5–15–1 Chapter 5: GASES

5–25–2 Figure 5.1a: The pressure exerted by the gases in the atmosphere can be demonstrated by boiling water in a large metal can (a) and then turning off the heat and sealing the can.

5–35–3 Figure 5.01b: As the can cools, the water vapor condenses, lowering the gas pressure inside the can. This causes the can to crumple (b). (cont’d)

5–45–4 A Gas 4 Uniformly fills any container. 4 Mixes completely with any other gas 4 Exerts pressure on its surroundings.

5–55–5 Figure 5.2: A torricellian barometer. The tube, completely filled with mercury, is inverted in a dish of mercury.

5–65–6 Figure 5.3: A simple manometer.

5–75–7 Pressure 4 is equal to force/unit area 4 SI units = Newton/meter 2 = 1 Pascal (Pa) 4 1 standard atmosphere = 101,325 Pa 4 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr mm Hg = torr

5–85–8 Figure 5.4: A J-tube similar to the one used by Boyle.

5–95–9 VxP=kVxP=k

5–10 Figure 5.5: Plotting Boyle's data from Table 5.1. (a) A plot of P versus V shows that the volume doubles as the pressure is halved. (b) A plot of V versus 1/P gives a straight line. The slope of this line equals the value of the constant k.

5–11 Figure 5.6: A plot of PV versus P for several gases at pressures below 1 atm.

5–12 Boyle ’ s Law * Pressure  Volume = Constant (T = constant) P 1 V 1 = P 2 V 2 (T = constant) V  1/P (T = constant) ( * Holds precisely only at very low pressures.) A gas that strictly obeys Boyle ’ s Law is called an ideal gas.

5–13 Ex. 5.2 As pressure increases, the volume of SO 2 decreases.

5–14 Ex. 5.3 Figure 5.7: A plot of PV versus P for 1 mol of ammonia. The dashed line shows the extrapolation of the data to zero pressure to give the "ideal" value of PV of L atm.

5–15 Figure 5.8: Plots of V versus T (ºC) for several gases.

5–16 Figure 5.9: Plots of V versus T as in Fig. 5.8 except here the Kelvin scale is used for temperature.

5–17 Charles ’ s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. V = bT (P = constant) b = a proportionality constant

5–18 Charles ’ s Law

5–19 Avogadro ’ s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas

5–20 Figure 5.10: These balloons each hold 1.0L of gas at 25ºC and 1 atm. Each balloon contains mol of gas, or 2.5 x molecules.

5–21 Ideal Gas Law We can bring all of these laws together into one comprehensive law: Boyle ’ s law: V = k/P (at const T and n) Charle ’ s law:V = bT(at const P and n) Avogardro ’ s law: V = an(at const T and P) ⇒ V = or PV = nRT

5–22 Ideal Gas Law PV = nRT R = proportionality constant = L atm   mol  P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins

5–23 As pressure increases, the volume decreases.

5–24 Gas stoichiometry V = = L (molar volume) Standard Temperature and Pressure “STP” P = 1 atmosphere T =  C The molar volume of an ideal gas is liters at STP

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5–26 Molar Mass of a Gas n = = = m/V = d Or

5–27 Dalton ’ s Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P P Total = n total (RT/V)

5–28 Figure 5.12: The partial pressure of each gas in a mixture of gases in a container depends on the number of moles of that gas.

5–29 Kinetic Molecular Theory 1.Volume of individual particles is  zero. 2.Collisions of particles with container walls cause pressure exerted by gas. 3.Particles exert no forces on each other. 4.Average kinetic energy  Kelvin temperature of a gas.

5–30 Figure 5.14: (a) One mole of N 2 (l) has a volume of approximately 35 mL and density of 0.81 g/mL. B) One mole of N 2 (g) has a volume of 22.4 L (STP) and a density of 1.2 x g/mL. Thus the ratio of the volumes of gaseous N 2 and liquid N 2 is 22.4/0.035 = 640 and the spacing of the molecules is 9 times farther apart in N 2 (g).

5–31 Figure 5.15: The effects of decreasing the volume of a sample of gas at constant temperature.

5–32 Figure 5.16: The effects of increasing the temperature of a sample of gas at constant volume.

5–33 Figure 5.17: The effects of increasing the temperature of a sample of gas at constant pressure.

5–34 Figure 5.18: The effects of increasing the number of moles of gas particles at constant temperature and pressure.

5–35 P is the pressure of the gas, n is the number of molecules of the gas, N A is the Avogadero’s number, m is the mass of each particles, is the average of the square of the velocities of the particles, and V is the volume of the gas. or

5–36 ∵ (KE) avg  T or Fromexperiment,

5–37 The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

5–38 Room mean square velocity : average of the squares of the particles velocity Room mean square velocity  rms = and (KE) avg = (2/3)RT R = L.atm.K -1.mol -1 = l K -1.mol -1

5–39 Figure 5.19: Path of one particle in a gas. Any given particle will continuously change its course as a result of collisions with other particles, as well as with the walls of the container. Mean free path : average distance between collisions O 2 at STP: 1 x m

5–40 Figure 5.20: A plot of the relative number of O 2 molecules that have a given velocity at STP.

5–41 Figure 5.21: A plot of the relative number of N 2 molecules that have a given velocity at three temperatures.

5–42 Effusion: describes the passage of gas into an evacuated chamber. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

5–43 Figure 5.22: The effusion of a gas into an evacuated chamber.

5–44 Effusion:

5–45 Figure 5.23: Relative molecular speed distribution of H 2 and UF 6.

5–46 Diffusion:

5–47 Figure 5.24: (top) When HCl(g) and NH 3 (g) meet in the tube, a white ring of NH 4 Cl(s) forms. (bottom) A demonstration of the relative diffusion rates of NH 3 and HCl molecules through air.

5–48 Figure 5.25: Plots of PV/nRT versus P for several gases (200 K).

5–49 Figure 5.26: Plots of PV/nRT versus P for nitrogen gas at three temperatures.

Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important). Ideal gas behavior: Low pressure and/or high temperature

5–51 Idea gas: Modification with volume P obs = (P ’ -correction factor) = P obs = P ’ -a(n/V) 2

5–52 Figure 5.27: (a) Gas at low concentration— relatively few interactions between particles. (b) Gas at high concentration—many more interactions between particles.

5–53 Figure 5.28: Illustration of pairwise interactions among gas particles.

5–54 Real Gases corrected pressure corrected volume P ideal V ideal ↑↑↑ Van der Waals equation:

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5–56 Figure 5.29: The volume taken up by the gas particles themselves is less important at (a) large container volume (low pressure) than at (b) small container volume (high pressure).

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5–58 Figure 5.30: The variation of temperature (blue) and pressure (dashed lines) with attitude. Note that the pressure steadily decreases with altitude, but the temperature increases and decreases.

5–59 Figure 5.31: Concentration (in molecules per million molecules of "air") for some smog components versus time of day.

5–60 Figure 5.33: A schematic diagram of the process for scrubbing sulfur dioxide from stack gases in power plants.