I. Boyle s Law - relates pressure with volume for a gas in a closed container at constant temperature * apparatus:

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1 I. Boyle s Law - relates pressure with volume for a gas in a closed container at constant temperature * apparatus: piston manometer enclosed gas Using the computer setup, obtain pressures at the following volumes, then print a graph of your results: olume (cm Pressure ( kpa P * GRAPH: * This is an inversely proportional relationship P

2 Conclusion questions Calculate the P product and record it in the third column of your data table. What do you notice? * All the P products are roughly the same (characteristic of inversely proportional relationships Is the graph linear? NO Is it directly proportional? NO Is it inversely proportional? YES The mathematical equation is known as Boyle s Law, and in words it says: at constant temperature, the pressure and volume of a gas are inversely proportional. The equation for this is: P K or more commonly: P P T. A sample of a gas under a pressure of 7.0 mmhg has a volume of 0 cm. If the pressure is increased to mmhg with no change in temperature, what will the new volume be? P P ( 7.0mmHg ( 0cm ( 900.0mmHg ( 7.0mmHg( 0cm ( 900.0mmHg cm S. If you have a.00 dm balloon at standard pressure, and you increase its pressure to 50.0 kpa, what will its new volume be? Assume the temperature is constant. P P ( 0.kPa (.00dm ( 50.0kPa ( 0.kPa(.00dm ( 50.0kPa dm

3 II. Charles Law at constant pressure, the volume and temperature of a gas are directly proportional. T K T T Here s something interesting: 6 5 o C +798 K * NOTE: TEMPERATURE MUST BE IN KELIN!!!! He olume (L 5 CH H O H N O What is this temperature? -7 o C absolute zero T. If you have a balloon under constant pressure whose volume is 0.5 ml at room temperature, and you put it in some boiling water, what will the new volume be? Assume pressure is constant..5ml T T 98K ( 0.5mL( 7K 98K ( 0 room temp 5 o C K boiling 00 o C + 7 7K ( 0.5mL ( 7K ( 98K 7K mL S. A sample of a gas has a volume of 55 cm when its temperature is 0.0 o C. What will the volume be at a temperature of 5.0 o C? Assume pressure is constant. 55 cm 8K 8K Temperature ( o C 7cm

4 III. Combined Gas Law: P T P T You can use this to find: - Boyle s Law: temperature is constant, remove T from equation - Charles Law: pressure is constant, remove P from equation - P vs. T Law: volume is constant (rigid container, remove from equation * Standard Temperature and Pressure (STP: T: 7K P: atm, 76θ Torr, 76θ mmhg, or 0. kpa T. If I have a 0.0 L container at STP, what will the volume be at 55 o C and kpa? (.kpa( 0.0L ( kpa P P 0 T T 7K 58K 0.kPa 0.0L 58K 7K kpa ( 0.kPa( 0.0L( 58K. L 7K kpa ( ( ( ( ( S. ( ( If I have a 5.0 L container at STP, what will the pressure be at 5 o C if the container expands to 5. dm? ( 0.kPa( 5.0L P ( 5.dm 7K 5K P atm 75. kpa 57Torr A sample of oxygen gas has a volume of 05 cm when its temperature is o C and its pressure is 0.8 kpa. What volume will the gas occupy at STP? (.8kPa( 05cm ( 0.kPa 0 95K 7K 57. cm 7

5 5. The Ideal Gas Law * Avogadro s Law - under constant temperature and pressure, equal volumes of any two gases will contain the same number of particles - mole - a number word 6.0 x 0 like dozen (, score (0, gross ( 60,000,000,000,000,000,000,000 OR 600 billion trillions. L carbon dioxide. L helium. L hydrogen - each of these boxes of gas contain 6.0 x 0 molecules of the gas - another wording: the volume of a gas is directly proportional to the number of moles of particles kn k - constant n - number of moles of particles * Ideal Gas Law - a state equation (does not require change to calculate P nrt R - universal gas constant R atm L mol K kpa L mol K T. A sample of hydrogen gas has a volume of 8.56 L at a temperature of 0 o C and a pressure of.5 atm. How many moles of hydrogen molecules are in this container? L atm P nrt (.5atm( 8.56L n 0.08 ( 7K mol K (.5atm( 8.56L n 0. 57molH ( 7K ( 0.08 * this value of R chosen to make P units match If you had a.50 L container with 0.980mol of helium gas (He in it, what pressure will it exert at room temperature? molehe.9ghe molHe ghe P(.50L ( 0.980mol( 0.08( 98K P 6. 85atm 69kPa

6 6 S. What volume will.00 mole of methane (CH occupy at STP? ( atm (.00mol( 0.08( 7K. L A.5mol sample of methane gas occupies a 50.0 dm container when kpa of pressure is exerted on it. What is the temperature of the sample? molech 0.0gCH. 5molCH 6gCH ( kpa( 50.0dm (.5mol( 8. T T 59K If you collect 5. ml of hydrogen gas at a pressure of 75 mmhg and a temperature of 9 o C, how many moles of hydrogen (H gas did you collect? ( 0.99atm( 0.05L n( 0.08( 9K n mol Look at the reaction for the decomposition of sodium chloride under electrolysis: NaCl(s Na(s + Cl (g atm 75 mmhg 0. 99atm 760mmHg If you begin this reaction with 5.0g of sodium chloride, and it produces 0.8 moles of chlorine gas, what volume of chlorine gas would be produced if the reaction was performed at 99.8 kpa of pressure and a temperature of 9 o C? ( 99.8kPa ( 0.8mol( 8.( 9K. L

7 7 I. Dalton s Law of Partial Pressures - in a mixture of gases, the total pressure of the mixture is equal to the sum of the pressures that each gas would exert by itself in the same volume. liter container liter container liter container 760 Torr 550 Torr 0 Torr * mathematical: P tot P + P +... OR P tot X P tot + X P tot +... X - mole fraction (% of total S. If you have a L container with nitrogen gas under a pressure of 88. kpa and you add some oxygen gas until the total pressure of the mixture is.9 kpa, what is the partial pressure of oxygen? P N + PO P tot 88.kPa + P O. 9kPa P O kPa If you have a mixture made up of 5.6% helium gas,.% argon gas, and.% neon gas which exerts a pressure of.5 atm in a.0 L container, what are the partial pressures of each gas? P He (0.56(.5atm 0.9atm P Ar (0.(.5atm 0.80atm P Ne (0.(.5atm 0.665atm * When a gas is collected in a lab, it is usually bubbled through, and contained by, water. Under normal conditions, water evaporates in an amount directly proportional to its temperature. As a result, any gas collected over water will be a mixture of the desired gas and water vapor. This water vapor exerts a pressure on the container known as the vapor pressure. apor pressure is directly proportional to the temperature of the water in degrees Celsius. The equation that describes the reaction is as follows: Mg (s + HCl (aq MgCl (aq + H (g If you began with 0.5g of magnesium ribbon, and reacted it with excess HCl, collecting it over water at a temperature of o C and an atmospheric pressu re of 99.6 kpa, and 0.0 moles of hydrogen gas was produced what volume should you expect? The vapor pressure of water at o C is.8 kpa. ( 97.kPa ( 0.0mol( 8.( 9K P H kpa 0. 56L

8 8 II. Graham s Law of Diffusion and Effusion - under constant temperature and pressure, gases diffuse at a rate inversely proportional to the square roots of their densities. v v rr (can use densities also * diffusion the process through which two or more different gases spontaneously mix with each other * effusion the process through which a gas in a closed container escapes through a small opening * Basic Rule: lighter gases diffuse and effuse more quickly than heavier gases T. What is the relative rate of diffusion for Neon ( 0. g/mol vs. Argon ( 0.0 g/mol? Which gas travels faster? *Place the heavier gas on the top of the fraction rr 0 0. Ar. Ne *This means that neon (the lighter gas diffuses. times more quickly than argon gas. If a mystery gas diffuses.8 times faster than carbon dioxide (.0 g/mol, what is the molecular mass of the mystery gas? rr.8 (.8 x x.9 x.9x x 0. g/mol.9 S. What is the relative rate of diffusion for Helium (.00 g/mol vs. Radon ( g/mol? Which gas travels faster? rr Rn 7. 5 Helium diffuses faster He If helium diffuses. times faster than a mystery gas, what is the molecular mass of the gas?. x x 7.7 x g/mol

9 9 III. Kinetic Theory of the Gas Laws - can we explain why they work the way they do? * ideal gas any gas which follows the five assumptions below - i.e. any gas that obeys the mathematical models perfectly - some gases are more ideal than others * 5 assumptions: Gases are composed of tiny particles of negligible volume separated by lots of space Gas particles travel in a straight-line motion until a collision occurs. All collisions are elastic. Particles display no attractive or repulsive forces for each other. 5 All particles have different velocities, but the average of the velocities remains the same unless the temperature changes. Temperature α ave.ke * Explain, using Kinetic theory why: - Boyle s Law * In this picture, as the volume decreases, the particles are forced closer together * As a result, there will be more collisions between the particles and the wall per square inch of wall space * Therefore, the pressure inside the container increases as well - Charles Law * As the temperature increases, the particles move more rapidly * As a result, there are more collisions with the wall of the container * Therefore the pressure inside the container increases * The container expands until the pressures (inside and outside are again equal

10 0 - Guy-Lussac s (P-T Law * As the temperature increases, the particles move more rapidly * As a result, the pressure inside the container increases * Because the container is rigid (constant volume, the container can t expand to relieve that pressure, so the pressure remains elevated - Dalton s Law + * When you combine two gases in the same size container, there are more particles per unit volume * More particles will have more collisions, so the pressure increases - Graham s Law vs. * Because heavier particles are larger, and motion of gases is random, the smaller particles are more likely to fit through the opening in the container, therefore the lighter gas effuses more quickly IX. When do gases not behave ideally? - extremely high pressures particles become so compressed that there is no longer a negligible volume (assumption # - extremely low temperatures at low temperatures, the particles are moving so slowly that the attractive forces become a factor, and particles no longer travel in straight paths (assumptions # & # - vander Waal s Equation corrects the ideal gas law (PnRT for all real gases