1. Kinetic Theory & Behavior of Gases

2.  Objective:  You will be able to describe the assumptions of kinetic theory as it applies to gases

3.  The word kinetic refers to motion.  The energy an object has because of its motion is called kinetic energy.  According to the kinetic theory, all matter consists of tiny particles that are in constant motion.  The particles in a gas are usually molecules or atoms.

4.  There are 3 basic Assumptions of the Kinetic Theory 1. Matter is composed of small molecules. The space between the matter is so big – the volume of the molecules themselves does NOT matter. Between the particles, there is empty space. No attractive or repulsive forces exist between the particles.

5.  2. The molecules are in constant motion. Motion is different for each of the different states of matter.  Solids will bend and vibrate as they remain fairly stationary.  Liquids flow and glide easily through space.  Gases move continuously in straight lines. The motion of the particles in a gas is rapid, constant, and random.  As a result, gases fill their containers regardless of the shape and volume of the containers. An uncontained gas can spread out into space without limit. The particles travel in straight-line paths until they collide with another particle, or another object, such as the wall of their container.

6.  3. When molecules collide (with each other or the walls of the container) these collisions are elastic.  Elastic means NO ENERGY is transferred or lost in the collision.  During an elastic collision, kinetic energy is transferred without loss from one particle to another, and the total kinetic energy remains constant.  Question to Ponder: Are these 3 assumptions fair????

7.  Gas pressure results from the force exerted by a gas per unit surface area of an object.  Gas pressure is the result of simultaneous collisions of billions of rapidly moving particles in a gas with an object.  If there are no particles, there cannot be collisions. Consequently, there is no pressure.  An empty space with no particles and no pressure is called a vacuum.

8.  A gas pressure that you are familiar with is that caused by a mixture of gases- air.  Air exerts pressure on Earth because gravity holds the particles in air in Earth’s atmosphere.  Atmospheric pressure results from the collisions of atoms and molecules in air with objects.  Atmospheric pressure decreases as you climb a mountain because the density of Earth’s atmospheric decreases as the elevation increases.

9. A barometer is a device that is used to measure atmospheric pressure. The height of the mercury column in the tube depends on the pressure exerted by particles in air colliding with the surface of the mercury in the dish. Atmospheric pressure depends on weather and on altitude. In fair weather at sea level, the atmospheric pressure is sufficient to support a mercury column about 760 mm high.

10. More Modern version of the Barometer

11.  The SI unit of pressure is the pascal (Pa ).  It represents a very small amount of pressure.  One standard atmosphere ( atm ) is the pressure required to support 760 mm of mercury in a mercury barometer at 25°C.  1 atm = 760 mm Hg = 760 torr = 101.3 kPa

12.  1) A pressure gauge records a pressure of 450 kPa. What is the measurement expressed in atmospheres and millimeters of mercury?

13.  2) What pressure in kilopascals and in atmospheres, does a gas exert at 385 mm Hg?

14.  3) The pressure at the top of Mount Everest is 33.7 kPa. Is that pressure greater or less than 0.25 atm?

15. Topic 2: Kinetic Energy and Temperature Objective: You will be able to define the relationship between Kelvin temperature and average kinetic energy.

16. Energy As a substance is heated, its particles absorb energy, some of which is stored within the particles. This stored portion of the energy, or potential energy, does not raise the temperature of the substance. The remaining absorbed energy speeds up the particles, which increases their kinetic energy. This increase in kinetic energy results in an increase in temperature. THEREFORE THERE IS A DIRECT RELATIONSHIP BETWEEN TEMPERATURE (KELVIN) AND KINETIC ENERGY

17. Average Kinetic Energy Average kinetic energy is used when discussing the kinetic energy of a collection of particles in a substance. At any given temperature the particles of all substances, regardless of physical state, have the same average kinetic energy.

18. An increase in the average kinetic energy of the particles causes the temperatures of a substance to rise. As a substance cools, the particles tend to move more slowly, and their average kinetic energy declines.

19.  Absolute zero (0 K, or -273.15°C) is the temperature at which the motion of particles theoretically ceases.  The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance.

20.  This equation shows you the relationship between Kinetic Energy and the velocity or speed of the molecules in any sample.  However, what does it tell you about the relationship between velocity and mass??

21.  The more mass the slower something moves!! An inverse relationship!

22. Maxwell-Boltzmann Curves: Show you the relationship between velocity and temperature Draw a M-B curve for 2 different temperatures and note what happens…

23. What temperaturehas the greatest speed? Why? What temperature has the slowest speed why? What happens the curve as they move to the higher temps? Why do you think that is?

24. Maxwell – Boltzmann: For different molecules…

25. What gas has the greatest speed? Why? What gas has the slowest speed why? What happens the curve as they move to the higher speeds? Why do you think that is?

26.  Objectives:  You will be able to describe the relationships among the temperature, pressure, and volume of a gas.

27.  If temperature is constant, as the pressure of a gas increases, the volume decreases.  In turn, as the pressure decreases, the volume increases.  In 1962, Boyle proposed a law to describe the relationship between pressure and volume.  Boyle’s Law states that for a given mass of gas at constant temperature, the volume of the gas varies INVERSELY with pressure.  P 1 x V 1 = P 2 x V 2

28.  1) A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume that the temperature remains constant)

29.  2) Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.50 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be?

30.  3) A gas with a volume of 4.00 L at a pressure of 205 kPa is allowed to expand to a value of 12.0 L. What is the pressure in the container if the temperature remains constant?

31.  As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant.  In 1787, the French physicist Jacques Charles studied the effect of temperature on the volume on the volume of a gas at constant pressure.  Charles’s law states that the volume of a fixed mass of gas is DIRECTLY proportional to its Kelvin temperature if the pressure is kept constant.  V 1 = V 2 T 1 = T 2

32.  1) A balloon inflated in a room at 24°C has a volume of 4.00 L. The balloon is then heated to a temperature of 58°C. What is the new volume if the pressure remains constant?

33.  2) If a sample of gas occupies 6.80 L at 325°C, what will its volume be at 25°C if the pressure does not change?

34.  3) Exactly 5.00 L of air at -50.0°C is warmed to 100.0°C. What is the new volume if the pressure remains constant?

35.  As the temperature of an enclosed gas increases, the pressure increases, if the volume is constant.  Joseph Gay-Lussac, a French chemist, discovered the relationship between the pressure and temperature of a gas in 1802.  Gay-Lussac’s law states that the pressure of a gas is DIRECTLY proportional to the Kelvin’s temperature if the volume remains constant  P 1 = P 2  T 1 = T 2

36.  1) The gas in a used aerosol can is at a pressure of 103 kPa at 25°C. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928°C?

37.  2) A sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K?

38.  3) The pressure in a car tire is 198 kPa at 27°C. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire? Assume that the volume is constant.

39.  The combined gas law describes the relationship among the pressure, temperature, and volume of an enclosed gas. (You really only need this law…)  This allows you to calculate with any of the three variables..  P 1 x V 1 = P 2 x V 2  T 1 T 2

40.  1) The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa pressure. What would the volume be at standard temperature and pressure (STP)?

41.  2) A gas at 155 kPa and 25°C has an initial volume of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125°C. What is the new volume?

42.  3) A 5.00-L air sample has a pressure of 107 kPa at a temperature of -50.0°C. If the temperature is raised to 102°C and the volume expands to 7.00 L, what will the new pressure be?

43.  Gas pressure results from collisions of particles in a gas with an object.  If the number of particles increases in a given volume, more collisions occur.  If the average kinetic energy of the particles increases, more collisions occur.  In both cases, the pressure increases.  Gas pressure depends only on the number of particles in a given volume and on their average kinetic energy.  Particles in a mixture of gases at the same temperature have the same average kinetic energy.

44.  The contribution each gas in a mixture makes to the total pressure is called the partial pressure exerted by that gas.  In a mixture of gases, the total pressure is the sum of the partial pressures of the gases. P total = P 1 + P 2 + P 3 + …  Dalton’s law of partial pressure states that, at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases.

45.  1) What is the partial pressure of oxygen (P O2 ) at 101.30 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

46.  2) Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are: P O2 = 20.0 kPa, P N2 = 46.7 kPa, and P He = 26.7 kPa.

47.  3) A gas mixture containing oxygen, nitrogen, and carbon dioxide has a total pressure of 32.9 kPa. If P O2 = 6.6 kPa and P N2 = 23.0 kPa, what is P CO2 ?

48. Ideal Gas Law  You cannot use the combined gas law to calculate the number of moles of a gas in a fixed volume at a known temperature and pressure.  To calculate the number of moles of a contained gas requires an expression that contains the variable n.

49. The number of moles of gas is directly proportional to the number of particles. The volume occupied by a gas at a specified temperature and pressure also must depend on the number of particles. So moles must be directly proportional to volume as well.

50.  If you know the values for P, V, T, and n for one set of conditions, you can calculate a value for the constant.  The ideal gas constant (R) has the value 8.31 (L·kPa)/(K·mol). PV=nRT

51. Practice Problems:  1) A deep underground cavern contains 2.24 x 106 L of methane gas (CH 4 ) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH 4 does the cavern contain?

52.  2) When the temperature of a rigid hollow sphere containing 685 L of helium gas is held at 621 K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain?

53.  3) A child’s lungs can hold 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37°C? Use a molar mass of 29 g for air, which is about 20% O 2 (32 g/mol) and 80% N 2 (28 g/mol).

54. Gas Law Stoichiometry:  We have learned how to solve for pressure under special pressure and volume circumstances known as STP – however we can now use the ideal gas law and stoichiometry to solve for any combination of pressure and volume!

55.  Just as with every stoichiometry problem you will first need 1. A balanced equation (to convert from moles to moles) 2. The ideal gas law (to solve for your unknown variable) 3. Combine them to find what the question is asking for

56.  Example 1: Using the following equation how many liters of oxygen react with 112 grams of ammonia at STP?  ___NH 3 (g) + ____O 2 (g) → ____NO 2 (g) + ____H 2 O (l)

57. Example 2: Using the following equation how many grams of nitrogen dioxide can be formed from 132 liters of oxygen at 2.4 atm and 28 degrees Celsius? ___NH 3 (g) + ____O 2 (g) → ____NO 2 (g) + ____H 2 O (l)

58.  Example :  What volume of oxygen can be formed from 100.0 grams of KClO 3 at 350 K and 0.50 atm?  ____KClO 3 ------> _____KCl + ___O 2 (g) 

59.  Most gases are collected over water. Nitrogen is collected over water at a pressure of 110 kPa and 33  C. (The P H2O at 33  C is 35 torr.) According to the following equation, how many grams of ammonia are formed from this amount of nitrogen in a 5.0L container? ____N 2 (g) + ____H 2 (g)------> ________NH 3 (g)