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Chapter 4. THE PROPERTIES OF GASES

Chapter 4. THE PROPERTIES OF GASES. THE NATURE OF GASES. 4.1 Observing Gases 4.2 Pressure 4.3 Alternative Units of Pressure. THE GAS LAWS. 4.4 The Experimental Observations 4.5 Applications of the Ideal Gas Law 4.6 Gas Density 4.7 The Stoichiometry of Reacting Gases

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Chapter 4. THE PROPERTIES OF GASES

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  1. Chapter 4. THE PROPERTIES OF GASES THE NATURE OF GASES 4.1 Observing Gases 4.2 Pressure 4.3 Alternative Units of Pressure THE GAS LAWS 4.4 The Experimental Observations 4.5 Applications of the Ideal Gas Law 4.6 Gas Density 4.7 The Stoichiometry of Reacting Gases 4.8 Mixtures of Gases 2013 General Chemistry I

  2. Prelude to Chapters 4 and 5. The Three States of Matter

  3. An Overview of the Physical States of Matter The Distinction of Gases from Liquids and Solids 1. Gas volume changes greatly with pressure. 2. Gas volume changes greatly with temperature. 3. Gases have relatively low viscosity. 4. Most gases have relatively low densities under normal conditions. 5. Gases are miscible.

  4. THE NATURE OF GASES (Sections 4.1-4.3) 4.1 Observing Gases Many of physical properties of gases are very similar, regardless of the identity of the gas. Therefore, they can all be described simultaneously. Samples of gases large enough to study are examples of bulk matter – forms of matter that consist of large numbers of molecules Two major properties of gases: Compressibility – the act of reducing the volume of a sample of a gas Expansivity - the ability of a gas to fill the space available to it rapidly

  5. 4.2 Pressure – Pressure arises from the collisions of gas molecules on the walls of the container. - – SI unit of pressure is the pascal (Pa)

  6. Measurement of Pressure • Barometer – A glass tube, sealed at one end, filled with liquid mercury, and inverted into a beaker also containing liquid mercury (Torricelli) where h = the height of a column, d = density of liquid, and g = acceleration of gravity (9.80665 ms-2)

  7. Manometer This is a U-shaped tube filled with liquid and connected to an experimental system, whose pressure is being monitored. • -Two types of Hg manometer: • open-tube and (b) closed • tube system

  8. 135s 135 Example 4.3 A student attaches a glass bulb containing neon gas to an open-tube manometer and calculates the pressure of the gas to be 0.890 atm. • If the atmospheric pressure is 762 Torr, what height difference • between the two sides of the mercury in the manometer did the • student find? (b) Which side is higher, the side of the manometer attached to the bulb or the side open to the atmosphere? (c) If the student mistakenly switches the numbers for the sides of the manometer when recording the data in the laboratory notebook, what would be the reported pressure in the gas bulb?

  9. Solution to Exercise 4.3

  10. 4.3 Alternative Units of Pressure - 1 bar = 105 Pa = 100 kPa - 1 atm = 760 Torr = 1.01325×105 Pa (101.325 kPa) - 1 Torr ~ 1 mmHg Weather map mbar

  11. THE GAS LAWS (Sections 4.4-4.6) 4.4 The Experimental Observations • Boyle’s law:For a fixed amount of gas at constant temperature, volume is inversely proportional to pressure. This applies to an isothermal system (constant T) with a fixed amount of gas (constant n).

  12. - For isothermal changes between two states (1 and 2),

  13. Charles’s law:For a fixed amount of gas under constant pressure, the volume varies linearly with the temperature. This applies to an isobaric system (constant P) with a fixed amount of gas (constant n).

  14. The Kelvin Scale of Temperature If a Charles’ plot of V versus T (at constant P and n) is extrapolated to V = 0, the intercept on the T axis is ~-273 oC. - Kelvin temperature scale T = 0 K = -273.15 oC, when V → 0. - Celsius temperature scale t (oC) = T (K) - 273.15 0 oC = 273.15 K

  15. Another aspect of gas behavior (Gay-Lussac’s Law) This applies to an isochoric system (constant V) with a fixed amount of gas (constant n).

  16. Avogadro’s Principle • Under the same conditions of temperature and pressure, a given number of gas molecules occupy the same volume regardless of their chemical identity. - This defines molar volume

  17. The Ideal Gas Law This is formed by combining the laws of Boyle, Charles, Gay-Lussac and Avogadro. • The ideal gas law: Gas constant, R = PV/nT. It is sometimes called a “universal constant” and has the value 8.314 J K-1 mol-1 in SI units, although other units are often used (Table 4.2).

  18. Table 4.2. The Gas Constant, R • The ideal gas law, PV = nRT, is an equation of state that summarizes the relations describing the response of an ideal gas to changes in pressure, volume, temperature, and amount of molecules; it is an example of a limiting law. • (it is strictly valid only in some limit: here, as P 0.)

  19. 4.5 Applications of the Ideal Gas Law - For conditions 1 and 2, - Molar volume - Standard ambient temperature and pressure (SATP) 298.15 K and 1 bar, molar volume at SATP = 24.79 L·mol-1 - Standard temperature and pressure (STP) 0 oC and 1 atm (273.15 K and 1.01325 bar) - Molar volume at STP

  20. EXAMPLE 4.4 In an investigation of the properties of the coolant gas used in an air-conditioning system, a sample of volume 500 mL at 28.0 oC was found to exert a pressure of 92.0 kPa. What pressure will the sample exert when it is compressed to 30 mL and cooled to -5.0 oC?

  21. Calculating the pressure of a given sample

  22. Using the combined gas law when one variable is changed

  23. Using the combined gas law when two variables are changed

  24. 143s Example 4.25 A sample of methane gas, CH4, was slowly heated at a constant pressure of 0.90 bar. The volume of the gas was measured at a series of different Temperatures and a plot of volume vs. temperature was constructed. The slope of the line was 2.88×10-4 L K-1. What was the mass of the sample of methane? Solution

  25. 4.6 Gas Density Molar concentration of a gas is the number moles divided by the volume occupied by the gas. Molar concentration of a gas at STP (where molar volume is 22.4141 L): This value is the same for all gases, assuming ideal behavior. Density, however, does depend on the identity of the gas.

  26. Gas Density Relationships • For a given P and T, the greater the molar mass, the greater its density. • At constant T, the density increases with P. In this case, P is increased • either by adding more material or by compression (reduction of V). • Raising T allows a gas to expand at constant P, increases V and • therefore reduces its density. Density at STP

  27. 4.7 The Stoichiometry of Reacting Gases • Molar volumes of gases are generally > 1000 • times those of liquids and solids. • e.g. Vm (gases) = ~ 25 L mol-1; Vm (liquid water) • = 18 mL mol-1 • Reactions that produce gases from condensed • phases can be explosive. e.g. sodium azide (NaN3) for air bags

  28. EXAMPLE 4.6 The carbon dioxide generated by the personnel in the artificial atmosphere of submarines and spacecraft must be removed form the air and the oxygen recovered. Submarine design teams have investigated the use of potassium superoxide, KO2, as an air purifier because this compound reacts with carbon dioxide and releases oxygen: 4 KO2 (s) + 2 CO2(g) → 2 K2CO3(s) + 3 O2(g) Calculate the mass of KO2 needed to react with 50 L of CO2 at 25 oC and 1.0 atm. Vm = 24.47 Lmol-1; 1 mol CO2 -> 2 mol KO2; MKO2 = 71.10 gmol-1

  29. 148s Example 4.59 A 15.0-mL sample of ammonia gas at 1.00×102 Torr and 30 oC is mixed with 25.0 mL of hydrogen chloride gas at 1.50×102 Torr and 25 oC, and the following reaction takes place: NH3(g) + HCl(g) NH4Cl(s) (a) Calculate the mass of NH4Cl that forms.

  30. 148s

  31. 148s (b) Identify the gas in excess and determine the pressure of the excess gas at 27 oC after the reaction is complete (in the combined volume of the original two flasks).

  32. 4.8 Mixtures of Gases – A mixture of gases that do not react with one another behaves like a single pure gas. • Partial pressure: The total pressure of a mixture of gases is the sum • of the partial pressures of its components (John Dalton). P = PA + PB + … for the mixture containing A, B, … - Humid gas: P = Pdry air + Pwater vapor (Pwater vapor = 47 Torr at 37 oC) • mole fraction: the number of moles of molecules of the gas expressed as a fraction of the total number of moles of molecules in the sample.

  33. EXAMPLE 4.7 Air is a source of reactants for many chemical processes. To determine how much air is needed for these reactions, it is useful to know the partial pressures of the components. A certain sample of dry air of total mass 1.00 g consists almost entirely of 0.76 g of nitrogen and 0.24 g of oxygen. Calculate the partial pressures of these gases when the total pressure is 0.87 atm.

  34. Chapter 4. THE PROPERTIES OF GASES MOLECULAR MOTION 4.9 Diffusion and Effusion 4.10 The Kinetic Model of Gases 4.11 The Maxwell Distribution of Speeds REAL GASES 4.12 Deviations from Ideality 4.13 The Liquefaction of Gases 4.14 Equations of State of Real Gases 2012 General Chemistry I

  35. MOLECULAR MOTION (Sections 4.9-4.11) 4.9 Diffusion and Effusion • Diffusion: gradual dispersal of one substance through another substance • Effusion: escape of a gas through a small hole into a vacuum

  36. Graham’s law: At constant T, the rate of effusion of a gas is inversely proportional to the square root of its molar mass: Strictly,Graham’s law relates to effusion, but it can also be used for diffusion. For two gases A and B with molar masses MA and MB,

  37. Rate of effusion and average speed increase as the square root of the temperature: • Combined relationship: The average speed of molecules in a gas is directly proportional to the square root of the temperatureand inversely proportional to the square root of the molar mass.

  38. 152s Example 4.73 A sample of argon gas effuses through a porous plug in 147 s. Calculate the time required for the same amount of (a) CO2, (b) C2H4, (c) H2, and (d) SO2 to effuse under the same conditions of pressure and temperature.

  39. 4.10 The Kinetic Model of Gases • Kinetic molecular theory (KMT) of gases makes four assumptions: 1. A gas consists of a collection of molecules in continuous random motion. 2. Gas molecules are infinitesimally small points. 3. The molecules move in straight lines until they collide. 4. The molecules do not influence one another except during collisions. - Collision with walls: consider molecules traveling only in one dimensional x with a velocity of vx.

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