = nRT V - a n 2 and rearranged to P + a n 2 = nRT V V V 28 2019-05-12 Real gases: The effects of Size and Intermolecular Forces (Sec. 5.7, p. 181-185) Van der Waals Equation - used to calculate properties of gas under non-ideal conditions P +a n V 2 x V - nb = nRT - describes non-ideal behaviour of gases Real Gas (or nonideal gas) - one that does not obey the assumptions that define an ideal gas 29