Name: CHAPTER 14: The Behavior of Gases Period: RELATIONSHIPS BETWEEN PRESSURE, VOLUME & TEMPERATURE OF A GAS Boyle s Law-Pressure and Volume Volume (ml) Pressure ( ) 60 50 40 30 20 10 Practice problem: A gas occupies a volume of 7.5 L at 550 mmhg. What volume will it occupy at 850 mmhg? You Try: A gas occupies a volume of 7.5 L at 550 mmhg. What is the pressure of a gas that has a volume of 8.50 L? Charles s Law Volume and Temperature Temp. (K) 100 200 400 800 Volume (L) Type of relationship? DIRECT Equation P 1 = P 2 T 1 T 2 Practice problem: If a gas occupies 10.0 L at 50 C, what volume will it occupy at 150 C? Temperature MUST be in Kelvins (K = ºC + 273) You Try: If a gas occupies 33.7 L at 16 C, what temperature will it be when it occupies a volume of 67.4 L?
Gay-Lussac s Law - Pressure and Temperature Temp. (K) 100 200 400 800 Pressure (atm) Practice problem: If a gas exerts a pressure of 2.5 atm at 100 C, what pressure would it exert at 200 C? Type of relationship? DIRECT Equation V 1 = V 2 T 1 T 2 You Try: The pressure of a gas is 650mmHg at 23 C. At what temperature will its pressure drop to 425mmHg? Combined Gas Law Equation: P 1 V 1 = P 2 V 2 T 1 T 2 Practice Problem: If a gas occupies 5.0 L at 1.25 atm and 75 C, what volume will it occupy at 0.5 atm and 125 C?
GAS LAW PRACTICE PROBLEMS Before beginning, write out all four formulas in the box below: 1. A gas occupies 450mL at 23 C. Determine its volume at 75 C if the pressure remains constant. 529 ml 2. A gas in an expandable container has a pressure of 1.2atm when the volume is 10.0L. Determine its volume if the pressure is reduced to 0.85atm and the temperature remains constant. 14.1 L 3. A gas exerts a pressure of 106kPa in a sealed, rigid container at 25 C. At what temperature will it exert a pressure of 149kPa? 419 K
4. A gas exerts a pressure of 1.2atm in a 525mL container. Find the pressure of the same gas in a 2.5L container. 0.25 atm 5. The temperature of a gas sample at standard pressure is 25 C. Find its pressure if it is heated to 98 C. _1.2 atm 6. A gas occupies 240mL at 23 C and 650mmHg. It is transferred to a 375mL container at 30 C. Find the pressure in the new container. 7. A gas occupies 525mL at 30 C and 1.2 atm. What volume will it occupy at STP? 425.8mmHg 568 ml
Ideal Gas Law: Adding in the Mole moles and pressure direct proportion moles and volume direct proportion moles and temperature inverse proportion Ideal Gas Law equation: PV = nrt Determining R : Other values for R : 8.31 kpa. L 0.0821 L. atm 62.4 mhg. L mol. K mol. K mol. K Example: 1. What volume is occupied by 0.250 mol of carbon dioxide gas at 25 0 C and 371mm Hg? 12.5 L 2. Find the mass of oxygen in a 750mL container at 745mmHg and 23 C. 0.97 g O 2 3. At what temperature will 12.0g of nitrogen occupy 32.0L if the pressure is 100kPa? 895.5 K
GAS STOICHIOMETRY 1. Write the balanced equation when sodium reacts with water: 2 Na + 2 HOH 2 NaOH + H 2 How many liters of hydrogen gas will be produced if a 25.0g sample of sodium reacts with excess water at STP? 25.0g Na 1 mol Na 1 mol H 2 22.4L H 2 12.2 L 23.0 g Na 2 mol Na 1 mol H 2 What if the problem isn t at STP? How many liters of hydrogen gas will be produced at 280.0 K and 96.0 kpa if 40.0 g of sodium react with excess water? 2 Na + 2 HOH 2 NaOH + H 2 40g Na 1 mole Na 1 mole H 2 23.1 g Na 2 moles Na = 0.8658 mol PV = nrt 96kPa (V) = 0.8658 mole (8.31 kpa L/ mole K) 280K V = 21.0 L TRY: 2. Write the balanced that occurs when aluminum carbonate decomposes to form aluminum oxide and carbon dioxide. Al 2 (CO 3 ) 3 Al 2 O 3 + 3 CO 2 What volume of carbon dioxide, at 295.0 K and 880 mmhg, will be formed if 50.0g of aluminum carbonate decompose? 50g Al 2 (CO 3 ) 3 1 mole Al 2 (CO 3 ) 3 3 mole CO 2 = 0.641 mol 234g Al 2 (CO 3 ) 3 1 mole Al 2 (CO 3 ) 3 PV = nrt 880mmHg (V) = 0.641 mole (62.4mmHg L/ mole K) 295K V = 13 L
MORE GAS STOICHIOMETRY 1. Write the reaction for the combustion of acetylene, (C 2 H 2 ), the gas that is used in welding torches. 2 C 2 H 2 + 5 O 2 4 CO 2 + 2 H 2 O a. What volume of oxygen is needed to react with 100.0g of acetylene at 88 C and 1.4atm? 100.0 g C 2 H 2 1 mol C 2 H 2 4 mol O 2 = 7.69 mol O 2 26.0 g C 2 H 2 2 mol C 2 H 2 PV = nrt 1.4atm (V) = 7.69mol (0.0821 L atm/mol K) (361K) V = 162.8 L (160L) b. What mass of water will be formed if 20.7L of carbon dioxide, at 1.05atm and 25 C form? 2 C 2 H 2 + 5 O 2 4 CO 2 + 2 H 2 O 1.05atm(20.7L) = n(0.0821 L atm/mol K)(298 K) n = 0.8884mol 0.8884mol CO 2 2 mol H 2 O 18.0g H 2 O = 8.00g H 2 O 4 mol CO 2 1 mol H 2 O
DALTON S LAW AND PARTIAL PRESSURE OF GASSES H 2 N 2 H 2 CO 2 H 2 N 2 CO 2 H 2 N 2 DALTON S LAW: the total pressure of a system is equal to the sum of the pressures of all the gases in the system P T = P 1 + P 2 + P n a. The container above contains 4.0moles of hydrogen, 3.0 moles of nitrogen and 2.0 moles of carbon dioxide. The total pressure of the container is 450mmHg. Determine the partial pressure of each gas. P H 2 = 4 moles H 2 x 450 mmhg = 200 mmhg 9 moles total P N 2 = 3 moles N 2 x 450 mmhg = 150 mmhg 9 moles total P CO 2= 2 moles CO 2 x 450 mmhg = 9 moles total 100 mmhg b. The pressure of nitrogen in the classroom is approximately 0.82atm. The pressure of oxygen in the room is approximately 0.20atm and the pressure of water vapor in the room is approximately 0.02atm. a. The total pressure in the room is 1.10atm. Assuming carbon dioxide is the only other gas present, find the pressure of carbon dioxide in the room. 1.10 atm = 0.82 atm + 0.2 atm + 0.02 atm + P CO2 0.06 atm = P CO2 b. Find the number of moles of oxygen in the room if the room holds 8500 moles of air. 0.02 atm O 2 = x moles O 2 1.1 atm total 8500 moles total 154.55 atm = moles O 2
COLLECTING GASSES OVER WATER. Oxygen gas is collected by water displacement in a 250mL flask at 30ºC and a barometric pressure of 95.00kPa. The vapor pressure of water at 30ºC is 31.82kPa. 1. Determine the pressure of the dry oxygen in the flask. P atm = P H2O + P gas 95.00 kpa = 31.82 kpa + P gas 63.18 kpa = P gas 2. Determine the number of moles of dry oxygen in the flask. 63.18kPa (0.25 L) = n (8.31)(303K) 0.0063 mol = n Eudiometer Lab: A student reacts 0.045g of magnesium with excess hydrochloric acid in a eudiometer tube set-up like the one used in our lab. The temperature in the room is 22 C, and the atmospheric pressure is 755mmHg. The vapor pressure of water at 22 C is 19.8mmHg. a. Determine the pressure of the dry hydrogen gas. P atm = P H2O + P gas 755mmHg = 19.8mmHg + P gas 735.2 mmhg = P gas b. Write the equation for the reaction that occurs in the lab. Mg + 2 HCl MgCl 2 + H 2 c. Predict the volume of hydrogen gas that should form in the lab, in ml. 0.045g Mg 1 mol Mg 1 mol H2 = 0.00185mol 24.3g Mg 1 mol Mg 735.2 (V) = (0.00185) (62.4)(295) V = 0.0464L = 46.4mL d. The student measures the volume of hydrogen gas collected as 42.1mL. Determine his percent yield and percent error. 42.1 x 100 = 90.7% yield 100 90.7 = 9.3% error 46.4
USING THE IDEAL GAS LAW TO FIND MOLAR MASS AND DENSITY Molar Mass = mass of gas moles of gas What is the molar mass of the element that has a mass of 89.78g and occupies 45 L at 2.5 atm and 35 o C.? Identify the element. 2.4atm (45L) = n (0.0821)(308K) n=4.4 mol MM = 89.78g 4.4 mol = 20.4 g/mol = Neon TRY: Find the molar mass of a gas if 0.75g of the gas fill a 500mL flask at 23 C and 747mmHg. 747mmHg (0.5L) = n (62.4)(296K) n=0.02 mol MM = 0.75g 0.02 mol = 37.5 g/mol Density = mass of gas L of gas What is the density of carbon disulfide (gas) at STP? 1atm(1L) = n (0.0821)(273) n=0.0446 0.0446 moles 76.2 g = 3.4g/1L 1 mole What is the density of nitrogen gas at 102kPa and 45 C? 102 kpa(1l) = n (8.31)(318) n=0.0386 0.0386 moles 28 g = 1.08g/1L 1 mole
MOVEMENT OF GAS PARTICLES: MAXWELL-BOLTZMAN DISTRIBUTION a. If both samples contain the same gas, which sample is at a higher temperature? B (higher speed = higher temp) b. If both samples are at the same temperature, which gas has the higher molar mass? A (lower speed, lower temp) GRAHAM S LAW: PARTICLE SPEED AND MASS Temperature is the average kinetic energy of particles in a sample. Kinetic energy is related to particle speed and mass. If two particles are at the same temperature, the lighter one will have the higher speed. If a sample of hydrogen and a sample of nitrogen are each is a sealed 1.0L container at the same temperature and the same pressure: a. which sample contains more molecules? same b. which sample is heavier? N 2 c. which sample has the greater average kinetic energy? same d. in which sample are the particles moving faster? H 2