AP Chemistry Chapter 10. Gases Chapter 10. Gases

AP ChemistryChapter 10. GasesChapter 10. GasesCommon Student Misconceptions Students need to be told to always use temperature in Kelvin in gas problems.Students should always use units in gas-law problems to keep track of required conversions.Due to several systems of units, students often use ideal gas constants with units inconsistent withvalues.Students often confuse the standard conditions for gas behavior (STP) with the standard conditions inthermodynamics.Ideal gas behavior should discussed as just that, ideal; students should be reminded that real gases donot behave ideally, especially at high pressures and/or low temperatures.Students expect a change in the gas particle distribution upon temperature changes at constant V.Students commonly confuse effusion and diffusion.Lecture Outline10.1 Characteristics of Gases All substances have three phases: solid, liquid and gas. Substances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.Properties of Gases very low density (V(g) 1000 X V(l or s)), individual molecules/atoms act almost independently ofeach otherhighly compressible and expandable: they have an indefinite volume, fill their containersfluiddiffuse through each other (small) homogeneous mixtures with each otherhave massexert pressure1 mol at STP 22.4 L(STP 0oC or 273 K; 1 atm)Gases only occupy a small fraction of the volume of their containers. As a result, each molecule of gas behaves largely as though other molecules were absent.-1-

AP Chemistry 10.2 PressureChapter 10. GasesPressure is the force acting on an object per unit area:P FAUnits: Force measured in Newtons (N) SI units of pressure pascals. 1 Pa 1 N/m2 1 N 1 kg-m/s2 related unit the bar, which 105 Pa.Pressure measured in:Pascals (1 N/m2)Torrmm HgAtmospheresStandard Pressure (sea level) 760 mm Hg 760 Torr 30 inches of Hg 1 atm 101.325 kPaAtmospheric Pressure Gravity exerts a force on the Earth’s atmosphere. A column of air 1 m2 in cross section extending to the top of the atmosphere exerts a force of 105N. Thus, the pressure of a 1 m2 column of air extending to the top of the atmosphere is 100 kPa or 1bar.Instruments for Measuring Gas PressureBarometer – instrument used to measure atmospheric pressure Invented by Evangelista Torricelli in 1643 Atmospheric pressure is measured with a barometer. If a tube is completely filled with mercury and then inverted into a container of mercury open tothe atmosphere, the mercury will rise 760 mm up the tube. Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column. Important non-SI units used to express gas pressure include: atmospheres (atm) millimeter of mercury (mm Hg) or torr 1 atm 760 mm Hg 760 torr 1.01325 x 105 Pa 101.325 kPa. Atmospheric pressure presses down on a bowl of mercury, which causes a column of mercury equalto that pressure to rise into the vacuum column, 760 mm Hg-2-

AP ChemistryChapter 10. GasesManometer – instrument used to measure gas pressureGas pressure atmospheric pressure pressure of liquid in U-tubeAsk: Is the gas pressure higher or lower than atmospheric pressure?If higher, add the pressure of the liquid.If lower, subtract the pressure of the liquid.Sample Exercise 10.1 (p. 397)a)Convert 0.357 atm to torr. (271 torr)b)Convert 6.6 x 10-2 torr to atm. (8.7 x 10-5 atm)c)Convert 147.2 kPa to torr. (1104 torr)-3-

AP ChemistryChapter 10. GasesPractice Exercise 10.1a) In countries that use the metric system, such as Canada, atmospheric pressure in weather reports ismeasured in units of kPa. Convert a pressure of 745 torr to kPa.(99.3 kPa)b) An English unit of pressure sometimes used in engineering is pounds per square inch (lb/in.2), or psi:1 atm 14.7 lb/in.2. If a pressure is reported as 91.5 psi, express the measurement in atmospheres.(6.22 atm)Sample Exercise 10.2 (p. 397)On a certain day the barometer in a laboratory indicates that the atmospheric pressure is 764.7 torr. Asample of gas is placed in a vessel attached to an open-ended mercury manometer. A meter stick is usedto measure the height of the mercury above the bottom of the manometer. The level of mercury in theopen-end arm of the manometer has a measured height of 136.4 mm, and that in the arm that is in contactwith the gas has a height of 103.8 mm.What is the pressure of the gas?a) in atmospheres? (797.3 torr)b) in kPa? (106.3 kPa)Practice Exercise 10.2Convert a pressure of 0.975atm into Pa and kPa. (9.88 x 104 Pa and 98.8 kPa)-4-

AP ChemistryChapter 10. Gases10.3 The Gas LawsTo describe a gas, you need: Volume Pressure Temperature (K) # particles “Gas Laws”The Pressure-Volume Relationship: Boyle’s LawP1V1 P2V2e.g. weather balloons: As the weather balloon ascends, the V . As the weather balloon gets further from Earth’s surface, the atmospheric P . Boyle’s law: The V of a fixed quantity of gas, at constant T, is inversely proportional to its P. Mathematically:V constant 1or PV constantP a) A plot of V versus P is a hyperbola.b) Similarly, a plot of V versus 1/P must be a straight line passing through the origin. The working of the lungs illustrates this: As we breathe in, the diaphragm moves down, & the ribs expand. Therefore, the V of the lungs . According to Boyle’s law, when the V of the lungs , the P . Therefore, the P inside the lungs atmospheric P. Atmospheric P then forces air into the lungs until the P once again equals atmospheric P. As we breathe out, the diaphragm moves up & the ribs contract. Therefore, the V of the lungs . By Boyle’s law, the P and air is forced out.-5-

AP ChemistryChapter 10. GasesAn illustration of Boyle’s experiment relating pressure and volume.In (a) the volume of the gas trapped in the J-tube is 60 mL when the gas pressure is 760 torr. When additionalmercury is added, as shown in (b), the trapped gas is compressed. The volume is 30 mL when its total pressure is1520 torr, corresponding to atmospheric pressure plus the pressure exerted by the 760-mm column of mercury.The Temperature-Volume Relationship: Charles’s Law V1 V2T1T2 Hot-air balloons expand when they are heated. Charles’s law: The V of a fixed quantity of gas at constant P is directly proportional to its absolute T. Mathematically:V constantTNote that the value of the constant depends on the P and number of moles (n) of gas.A plot of V versus T is a straight line.When T is measured in oC, the intercept on the temperature axis is –273.15oC.We define absolute zero, 0 K –273.15 oC.V constant T or The Pressure-Temperature Relationship: Gay-Lussac’s Law P1 P2T1 T2 For a fixed amount of gas (fixed number of moles) at a fixed volume, the pressure is proportional tothe temperature.P constant x T or P constantT-6-

AP ChemistryChapter 10. GasesConcept quiz:Constant TemperatureWhat happens to pressure when volume decreases?Constant PressureWhat happens to volume when temperature increases?Constant VolumeWhat happens to pressure when temperature increases?Constant Volume and TemperatureWhat happens to pressure when the # of particles is increased?Constant Temperature and PressureWhat happens to volume when the # of particles is increased?Practice Problems – Gas LawsBoyle's LawThe pressure on 2.50 L of anaesthetic gas is changed from 760 mm Hg to 304 mm Hg. What will be thenew volume if the temperature remains constant?Charles's LawIf a sample of gas occupies 6.8 L at 327oC, what will be its volume at 27oC if the pressure does notchange?Gay-Lussac's LawA gas has a pressure of 50.0 mm Hg at 540 K. What will be the temperature if the pressure is 70.0 mmHg and the volume does not change?-7-

AP ChemistryChapter 10. GasesThe Quantity-Volume Relationship: Avogadro’s Law Gay-Lussac’s law of combining volumes: At a given temperature and pressure the volumes of gasesthat react with one another are ratios of small whole numbers. Avogadro’s hypothesis: Equal volumes of gases at the same temperature and pressure contain thesame number of molecules.Gay-Lussac's experimental observation of combining volumes is shown together with Avogadro'sexplanation of this phenomenon. Avogadro’s law: The volume of gas at a given temperature and pressure is directly proportional tothe number of moles of gas. Mathematically:V constant x n We can show that 22.4 L of any gas at 0 oC and 1 atmosphere contains 6.02 x 1023 gas molecules.-8-

AP ChemistryChapter 10. GasesSample Exercise 10.3 (p. 401)Suppose we have a gas confined to a piston. Consider the following changes:a)Heat the gas from 298 K to 360 K, while maintaining the present position of the piston.b)Move the piston to reduce the volume of gas from 1L to 0.5 L.c)Inject additional gas through the gas inlet valve.Indicate how each of these changes will affect:1.the average distance between molecules2.the pressure of the gas3.the number of moles of gas present in the cylinder.Practice Exercise 10.3What happens to the density of a gas asa) the gas is heated in a constant-volume container;b) the gas is compressed at constant temperature;c) additional gas is added to a constant-volume container?-9-

AP ChemistryChapter 10. Gases10.4 The Ideal-Gas Equation Summarizing the Gas Lawso Boyle: V 1/P (constant n, T)o Charles: V T (constant n, P)o Avogadro: V n (constant P, T)o Combined: V nT/P Ideal gas equation: PV nRT An ideal gas is a hypothetical gas whose P, V, and T behavior is completely described by theideal-gas equation. R gas constant 0.08206 L atm/mol K Define STP (standard temperature and pressure) 0oC, 273.15 K, 1 atm. The molar volume of 1 mol of an ideal gas at STP is 22.4 L.PV nRTV nRT 1 mol 0.08206 L·atm/mol·K 273.15 K 22.41 LP1.000 atmComparison of molar volumes at STP.One mole of an ideal gas at STP occupies a volume of 22.41 L.One mole of various real gases at STP occupies close to this ideal volume.- 10 -

AP ChemistryChapter 10. GasesSample Exercise 10.4 (p. 403)Calcium carbonate, CaCO3(s), decomposes upon heating to give CaO(s) and CO2(g). A sample of CaCO3 isdecomposed, and the carbon dioxide is collected in a 250-mL flask. After the decomposition is complete,the gas has a pressure of 1.3 atm at a temperature of 31oC. How many moles of CO2 gas were generated?(0.013 mol CO2)Practice Exercise 10.4Tennis balls are usually filled with air or N2 gas to a pressure above atmospheric pressure to increase their“bounce”. If a particular tennis ball has a volume of 144 cm3 and contains 0.33 g of N2 gas, what is thepressure inside the ball at 24oC (in atmospheres)?(2.0 atm)Relating the Ideal-Gas Equation and the Gas Laws If PV nRT and n and T are constant, then PV is constant and we have Boyle’s law. Other laws can be generated similarly. In general, if we have a gas under two sets of conditions, thenP1V1 P2V2 n1T1 n2T2 We often have a situation in which P, V and T all change for a fixed number of moles of gas. For this set of circumstances,PV nR constantT- 11 -

AP ChemistryChapter 10. GasesSample Exercise 10.5 (p. 405)The gas pressure in an aerosol can is 1.5 atm at 25oC. Assuming that the gas inside obeys the ideal-gasequation, what would the pressure be if the can were heated to 450oC?(3.6 atm)Practice Exercise 10.5A large natural-gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold dayin December when the temperature is -15oC (4oF), the volume of gas in the tank is 3.25 x 103 m3. What isthe volume of the same quantity of gas on a warm July day when the temperature is 31oC (88oF)?(3.83 x 103 m3)Sample Exercise 10.6 (p. 406)An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend in altitude untilthe pressure is 0.45 atm. During ascent the temperature of the gas falls from 22oC to -21oC. Calculate thevolume of the balloon at its final altitude.(11 L)- 12 -