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Chapter 5 Helleur Principles of Chemistry: A Molecular Approach, 1st Ed. Nivaldo Tro Chapter 5 Gases 1 Gases Pushing • Gas molecules are constantly in motion. • As they move and strike a surface, they push on that surface. 9 push = force • If we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting. 9 pressure = force per unit area 2 Measuring Air Pressure • Use a barometer. • column of mercury • supported by air pressure force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury gravity 3 1 Chapter 5 Helleur Common Units of Pressure Average Air Pressure at Sea Level 101.325 Unit kilopascal (kPa) atmosphere (atm) 1 (exactly) millimeters of mercury (mmHg) 760 (exactly) torr (torr) 760 (exactly) pounds per square inch (psi, lbs./in2) 14.7 4 Example 5.1 A bicycle tire has a pressure of 132 psi. Convert this pressure to mmHg? Given: 132 psi Find: mmHg Conceptual Plan: psi atm mmHg Relationships: 1 atm = 14.7 psi, 1 atm = 760 mmHg Solution: 5 The Simple Gas Laws 1) Boyle’s Law • Pressure of a gas is inversely proportional to its volume. 9 constant T and amount of gas 9 graph P vs. V is curve 9 graph P vs. 1/V is straight line • As P increases, V decreases by the same factor. • P × V = constant P1 × V1 = P2 × V2 (at constant T and mol of gas) 6 2 Chapter 5 Helleur Boyle’s Experiment • added Hg to a J-tube with air trapped inside • used length of air column as a measure of volume 7 Boyle’s Law: A Molecular View Pressure is caused by the molecules striking the sides of the container. When you decrease the volume of the container with the same number of molecules in the container, more molecules will hit the wall at the same instant. This results in increasing the pressure. 8 Example 5.2 A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm? Given: V1 = 7.25 L, P1 = 4.52 atm, P2 = 1.21 atm Find: V2, L Conceptual Plan: Relationships: P1 V1, P1, P2 V2 · V1 = P2 · V2 Solution: 9 3 Chapter 5 Helleur 2) Charles’s Law • Volume is directly proportional to temperature. 9constant P and amount of gas 9graph of V vs. T is straight line • As T increases, V also increases. • Note: Kelvin T = Celsius T + 273.15 • V = constant × T 9if T measured in Kelvin T is in units of K 10 Charles Law A Problem to Consider • A sample of methane gas that has a volume of 3.8 L at 5.0°C is heated to 86.0°C at constant pressure. Calculate its new volume. using and converting temp to units of K i.e, T1(K)= 5.0 oC + 273.15 = 278.2 K V2= V1 x T2 T1 = (3.8L) (359.2K ) = 4.9 L 278.2 K Copyright © Houghton Mifflin Company. All rights reserved. Presentation of Lecture Outlines, 5–11 3) Avogadro’s Law • volume directly proportional to the number of gas molecules 9V = constant × n 9while P and T remain constant 9more gas molecules = larger volume • count number of gas molecules by moles • Equal volumes of gases contain equal numbers of molecules. 9The identity gas doesn’t matter. 12 4 Chapter 5 Helleur Clicker # 5-1 Equal volumes of propane, C3H8, and carbon monoxide at the same temperature and pressure have the same a. density. b. number of molecules. c. number of atoms. 1) a only 2) b only 3) c only 4) a and b only 5) a, b, and c Example 5.4 A 0.225-mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L? Given: V1 = 4.65 L, V2 = 6.48 L, n1 = 0.225 mol Find: n2, and added moles Conceptual Plan: V1, V2, n1 n2 Relationships: mol added = n2 – n1, Solution: 14 Standard Conditions • Since the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy. We call these standard conditions. Called STP (standard temperature and pressure) • standard pressure = 1.00 atm • standard temperature = 273.15 K (or 0.00 oC) 15 5 Chapter 5 Helleur Molar Volume at STP 9The volume of one mole of gas is called the molar gas volume, Vm. 9Volumes of gases are often compared at standard temperature and pressure (STP), chosen to be 0.00 oC and 1.00 atm pressure. At STP, the molar volume, Vm, that is, the volume occupied by one mole of any gas, is 22.4 L/mol or 6.022 × 1023 molecules of gas Molar Volume is the same for any gas 17 A Problem to Consider How many moles of gas at STP are in 39.3 L ? moles of gas = VSTP 22.4 L/mol moles of gas = 39.3 L 22.4 L/mol moles of gas = 1.75 mol Copyright © Houghton Mifflin Company. All rights reserved. Presentation of Lecture Outlines, 5–18 6 Chapter 5 Helleur Clicker # 5-2 Which of the following will have the greatest volume at STP? a. b. c. d. e. 5.0 g H2 5.0 g N2 5.0 g O2 5.0 g CO All of the above have the same volume. Practice—How many liters of O2 at STP can be made from the decomposition of 100.0 g of PbO2? 2 PbO2(s) → 2 PbO(s) + O2(g) (PbO2 = 239.2 g/mole, O2 = 32.00 g/mol) Answer: 4.68 L O2 20 4) Ideal Gas Law • • • • • By combining the gas laws we can write a general equation. R is called the gas constant. The value of R depends on the units of P and V. 9We will use 0.08206 and convert P to atm and V to L. The other gas laws are found in the ideal gas law if two variables are kept constant. This allows us to find one of the variables if we know the other three. 21 7 Chapter 5 Helleur Example 5.6 How many moles of gas are in a basketball with total pressure 24.3 psi and volume of 3.24 L at 25 °C? Given: V = 3.24 L, P = 24.3 psi, t = 25 °C Find: n, mol Conceptual P, V, T, R n Plan: Relationships: Solution: 22 Clicker # 5-3 How many moles of helium are found in a balloon that contains 5.5 L of helium at a pressure of 1.15 atm and a temperature of 22.0 ºC? a. b. c. d. e. 3.5 0.26 2.6 0.35 3.8 Density at Standard Conditions • Density of a gas is generally given in g/L. • mass of 1 mole = molar mass • volume of 1 mole at STP = 22.4 L Density at STP = Molar mass VSTP 24 8 Chapter 5 Helleur Practice—Calculate the density of N2(g) at STP. Given: Find: Conceptual Plan: N2 dN2, g/L MM d Relationships: Solution: 25 Application of the gas laws: 1) Gas Density (when not at STP) • Density is directly proportional to molar mass. 26 Example 5.7 Calculate the density of N2 at 125 °C and 755 mmHg. Given: Find: Conceptual Plan: dN2, g/L P, MM, T, R d Relationships: Solution: 27 9 Chapter 5 Helleur Clicker 5-4 Which of the following gases has the greatest density at 2.5 atm and 25°C? 1) N2O 2) F2 3) HNF2 4) C3H8 5) NF3 Application of the gas laws: 2) Molar Mass of a Gas • One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample (ms) until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law to calculate moles 29 Example 5.8 Calculate the molar mass of a gas with mass of 0.311 g that has a volume of 0.225 L at 55 °C and 886 mmHg. Given: Find: molar mass, g/mol Conceptual P, V, T, R n Plan: n, m MM Relationships: Step 2 Step 1 30 10 Chapter 5 Helleur Practice—What is the molar mass of a gas if 12.0 g occupies 197 L at 3.80 × 102 torr and 127 °C? Identify the gas from the periodic table. Answer: 4.00 g/mol 31 Our air Mixtures of Gases • When gases are mixed together, their molecules behave independently of each other. 9 All the gases in the mixture have the same volume. ¾ All completely fill the container ∴ each gas’s volume = the volume of the container. 9 All gases in the mixture are at the same temperature. ¾ Therefore, they have the same average kinetic energy. • Therefore, in certain applications, the mixture can be thought of as one gas. 9 Even though air is a mixture, we can measure the pressure, volume, and temperature of air as if it were a pure substance. 9 We can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules. 32 Partial Pressure • The pressure of a single gas in a mixture of gases is called its partial pressure. • We can calculate the partial pressure of a gas (Px) if 9 we know what mole fraction of the mixture it composes and the total pressure (Ptot) 9 or, we know the number of moles of the gas (nx) in a container of known volume and temperature • The sum of the partial pressures of all the gases in the mixture equals the total pressure. 9 Dalton’s Law of Partial Pressures 9 because the gases behave independently 33 11 Chapter 5 Helleur The partial pressure of each gas in a mixture can be calculated using the ideal gas law. Eq #1 Eq #2 34 Example 5.9 Determine the mass of Ar (mAr) in the mixture of Ar, He and Ne given: PHe = 341 mmHg, PNe = 112 mmHg, Ptot = 662 mmHg and, at a V = 1.00 L, T = 298 K Solution on next page Conceptual Plan Ptot, PHe, PNe PAr PAr, V, T nAr mAr PAr = Ptot – (PHe + PNe) Relationships: step 1 step3 step 2 Step 4 36 12 Chapter 5 Helleur Clicker 5-5 A gas phase mixture of H2 and N2 has a total pressure of 784 torr with an H2 partial pressure of 124 torr. What mass of N2 gas is present in 2.00 L of the mixture at 298 K? a. 0.0133 g b. 0.0710 g c. 0.374 g d. 0.994 g e. 1.99 g Mole Fraction The fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes. The ratio of the moles of a single Eq #3 component to the total number of moles in the mixture is called the mole fraction, χ. Eq #4 The partial pressure of a gas is equal to the mole fraction of that gas times the total pressure. 38 Example 5.10 Find the mole fractions and partial pressures in a 12.5-L tank with 24.2 g He and 4.32 g O2 at 298 K. Conceptual mgas Plan: ngas χgas, Ptotal χgas ntot, V, T, R Ptot Pgas Step 1 Step 3 Step 2 Step 4 39 13 Chapter 5 Helleur Collecting Gases over water • Gases are often collected by having them displace water from a container. • The problem is that since water evaporates, there is also water vapor in the collected gas. • The partial pressure of the water vapor, called the vapor pressure, depends only on the temperature. 9 so you can use a table to find out the partial pressure of the water vapor in the gas you collect • If you collect a gas sample with a total pressure of 758.2 mmHg* at 25 °C, the partial pressure of the water vapor will be 23.78 mmHg—so the partial pressure of the dry gas will be 734.4 mmHg. Eq #5 P =P -P 9 *Table 5.3 (next slide) gas tot water vap. 40 Clicker # 5-6 The partial pressures of CH4, N2, and O2 in a sample of gas were found to be 100., 450., and 200. mmHg, respectively. Calculate the mole fraction of nitrogen. 1) 0.133 2) 0.267 3) 0.333 4) 0.600 5) 0.733 Vapor Pressure of Water 42 14 Chapter 5 Helleur Collecting Gas by Water Displacement 43 Example 5.11 1.02 L of O2 is collected over water at 293 K with a total pressure of 755.2 mmHg. Find mass O2. Given: V = 1.02 L, P = 755.2 mmHg, T = 293 K or T= 20oC Find: mass O2, g Conceptual Ptot, PH2O Plan: PO2 PO2,V,T nO2 gO2 Step3 Step1 Solution: .3) Step 2 Step 4 O2 44 Practice—0.120 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure (in mmHg). [Need to use Table 5.3] Answer: 334 mm Hg 45 15 Chapter 5 Helleur Reactions Involving Gases • The principles of reaction stoichiometry from • Chapter 4 can be combined with the gas laws for reactions involving gases. In reactions of gases, the amount of a gas is often given as a volume. 9 instead of moles 9 As we’ve seen, you must state pressure and temperature. • The ideal gas law allows us to convert from the • volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio. When gases are at STP, use 1 mol = 22.4 L. P, V, T of Gas A mole A mole B P, V, T of Gas B 46 Example 5.12 What volume of H2 is needed to make 35.7 g of CH3OH at 0.971 atm and 355 K? CO(g) + 2 H2(g) → CH3OH(g) Given: mCH3OH = 37.5 g, P = 0.971 atm, T = 355 K Find: VH2, L Conceptual g CH3OH Plan: mol CH3OH mol H2 P, n, T, R V Step 1 Step2 H2 47 Example 5.13 How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP? O2(g) + 2 H2(g) → 2 H2O(g) Answer: 0.998 g H2O 16 Chapter 5 Helleur Properties of Gases • 1) Expand to completely fill their container • 2) Take the shape of their container • 3) Low density 9much less than solid or liquid state • 4) Compressible • 5) Mixtures of gases are always homogeneous • 6) Fluid 49 Kinetic Molecular Theory • 1) The particles of the gas (either atoms or molecules) are constantly moving. • 2) The attraction between particles is negligible. • 3) When the moving gas particles hit another gas particle or the container, but they bounce off [ elastic collision]. 9like billiard balls 50 Kinetic Molecular Theory • 4) There is a lot of empty space between the gas particles. 9compared to the size of the particles • 5) The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature. 9As you raise the temperature of the gas, the average speed of the particles increases. ¾But don’t be fooled into thinking all the gas particles are moving at the same speed!! 51 17 Chapter 5 Helleur Gas Properties Explained— Pressure • Because the gas particles are constantly moving, they strike the sides of the container with a force. • The result of many particles in a gas sample exerting forces on the surfaces around them is a constant pressure. 52 Gas Properties Explained— Compressibility Because there is a lot of unoccupied space in the structure of a gas, the gas molecules can be squeezed closer together. 53 Gas Laws Explained— Boyle’s Law • Boyle’s law states that the volume of a gas is inversely proportional to the pressure. • Decreasing the volume forces the molecules into a smaller space. • More molecules will collide with the container at any one instant, increasing the pressure. 54 18