CHS1440 Ch 5 (F 24) PDF

Chapter 5 Gases  Chapter 5 Objectives Use the ideal gas law for calculating changes in the conditions of gases. Use the concept of partial pressure to work with mixtures of gases. Perform stoichiometric calculations for reactions involving gases as reactants or products. State the pos...

Chapter 5 Gases  Chapter 5 Objectives Use the ideal gas law for calculating changes in the conditions of gases. Use the concept of partial pressure to work with mixtures of gases. Perform stoichiometric calculations for reactions involving gases as reactants or products. State the postulates of the kinetic theory of gases (KMT). Describe qualitatively how the postulates of the kinetic theory account for the observed behavior of gases. Distinguish between the ideal gas and the real gas.  Properties of Gases Expand to fill the volume of any container. Mix with one another readily and thoroughly. Change volume dramatically with changing temperature; Have highly variable densities, depending on conditions. Have much lower densities than solids or liquids;  Properties of Gases The ideal gas law: PV = nRT pressure (P), volume (V), 𝒎𝒂𝒔𝒔 moles of gas present (n), and 𝒎𝒐𝒍𝒆𝒔 = 𝒎𝒐𝒍𝒂𝒓 𝒎𝒂𝒔𝒔 absolute temperature (T in K). R = 0.08206 L atm mol-1 K-1 (universal gas constant)  Gas Pressure Gas pressure results from molecular collisions between gas molecules and container walls. Each collision imparts a small amount of force. Summation of the forces of all collisions produces the macroscopic property of pressure. Measuring Gas Pressure The height of the Hg column is proportional to atmospheric pressure. Units of Pressure (GIVEN) 1 torr = 1 mm Hg 1 atm = 1 atm = 760 torr =  The Gas Laws Gases change significantly when the conditions in which they are found are altered. Charles’s Law: V  T 1 Boyle’s Law: V P Avogadro’s Law: V  n PV = nRT The empirical gas laws led to the ideal gas law.  Charles’s Law Jacques Charles studied relationship between V & T. Plots of V vs T for different gas samples converged to the same temperature at zero volume. Q. A gas has an initial volume of 39 mL at an unknown pressure. If the same sample occupies 514 mL at 720 torr, what was the initial pressure? Given 3 values! V1 = 39 mL; find P1 V2 = 514 mL; P2 = 720 torr Q. A gas has a volume of 3.86 L at 45 oC. What will the volume of the gas be if its temperature is raised to 87 oC. Assume constant pressure. Q. Solve for the missing term using an appropriate relationship Given 3 values! V1 = 2.0 L; T1 = 15oC Find V2; T2 = 34oC Q. How many moles of an ideal gas are there if the volume of the gas is 158 L at 14oC, at a pressure of 89 kPa? Use ideal gas law: PV = nRT, which links these 4 terms. Q. Determine the mass of 1.4 L of SO2 gas at STP (standard temp and pressure for a gas: 0oC & 1 atm). Use ideal gas law: PV = nRT, which links these 4 terms. Molar Gas Volume: PV = nRT At the same T and P, equal volumes of gases contain the same number of molecules (or moles) of gas. N2 O2 Temperature 273.15 K 273.15 K 273.15 K Pressure 1.00 atm 1.00 atm 1.00 atm Volume 22.4 L 22.4 L 22.4 L M. Mass 28.0 g 32.0 g 16.0 g # gas 6.021023 6.021023 6.021023 molecules = 1 mol Which gas will have the greatest volume at STP? 2.0 g N2 2.0 g O2 2.0 g CH4 e.g., N2(g) + 3H2(g) → 2NH3(g) 1.2 L 3.6 L ?L At a constant temperature and pressure, what volume of NH3(g) in L will be produced? Partial Pressure Air is a mixture of gases. Gas laws do not depend on identity of gases. Pressure due to total moles gas present. The pressure exerted by a component of a gas mixture is called …..  Partial Pressure PT = i Pi Dalton’s law of partial pressures: The total pressure (PT) of a mixture of gases is the sum of the partial pressures of the component gases (Pi ). In the reaction, 2 H2O2(liq) → 2 H2O(g) + O2(g) final pressures are: 0.42 atm 0.21 atm These are the partial pressures of H2O and O2. What is the total pressure in the flask? Ptotal in gas mixture = PA + PB + PC …, so, Ptotal = Partial Pressure Dalton’s law can be expressed in terms of mole fraction. Mole fraction (Xi) for a gas in a gas mixture, is the moles of the gas (ni) divided by the total moles of gas present, (ntotal). ni Pi = X i  PT Xi = Xi = Pi ntotal ni = Xi nT Ptotal The partial pressure of each gas, Pi, is related to its mole fraction (Xi). Q. A gas sample is made entirely of carbon dioxide and water, and there are 259 moles of CO2 and 513 moles of water. If the total pressure of the sample is 21 atm, what is the partial pressure of each gas? total pressure, PT = (PCO2 + PH2O) = 21 atm Stoichiometry of Reactions Involving Gases For chemical reactions involving gases, the ideal gas law (IGL) is used to determine the moles of gas involved in a reaction: C(s) + 2H2(g) → CH4(g) 2 types of questions (see below) PV = nRT: ideal gas eqn mass C → moles C → moles H2/CH4 → IGL, P/V IGL; moles, n, H2/CH4 → moles C → mass C Solve for P, or V with ideal gas law Q. The first step in processing zinc metal from its ore, ZnS, is to react it with O2 gas according to the reaction below. If 620 kg of ZnS is to be reacted, what volume of oxygen (O2) at 0.977 atm and 34.0°C is needed (at a minimum) to carry out this reaction? 2 ZnS(s) + 3 O2(g) → 2 ZnO(s) + 2 SO2(g) Solve for moles; then volume O2 (PV = nRT) Q. If a 0.050 g-sample of B4H10, burns completely in oxgen, what will be the pressure of the gaseous water in a 4.25- L flask at 30.0 oC? 2 B4H10(s) + 11 O2(g) → 4 B2O3 (s) + 10 H2O(g) Solve moles B4H10; moles H2O; PV = nRT of H2O(g) Q. One way to generate oxygen gas is to heat potassium chlorate, KClO3 (the other product is KCl). If 386 mL of oxygen at 41oC and 97.8 kPa is generated by this reaction, what is the minimum mass of KClO3 used? 2KClO3(s) ⎯⎯→ heat 2KCl(s) + 3O2(g) solve for moles of O2; solve for moles KClO3;  mass Kinetic-Molecular Theory and Ideal versus Real Gases In many important practical settings, gases do not always behave ideally, especially at very HIGH pressure and/or very LOW temperature. Nonideal gas behavior can be explained using Kinetic Molecular Theory (KMT). KMT provides connections between: observed macroscopic properties of gases; the gas law equation, and the behavior of gas molecules on a microscopic scale.  Postulates of the Model Gases are made up of large collections of particles, which are in constant, random motion. Gas particles are infinitely small and occupy negligible volume. Gas particles move in straight lines except when they collide with other particles or with the container walls. These collisions are elastic, so kinetic energy of particles is conserved. Particles interact with each other only when collisions occur.  Postulates of the Model The average kinetic energy of a gas, KEavg, is proportional to the absolute temperature of the gas, but does not depend upon the identity of the gas. 1 3 KEavg = m rms 2 KEavg = RT 2 2 As temperature increases, average speed for gas molecules increases. Faster moving molecules collide more often and with greater force, exerting a higher pressure. Postulates of the Model Graph: As T increases, average speed increases. As T increases, the fraction of molecules moving at higher speeds increases. Maxwell-Boltzmann distribution of speeds for C3H8(g)  Postulates of the Model At a fixed temperature, as the molar mass increases, the average speed for the gas molecules decreases.  Limitations of the KMT a) @ high pressure: volume of particles no longer negligible b) @ low temperature: particles move slowly enough to interact  Correcting the Ideal Gas Equation van der Waals equation is commonly used to describe the behavior of real gases.  n  2 P + a  (V − nb ) = nRT   V   a corrects for attractive forces (IMFs) @ low T. b corrects for the volume occupied by gas particles (@ high P). Q. The molecules of a real gas a) are attracted to each other. b) are liquids or solids. c) are always polar. d) always move in circles. e) have zero kinetic energy. Q. Which has the highest average velocity, and effusion and diffusion rates? a) CH4 b) N2 c) Ne d) SO3 e) Ar Q. Which gas has the greatest average kinetic energy at STP (0 oC, 1 atm)? a) He b) Ne c) Ar d) All have the same average K. E. @ STP. e) Kr Q. Which gas closely resembles the ideal gas at a lower temperature? a) He b) Ne c) Ar d) H2O e) Kr