GASES. Unit #8. AP Chemistry

Transcription

1 GASES Unit #8 AP Chemistry

2 I. Characteristics of Gases A. Gas Characteristics: 1. Fills its container a. no definite shape b. no definite vol. 2. Easily mixes w/ other gases 3. Exerts pressure on its surroundings II. Gas Pressure A. Pressure force exerted by a gas on a surface B. Standard Atmospheric Pressure and the Barometer force resulting from the mass of the air being pulled toward the center of the earth by gravity; the force resulting from the weight of the air. Sample Exercise 10.1 a) convert atm to torr b) convert 6.6 x 10-2 torr to atm. c) convert Kpa to torr. C. Manometers basic instrument for measuring pressure of gas in a container III. The Gas Laws A. Boyle s Law the volume of a given sample of constant temperature varies inversely w/ the pressure PV k Where k is a constant P vs. V plot gives a hyperbola V vs. 1/P plot gives straight line slope k Holds low pressures (more ideal ) see fig. 5.6 p. 194

3 B. Charles s Law the vol. of a give sample of constant pressure is directly proportional to the temp. in Kelvins V bt Where T is the temp. in Kelvins and b is the proportionality constant Volumes of all gases extrapolate to same temp. -273ºC 0 K absolute zero K ºC Sample Exercise 5.4: Charles s Law (p. 196) A sample of gas at 15ºC and 1 atm has a volume of 2.58 L. What volume will this gas occupy at 38ºC and 1 atm? (p. 233 #32) C. Avogadro s Law equal volumes of gases at the same temp. and press. contain the same # of particles V an Where a is a proportionality constant and n the # of moles for a gas at constant temp. and press. the volume is directly proportional to the # of moles of gas Sample Exercise 5.5: Avogadro s Law (p. 197) Suppose we have a 12.2-L sample containing 0.50 mol oxygen gas (O 2 ) at a pressure of 1 atm and a temperature of 25ºC. If all this O 2 were converted to ozone (O 3 ) at the same temperature and pressure, what would be the volume of the ozone? (p. 233 #33, 34)

4 IV. The Ideal Gas Equation A. The Ideal Gas Equation: PV nrt Where R is the universal gas constant and has a value of L atm/k mol B. Standard Temperature and Pressure (STP) Temperature 0ºC or 273 K Pressure 1 atm or kpa or 760 mmhg or 760 torr * Molar volume STP Sample Exercise 5.6: Ideal Gas Law I (p. 199) A sample of hydrogen gas (H 2 ) has a volume of 8.56 L at a temperature of 0ºC and a pressure of 1.5 atm. Calculate the moles of H 2 molecules present in this gas sample. (p. 233 #35, 37, 39) Sample Exercise 5.7: Ideal Gas Law II (p. 199) Suppose we have a sample of ammonia gas with a volume of 7.0 ml at a pressure of 1.68 atm. The gas is compressed to a volume of 2.7 ml at a constant temperature. Use the ideal gas law to calculate the final pressure. (p. 233 #41)

5 Sample Exercise 5.8: Ideal Gas Law III (p. 200) A sample of methane gas that has a volume of 3.8 L at 5ºC is heated to 86ºC at a constant pressure. Calculate its new volume. (p. 233 #43, 44) Sample Exercise 5.9: Ideal Gas Law IV (p. 201) A sample of diborane gas (B 2 H 6 ), a substance that bursts into flame when exposed to air, has a pressure of 345 torr at a temperature of -15ºC and a volume of 3.48 L. If conditions are changed so that the temperature is 36ºC and the pressure is 468 torr, what will be the volume of the sample? (p. 234 #45) Sample Exercise 5.10: Ideal Gas Law V (p. 202) A sample containing 0.35 mol argon gas at a temperature of 13ºC and a pressure of 568 torr is heated to 56ºC and a pressure of 897 torr. Calculate the change in volume that occurs. (p. 234 #47)

6 V. Molar Mass and Gas Density A. The Equation Derived: n grams of gas mass _ molar mass molar mass m _ molar mass Substitute into the ideal gas equation: nrt (m/molar mass) RT P V V mrt V(molar mass) According to the equation for density: d m, so P V drt _ molar mass Therefore, Molar mass drt P Sample Exercise 5.14: Gas Density/Molar Mass The density of a gas was measured at 1.50 atm and 27ºC and found to be 1.95 g/l. Calculate the molar mass of the gas. (p. 235 #59, 61) VI. Gas Mixtures and Partial Pressure A. Partial Pressure the pressure that a particular gas would exert if it was alone in the container B. Dalton s Law of Partial Pressure for a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it was alone. P TOTAL P 1 + P 2 + P 3 +

7 Sample Exercise 5.15: Dalton s Law I Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent the bends. For a particular dive, 46 L He at 25ºC and 1.0 atm and 12 L O 2 at 25ºC and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25ºC. (p. 235 #63, 65) C. Mole Fraction the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture. χ 1 n 1 _ n 1 _ n TOTAL n 1 + n 2 + n From the ideal gas equation we know that the number of moles of a gas is directly proportional to the pressure of the gas, since Therefore, n 1 P 1 V_, n 2 P 2 RT V_ RT n χ 1 1 _ n TOTAL P 1 _ P TOTAL Sample Exercise 5.16: Dalton s Law II The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O 2 present. (p. 235 #67)

8 Sample Exercise 5.17: Dalton s Law III The mole fraction of nitrogen in the air is Calculate the partial pressure of N 2 in air when the atmospheric pressure is 760 torr. (p. 235 #68) VII. Gas Stoichiometry A. Collecting Gas over Water a mixture of gases results whenever a gas is collected by displacement of water (water vapor is present in addition to the gas being collected) Water molecules escape from surface and collect in space above When rate of escape rate of return, pressure from H 2 O vapor remains constant vapor pressure of H 2 O Sample Exercise 5.18: Gas Collection over Water A sample of solid potassium chlorate (KClO 3 ) was heated in a test tube (see fig. 5.13) and decomposed by the following reaction: 2KClO 3 (s) 2KCl(s) + 3O 2 (g) The oxygen produced was collected by displacement of water at 22ºC at a total pressure of 754 torr. The volume of the gas collected was L, and the vapor pressure of water at 22ºC is 21 torr. Calculate the partial pressure of O 2 in the gas collected and the mass of KClO 3 in the sample that was decomposed. (p. 235 #69, 71)

9 VIII. Kinetic Molecular Theory A. The Model attempts to explain the properties of an ideal gas by describing the particles: 1. The particles are so small compared w/ the distances between them that the volume of the individual particles can be assumed to be negligible (zero). See Figure The particles are in constant motion. The collisions of the particles w/ the walls of the container are the cause of the pressure exerted by the gas. 3. The particles are assumed to exert no force on each other; they are assumed neither to attract nor repel one another. 4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. B. Root- mean Square Velocity (see p for derivation): C. KMT application to the Gas Laws P & V (Boyle s Law) P (nrt) 1/V (constant) P & T (Lussac s Law) P (nr/v) T (constant) V & n (Avogadro s Law) V (RT/P) n (constant) Mixture of gases (Dalton s Law) KMT assumes that all gas particles are independent of each other V & T (Charles s Law) V (nr/p) T (constant)

10 IX. Molecular Effusion and Diffusion A. Effusion the passage of a gas through a tiny orifice into an evacuated chamber B. Gram s Law of Effusion the relative rates of effusion of two gases at the same temperature and pressure are given by the inverse ratio of the square roots of the masses of the gas particles: Rate of effusion for gas 1 Rate of effusion for gas 2 M 2 M 1 C. Diffusion (see p ) Sample Exercise 5.20: Effusion Rates Calculate the ratio of the effusion rates of hydrogen gas (H 2 ) and uranium hexafluoride (UF 6 ), a gas used in the enrichment process to produce fuel for nuclear reactors (see Fig. 5.23). X. Deviations from Ideal Behavior A. The Van der Waals Equation

11 B. Sample Exercise If mol of an ideal gas were confined to 22.4 L at 0.0 C, it would exert a pressure of atm. Use the Van der Waals equation and the constants in Table 10.3 to estimate the pressure exerted by mol of Cl 2 (g) in 22.4 L at 0.0 C