CP Chemistry Unit 8: Gases and phases of matter Important Vocab Pressure Gases Solids Liquids Diffusion Effusion Fluid Phase State Elastic collisions Ideal gas Real gas atmospheres Kinetic molecular theory Barometer Manometer Newton Standard temperature and pressure Pascal mm Hg Absolute zero Combined gas law Boyle’s law Charles’ law Ideal gas law Partial pressure Gas constant Compression Expansion Physical Characteristics of Gases Kinetic energy is: the energy of motion, often abbreviated as KE The Kinetic Molecular Theory (KMT) describes: the motion of particles in a substance, in particular this is used to describe the motion of gas molecules There are 5 premises of the KMT (these are important, but mostly common sense): a. Gases are made of particles, which are constantly moving in rapid, straight line motion. This means that gases apply a force to the side of a container, which in turn creates pressure. Anything that increases this force, increases pressure. b. The volume of a gas is mostly composed of empty space. This means gases: highly compressible and can be infinitely expanded c. The temperature of a gas (in Kelvin) is directly proportional to the average KE of the molecules. This means that by increasing the temperature of a gas, that the molecules will, on average, move faster AND strike the sides of a container with more force. d. The collisions between gas molecules are perfectly elastic. This means all KE is transferred between molecules and that the shape of the molecules do not change. e. Gas molecules do not interact with each other (they have no intermolecular forces) [Type text] Page 1 An ideal gas is a gas that: that perfectly follows the KMT Think: Is this actually what occurs? This means that: a. ideal gas molecules are considered to have NO volume b. ideal gas molecules are not attracted nor repelled by each other How does a real gas deviate from an ideal gas? When does this happen?: Real gases tend to occur more often at low temperatures and high pressures. Under these conditions, the gas molecules take up more of the volume of the gas themselves (they are more significant) AND they are more likely to interact with each other. Think of it this way: If you are late to class, are you going to stop and talk/interact with your friends in the hallway? What about it you have 3 minutes to still arrive at class and are already there? 8-­‐2 Force is: strength or energy as an attribute of physical action or movement.
The unit of force is the: Newton, N Area is: length times width The unit of area is the: m2 (or another version of this) Pressure is: Force/Area Units of pressure are: N/m2 OR Pascals (Pa) How are pressure and force different? Example 1: When walking vs. crawling on ice – which applies more pressure? Did your weight change? Example 2: When hitting a board with a hammer, why does a nail go through the board whereas the hammer does not? What is standard pressure? How strong is “standard pressure” Standard pressure the normal pressure at sea level in the atmosphere and is defined as 1 atm = 760 mm Hg = 101.3 kPa = 760 torr It is quite strong! – think of the can crush experiment! What crushed the can? Air pressure is created by _weight of ______ the air ____above you____________. This means that when a person climbs a mountain: [Type text] Page 2 The air pressure decreases as you climb higher. Why? The air pressure would increase when climbing down into a valley (such as Death Valley). Why? Think of air as “an ocean of air”. What happens when you dive below the water level? Air pressure is measured by a __Barometer_______. A picture of this is: A barometer works when the atmospheric pressure pushes on the mercury. The height of the mercury is equal to the air pressure. Normally, the height of the mercury would be 760 mm. (this is where the unit 760 mm Hg comes from) How does one convert between units of pressure? a. How many mm Hg is 200 atm? b. The air pressure today is 750 torr. How many kPa is this? 200 atm * 760 mm Hg = 152,000 mm Hg 750 torr * 101.3 kPa = 100. kPa 1 atm 760 torr c. Your tire pressure is 40 psi. d. A reaction occurs at 5.0 atm. How many mm Hg is How many atm is this? (14.7 psi = 1 atm) this? 40 psi * 1 atm = 2.72 atm 5.0 atm * 760 mm Hg = 3800 mm Hg 14.7 psi 1 atm 8-­‐3 [Type text] Page 3 Some properties of gases are: a. Volume V b. Temperature T c. Pressure P d. moles n How are the pressure and volume of a gas related? These are inversely related (if T and n are constant) Example: What happens when you squeeze a balloon? When balloon is inflated? What equation describes this? Boyle’s Law P1V1 = P2V2 How are the temperature and volume of a gas related? These are directly related Example: What happens to your car tires in the summer? If you buy a balloon in the winter time and leave the store, what happens to the balloon? What equation describes this? (if P and n are constant) Charle’s Law V1 = V2 T1 T2 Important to remember to: Put the temperature into Kelvin. Charles’ Law was used to discover: absolute zero This was done by: graphing volume vs. temperature for a gas The smallest volume is zero, therefore that must be the coldest possible temperature How are the pressure and temperature of a gas related? These are directly related (if V and n are constant) Example: What happens to a gas when it is released from a high pressure container? What happens to a gas when it is condensed into a high pressure environment? What equation describes this? Guy-­‐Lussac’s Law P1 = P2 T1 T2 Remember to: Put temperature into Kelvin. [Type text] Page 4 These laws are all combined into the __combined__________ gas law. The combined gas law is basically all three laws put together Example 1: When Temp is constant, it cancels out Example 2: When Volume is constant, it cancels out Examples of using the combined gas law: P1V1 = P2V2 T1 T2 P1V1 = P2V2 T1 T2 a. A sample of gas has a volume of 10.0 L at STP conditions. What will the new volume of the gas be at 300 K and a pressure of 1.20 atm? V2 = P1V1T2 = (1 atm)(10.0L)(300K) = 9.16 L P2T1 (1.2 atm)(273 K) b. Propane is stored under high pressure. A sample of propane, stored in a rigid metal container with a volume of 20.0 L, has a pressure of 12.0 atm at standard temperature. What pressure would this gas have on a hot summer day where the temperature reaches 100.0 °C? P2 = P1V1T2 = (12. atm)(20.0L)(373K) = 16.4 atm V2T1 (20.0 L)(273 K) c. Helium is transferred from a tank of gas at CVS to a balloon. The balloon is brought outside on a cold winter day where the temperature is -­‐10.0°C and the pressure is 750 mm Hg, and the balloon has a volume of 5.0 L. What volume did the balloon occupy inside the store at 25°C and standard pressure? V2 = P1V1T2 = (750 mm Hg)(5.0L)(298K) = 6.0 L P2T1 (760 mm Hg)(263 K) d. Recently, a delivery truck filled your propane tank, which is used to heat your home. The truck claims that 200.0 L of propane was delivered into your tank at a temperature of 10°C and a pressure of 3.0 atm. The cost of propane is $2.50 /L as measured at STP conditions and you received a bill of $1447. Are you being ripped off? No. V2 = P1V1T2 = (3.0 atm)(200.0L)(273K) = 579 L ; (2.50 $/L)(579 L) = 1447 L P2T1 (1.0 atm)(283 K) [Type text] Page 5 Dalton’s law of partial pressure says: The total pressure for a mixture of gases is the sum of the individual partial pressures of the gases in the mixture. This law can only be used if: The volume and temperature are constant/the same. Examples of using the law: a. A 10.0 L container has a mixture of gases, including argon (pressure = 2.0 atm), neon (pressure = 1.0 atm) and nitrogen (pressure = 3.0 atm). If each gas is separated into different containers, what is the pressure of each gas in the new containers? (temperature remains constant). New container volumes Ar = 5.0 L, Ne = 2.0 L and nitrogen = 20.0 L Ptotal = PAr + PNe + PN2 = 6.0 atm P2 Ar = P1V1 = (2.0 atm)(10.0L) = 4.0 atm P2 Ne = P1V1 = (1.0 atm)(10.0L) = 5.0 atm V2 (5.0 L) V2 (2.0 L ) P2 N2 = P1V1 = (3.0 atm)(10.0L) = 1.5 atm V2 (20.0 L) Note that the new Ptotal = PAr + PNe + PN2 = 10.5 atm b. Hydrogen gas is collected over water at 25.°C from the reaction of zinc with hydrochloric acid. The total pressure of the wet gas collected is 1.20 atm. What is the pressure of the hydrogen collected? Zn + 2HCl à ZnCl2 + H2 Vapor pressure of water at this temp = 23.8 mm Hg (internet) 23.8 mm Hg * 1atm = 0.0313 atm Ptotal = PH2O + PH2 = 1.20 atm 760 mm Hg PH2 = Ptotal – PH2O = 1.20 atm – 0.0313 atm = 1.17 atm The first quiz cover up to here in the notes. 8-­‐4 Avogadro’s law states: The volume of a gas and the number of moles of gas are directly related. IF pressure and temp are constant. Example: A sample of gas has a volume of 22.4 L at STP conditions. If the pressure of the gas and temp of the gas are constant, and the moles of gas are tripled (X3), the volume will triple (3 X 22.4L = 67.2 L) The molar volume of a gas : _22.4___ L = ___1.0___ mole. *only at STP conditions [Type text] Page 6 Example problems: 1. How many moles of oxygen are there in 135 L of oxygen at STP? 135 L * 1 mole = 6.03 moles 22.4 L 2. At STP, 3 L of chlorine gas is produced. What is the mass of the gas? 3 L * 1 mole * 70.9 g Cl2 = 9.50 = 10 g Cl2 22.4 L 1 mole 3. What is the mass of 1.33 x104 mL of nitrogen gas? 13.3 L N2 * 1 mole * 28 g = 16.6 g N2 22.4 L 1 mol 4. A chemical reaction produced 98.0 mL of sulfur dioxide gas, SO2, at STP. What was the mass in grams of the gas produced? 0.098 L SO2 * 1 mole * 64.07 g = 0.280 g SO2 22.4 L 1 mol 5. If there are 100. grams of oxygen gas at STP, what is the volume of the gas? 100. g O2 * 1 mol * 22.4 L = 70.0 L O2 32 g 1 mol 6. If there are 40. L of neon in a container at STP, what it the mass of the gas? 40. L Ne * 1 mol * 20.18 g = 36 g Ne 22.4 L 1 mol 8-­‐5 The ideal gas law is: PV = nRT R = 0.0821 Latm/mol K OR 8.31 LkPa/mol K OR 62.3 LmmHg/mol K P = pressure T = temperature n = mol V = volume How do we determine which value of R to use?: look at the units of pressure! It is important to remember that temperature must be in: Kelvin___ The ideal gas law can also be written as: PM = DRT M = molar mass D = density P = pressure R = gas constant T = temperature [Type text] Page 7 Example problems: 7. What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K? P = nRT/V = (0.500 mol)(0.0821 Latm/molK)(298 K) = 1.22 atm 10.0 L 8. A gas sample occupies 8.77 L at 20°C. What is the pressure in kPa, given that there are 1.45 moles of gas in the sample? P = nRT/V = (1.45 mol)(8.31 LkPa/molK)(293 K) = 403 kPa 8.77 L 9. A sample of gas contains 20. grams of neon gas at 250 K and a pressure of 0.857 atm. What is the volume of the gas? 20 g Ne * 1 mol = 0.99 mol V = nRT/P = (0.99 mol)(0.0821 Latm/molK)(250L) = 24 L 20.18 g 0.857 atm 10. How many grams of carbon dioxide gas are there in a 45.1 L container at 34°C and 1.04 atm? n = PV/RT = (1.04 atm)(45.1L) = 1.86 mol 1.86 mol CO2 * 44.01 g = 82 g (307 K)(0.0821 Latm/molK) 1 mol 11. A sample of methane gas (CH4) with a mass of 2.0 grams is placed in a 250. mL container at 400 K. What is the pressure exerted by the gas? 2.0 g * 1 mol = 0.125 mol P = nRT/V = (0.125 mol)(8.31 LkPa/molK)(400 K) = 1662 kPa 16 g 0.250 L 12. What is the mass in grams of nitrogen gas in a 12. L container at 45°C and 600. kPa of pressure? n = PV/RT = (600 kPa)(12 L) = 2.73 mol 2.73 mol N2 * 28.02 g = 76 g (318 K)(8.31 LkPa/molK) 1 mol 13. What is the molar mass of a gas if 0.427 g of the gas occupies a volume of 125 mL at 20.0 °C and 0.98 atm? D = 0.427 g/0.125 L = 3.42 g/L PM = DRT ; M = DRT/P = (3.42 g/L)(0.0821 Latm/molK)(293) = 83.8 g/mol 0.98 atm [Type text] Page 8 14. What is the density of a sample of ammonia gas, NH3, if the pressure is 0.928 atm and the temperature is 63.0 °C? PM = DRT ; D = PM/RT = (0.928 atm)(17.04 g/mol) = 0.526 g/L (0.0821 Latm/molK)(366 K) 15. What is the density of argon gas at a pressure of 551 mm Hg and a temperature of 25 °C? PM = DRT ; D = PM/RT = (551 mmHg)(39.95 g/mol) = 1.18 g/L (62.4 L mmHg/molK)(298 K) Gas Stoichiometry 16. How many liters of hydrogen gas are produced according to the following reaction if 20. grams of aluminum metal react? Assume STP conditions. Al + HCl à AlCl3 + H2 Balanced reaction: 2Al + 6HCl à 2AlCl3 + 3H2 20. g Al * 1mol Al * 3 mol H2 * 22.4 L = 24.9 = 25. g H2 26.96 g 2 mol Al 1 mol H2 17. How many grams of oxygen react with 40. grams of iron at 740 mm Hg and 30 deg C? Fe + O2 à Fe2O3 Balanced reaction: 4Fe + 3O2 à 2Fe2O3 40 g Fe * 1 mole Fe * 3 mol O2 * 32 g = 17.2 = 17 g oxygen 55.85 g 4 mol Fe 1 mol O2 *note that the pressure and temperature do NOT matter here as mass is being solved for. 18. Octane (C8H18) is combusted in excess air at 100°C and a pressure of 2.0 atm. How many liters of carbon dioxide would be produced? *Note that we know the LR is octane due to the word excess for oxygen 2 C8H18 + 25 O2 à 16 CO2 + 18 H2O 50.0 g octane * 1 mol octane * 16 CO2 = 3.50 mol 114.26 g 2 C8H18 PV = nRT ; V = nRT/P = (3.50 mol)(0.0821 Latm/molK)(373 K) = 53.6 L 2.0 atm [Type text] Page 9 19. Calcium hydride, CaH2, reacts with water to form hydrogen gas CaH2 (s) + H2O (l) à Ca(OH)2 (aq) + H2 (g) This reaction is sometimes used to inflate life rafts, weather balloons and the like, where a simple compact means of generating hydrogen is desired. How many grams of CaH2 are needed to generate 64.5 L of hydrogen gas if the pressure of H2 is 814 torr at 32°C? Balanced equation: CaH2 (s) + 2H2O (l) à Ca(OH)2 (aq) + H2 (g) PV = nRT ; n = PV/RT = (814 torr)(64.5 L) = 2.76 mol H2 (62.4 LmmHg/molK)(305) 2.76 mol H2 * 1 mol CaH2 * 42.10 g = 116 g CaH2 1 mol H2 1 mole CaH2 20. Ammonium sulfate, an important fertilizer, can be prepared by the reaction of ammonia with sulfuric acid: NH3(g) + H2SO4 (aq) à (NH4)2SO4 (aq) Calculate the volume of NH3(g) needed at 42°C and 15.6 atm to react with 87 kg of sulfuric acid. Balanced equation: 2NH3(g) + H2SO4 (aq) à (NH4)2SO4 (aq) 87,000 g H2SO4 * 1 mol H2SO4 * 2 mol NH3 = 1774 mol NH3 98.09 g 1 mol H2SO4 PV = nRT ; V = nRT/P = (1774 mol)(0.0821 Latm/molK)(315) = 2941 = 2900 L NH3 15.6 atm 8-­‐6 Diffusion is: the spreading out of a gas from an area of higher concentration to an area of lower concentration. Example: when a person uses perfume/cologne, the odor travels away from the source (although this seems to occur slowly) Effusion is: the diffusion of a gas through a small opening Example: Why do helium balloons eventually sink? Where did the helium go? 1/2
Graham’s Law of Diffusion is: (V1/V2) = (M2/M1) *Note that V here is velocity, and not volume. It basically means: That at the same conditions of temp and pressure, that heavier gases will travel more slowly than lighter gases [Type text] Page 10 A simple example is: At the same temperature and pressure, hydrogen (molar mass of 2.02 g/mol) will travel faster than helium (molar mass of 4.0 g/mol) The real question is: will hydrogen travel TWICE as fast as He, since hydrogen is half the mass? Examples of using this equation: a. How much faster does nitrogen diffuse than oxygen gas at the same temperature? 1/2 V1 = (32/28) = 1.07 ; nitrogen will travel 1.07 times faster than oxygen V2 b. Which gas diffuses faster: neon or xenon? How much faster? V1 = (131.24/20.18)
V2 1/2 = 2.55 ; neon will travel 2.55 times faster than xenon (at the same temperature) c. Estimate the molar mass of a gas that effuses at 1.6 times the rate of carbon dioxide. Since the gas is faster than carbon dioxide, it must be lighter and will be M1. 1/2
V1 = 1.6 = (M2/M1) V2 M2 = molar mass of carbon dioxide = 44.01 g/mol 2
(1.6) = M2/M1 ; M1 = 44.01 g/mol = 17.2 g/mol 2.56 Note that if you get an answer with a larger molar mass, it cannot be correct as it would be slower. d.
Estimate the molar mass of a gas that diffuses 2 times the rate of chlorine gas. Since the gas is faster than chlorine, it must be lighter and will be M1. 1/2
V1 = 2 = (M2/M1) V2 M2 = molar mass of carbon dioxide = 70.9 g/mol 2
(2) = M2/M1 ; M1 = 70.9 g/mol = 17.7 g/mol 4 [Type text] Page 11