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PowerPoint to accompany Chapter 9a Gases
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Characteristics of Gases Like liquids and solids, they: Still have mass and momentum Have heat capacities & thermal conductivities Can be chemically reactive Unlike liquids and solids, they: Expand to fill their containers Are highly compressible Have extremely low densities
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
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Pressure Pressure is the amount of force applied to an area. Atmospheric pressure is the weight of air per unit of area. P = FAFA
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Units of Pressure Pascals 1 Pa = 1 N/m 2 = 1 Kg/ms 2 Bar 1 bar = 10 5 Pa = 100 kPa mm Hg or torr The difference in the heights in mm ( h ) of two connected columns of mercury Atmosphere 1.00 atm = 760 torr
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Standard Pressure Normal atmospheric pressure at sea level. This is ambient pressure, equal all around us, so not particularly felt It is equal to: 1.00 atm 760 torr (760 mm Hg) 101.325 kPa 14.696 psi
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Manometer Figure 9.2 Used to measure the difference between atmospheric pressure & that of a gas in a vessel.
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Manometer calculation: P atm = 102 kPa P gas > P atm P gas = P atm + h P gas = 102 kPa + (134.6mm – 103.8mm)Hg P gas = 102 kPa + (32.6mm Hg) Note 1mmHg = 133.322 Pa P gas = 102 kPa + (32.6x133.322x10 -3 kPa) P gas = 106 kPa = 1.06 bar =1.06/1.013 atm P gas = 1.046 atm
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
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Boyle’s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure: V ~ 1/P Figure 9.4
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia As P and V are inversely proportional A plot of V versus P results in a curve. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line. PV = k Figure 9.5
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Charles’s Law: initial warm balloon, T big, V big
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Charles’s Law: final cold balloon T & V little
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Charles’s Law The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. VTVT = k A plot of V versus T will be a straight line. Figure 9.7 V = kT
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Avogadro’s Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. Mathematically, this means: V = kn Figure 9.8
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
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Ideal-Gas Equation So far we’ve seen that: V 1/P (Boyle’s law) V T (Charles’s law) V n (Avogadro’s law) Combining these, we get, if we call the proportionality constant, R: nT P V = R i.e. PV = nRT (where R = 8.314 kPa L/mol K)
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia V = k (1/ P ) nT P V = R V P
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Ideal Gas Law Calculations Heat Gas in Cylinder from 298 K to 360 K at fixed piston position. (T incr. so P increases) Same volume, same moles but greater P P 1 = (nR/V 1 )T 1 or P 1 /T 1 = P 2 / T 2 P 2 = P 1 T 2 / T 1 P 2 = P 1 (T 2 /T 1 ) = P 1 (360/298) = 1.2081P 1
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Ideal Gas Law Calculations Move the piston to reduce the Volume from 1 dm 3 to 0.5 dm 3. (V decreases so P increases) Same moles, same T, but greater P P 1 V 1 = (nRT 1 ) = P 2 V 2 P 2 = P 1 V 1 / V 2 = P 1 (V 1 / V 2 ) P 2 = P 1 (1.0/0.5) = P 1 (2.0)
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Ideal Gas Law Calculations Inject more gas at fixed piston position & T. the n increases so P increases) Same volume, more moles but greater P P 1 = n 1 (RT 1 /V 1 ) or P 1 /n 1 = P 2 / n 2 P 2 = P 1 n 2 / n 1 for n 2 = 2 n 1 P 2 = P 1 (2)
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Ideal Gas Law Calculations R = (PV / nT) When kPa and dm 3 are used as is common R = 8.314 kPa dm 3 / mol K or J/mol K It is useful to write the ideal gas law this way so that R is the constant and other variables can change from initial to final conditions This again reduces the gas law to a simple arithmetic ratio calculation The only tricks are to ensure all units are consistent or converted as needed.
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia V = (nRT/P) = 1mol (8.314kPa dm 3 /molK)(273.15K)/100 kPa V/mol = 22.71 dm 3 = 22.71L
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Gas Densities and Molar Mass If we divide both sides of the ideal-gas equation by V and by RT, we get: nVnV P RT = Most of our gas law calculations involve proportionalities of these basic commodities.
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia
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Gas Densities and Molar Mass We know that moles molar mass = mass So multiplying both sides by the molar mass ( ) gives: n = m P RT mVmV = i.e. = P RT
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia Molecular Mass We can manipulate the density equation to enable us to find the molar mass of a gas: Becomes P RT = RT P =
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Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia End of Part 9a Ideal Gas Law
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