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Parts of chapters 2, 10, &11 All of Chapter 12 – Gas Laws

Parts of chapters 2, 10, &11 All of Chapter 12 – Gas Laws. CHEMISTRY GREATER LATROBE HIGH SCHOOL. TABLE OF CONTENTS. Introduction to Gases Boyles Law Charles Law Gay-Lusacc’s Law Combined Gas Law Ideal Gas Law Dalton’s Law Graham’s Law Phase Diagrams Surface Tension.

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Parts of chapters 2, 10, &11 All of Chapter 12 – Gas Laws

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  1. Parts of chapters 2, 10, &11All of Chapter 12 – Gas Laws CHEMISTRY GREATER LATROBE HIGH SCHOOL Gas Laws Unit

  2. TABLE OF CONTENTS • Introduction to Gases • Boyles Law • Charles Law • Gay-Lusacc’s Law • Combined Gas Law • Ideal Gas Law • Dalton’s Law • Graham’s Law • Phase Diagrams • Surface Tension Click on this picture on any slide to return to the table of contents All yellow text will take you to additional information Gas Laws Unit

  3. Introduction to Gases – Causes of change (Ch. 11.1 and 11.2) • Energy as Heat: • Heat and Temperature are not the same thing. • Heat • Temperature • Enthalpy – Total energy content of the sample. Gas Laws Unit

  4. Introduction to Gases – Causes of change (Ch. 11.1 and 11.2) • Molar Heat Capacity –(Cp)– this is the amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius (or 1 mole 1 Kelvin). • Practical example: snow fall • Calculations using Cp – These are done to determine the amount of energy change (H) in the process of warming or cooling matter. This is calculated according to the following equation: Gas Laws Unit

  5. Introduction to Gases – Causes of change (Ch. 11.1 and 11.2) • H = mCp T (H can be changed for Q) • m = mass, Cp = Specific Heat capacity (will be given, T = Change in temperature (Final T – Initial T) • m can also be replaced with n for moles if necessary) Gas Laws Unit

  6. Introduction to Gases – Causes of change (Ch. 11.1 and 11.2) • Problem #1: (Click for answer) • Assuming the density of water to be 1.0 g/mL. How much heat is lost by 4.0 L of water cooling from 87 C to 21 C? (Heat capacity for water = 4.180 J/g* C • Problem #2: (Click for answer) • If 980 kJ of energy is added to 6.2L of water at 18 C, what is the final temperature of the water? Gas Laws Unit

  7. Introduction to Gases – Causes of change (Ch. 11.1 and 11.2) • When heat is added or removed from a substance it can go through phase changes. Recall that there are three major states (phases) of matter (solid, liquid, and gas). A Heating Curve (in your book on page 44) shows the relationship between these states as the temperature changes. • ∆Hfus – energy required to melt one mole • ∆Hvap - energy required to vaporize one mole • ∆Hvap > ∆Hfus Gas Laws Unit

  8. State Changes and Phase Diagrmas • Review of what we know at this point about solids, liquids, and gases: • Solids – Constant shape, constant volume • Liquids – Variable shape, constant volume • Gases – Variable shape, variable volume • We now need a more detailed comparison of each of these. • Solids • Liquids • Gases Gas Laws Unit

  9. Phase Diagrams – Vapor Pressure and Boiling • Vapor Pressure – the pressure of a gas on top of a liquid. This is dependent only on the temperature. • This is key in understanding the process of boiling. For example: • What would happen to a an open jar of water over time? • What would happen to a closed jar of water over time? • Here water will evaporate until condensation = evaporation. Here vapor pressure is a max. • Boiling – this occurs when vapor pressure equals atmospheric pressure. • Substances with high vapor pressure at low temperatures are volatile (boil / vaporize easily) i.e. perfume Gas Laws Unit

  10. Phase Diagrams • Phase Diagrams – Graphically represent the relationship between the state of a substance and its pressure and temperature. • Processes shown phase diagram (click to go to diagram) • (1) – melting – solid to liquid • (2) – Freezing – liquid to solid • (3) – Boiling – liquid to gas • (4) – Condensing – gas to liquid • (5) – Sublimation – solid directly to gas (dry ice) • (6) – Deposition – gas directly to solid (frost) • (7) – Triple point – Temperature and pressure at which a substance exists as a solid, liquid, and gas at the same time. Gas Laws Unit

  11. Characteristics of Gases • Kinetic Molecular Theory – Describes the behavior of gases at the molecular level (Based on an ideal gas) • Ideal Gas – Imaginary gas (model) that describes the behavior of real gases at conditions close to STP (this will be explained later) Gas Laws Unit

  12. Characteristics of Gases (con’t) • 5 Assumptions of the KMT: • 1. Gases consist of large numbers of tiny particles • 2. Particles of a gas are in constant motion and therefore have KE • 3. Collisions between particles of a gas and container wall are completely elastic. • 4. There are no forces of attraction or repulsion between particle of a gas • 5. The Average kinetic energy of the particles of a gas is directly proportional to the Kelvin Temperature of the gas. • KE = ½ MV2 Gas Laws Unit

  13. Ideal Gases The volume of the particles is negligible There are no attractive forces between molecules Collisions between particles are elastic Real Gases Particles do have volume As temp. decreases the particles slow down and attractive forces increase Collisions between particles are inelastic Ideal versus Real Gases • Throughout this Unit we are going to focus on Ideal Gases, Ideal gases differ from real gases by the following Gas Laws Unit

  14. Characteristics of Gases (con’t) • Variables that describe a gas: • Temperature – measure of the average KE of the Particles of a gas (must be in Kelvin – T in K) • K = C + 273 • Volume – amount of space matter occupies • Can use L, mL, m3, or cm3 • Pressure – Force per unit area • Measure with barometer • Describes the forces that gases exert on the walls of a container. • Atmospheric Pressure = 1 atm = 760 mmHg = 760 torr = 101.3 Kpa = 29.9 inHg = 14.7 psi Gas Laws Unit

  15. Characteristics of Gases (con’t) • STP – Standard Temperature and Pressure • T = 273 K • P = 1 atm At these conditions all gasses occupy 22.4 L of space (standard molar volume) Gas Laws Unit

  16. Boyles Law • This Gas law discovered by Robert Boyle involves the relationship between pressure and volume at constant temperature. • Go to the following web site to see an illustration of this relationship (freeze mass and Temperature): • http://www.grc.nasa.gov/WWW/K-12/airplane/Animation/frglab2.html • This relationship is know as an inverse relationship. (when one variable gets bigger the other variable gets smaller) Gas Laws Unit

  17. Boyle’s Law (con’t) • Formula: • PV = k (k=constant, P=pressure, V=volume) • Since the pressure times the volume is constant this can be written as follows: (click on the formula to go to some practice problems) • P1V1 = P2V2 or • P1V1 = P2V2 • Boyle’s Law has many practical applications. It is applied in things such as breathing, scuba diving, submarines, and weather balloons. We will discuss several of these. Gas Laws Unit

  18. Charles Law • This gas law was discovered by Joseph Louis Gay-Lussac but is usually named for Jacques Charles Law because of the work he did. It involves the relationship between Volume and Temperature at constant pressure. • Go to the following web sites to see an illustration of this relationship (freeze mass and Pressure): • http://www.grc.nasa.gov/WWW/K-12/airplane/Animation/frglab2.html • http://fsc.fernbank.edu/chemistry/charles.html • This relationship is know as an direct relationship. (when one variable gets bigger the other variable gets bigger) Gas Laws Unit

  19. Charles Law • Formula: • V/T = k (k=constant, T=Temperature, V=volume) • Since the volume divided by the temperature is constant the following formula can be written: (click on the formula to go to some practice problems (choose solving problems or word problems) • V1/T1 = V2/T2 or • V1/T1 = V2/T2 • Charles’s Law also has many practical applications. It is applied in things such as effects of temperature changes on balloons, tires, hot air balloons, etc. Gas Laws Unit

  20. Gay-Lussac’s Law • This Gas law discovered by Joseph Louis Gay-Lussacinvolves the relationship between temperature and Pressure at constant volume. • Go to the following web site to see an illustration of this relationship (freeze mass and volume): • http://www.grc.nasa.gov/WWW/K-12/airplane/Animation/frglab2.html • This relationship is also a direct relationship. Gas Laws Unit

  21. Gay-Lussac’s Law • Formula: • P/T = k (k=constant, T=Temperature, P=pressure) • Since the volume divided by the temperature is constant the following formula can be written: (click on the formula to go to some practice problems (choose solving problems or word problems) • P1/T1 = P2/T2 • Gay-Lussac’s law also has many practical applications. For example: This is why on the side of spray cans it will tell you to keep the can stored at certain temperatures. This is why inflatable devices such as tires or balls go flat in the winter time. Gas Laws Unit

  22. The Combined Gas Law • This gas law encorporates all three of the basic gas law (Boyle’s, Charles’s, and Gay-Lussac’s) • Click here to see a graphical illustration of this. • It is often used for converting a temperature, pressure, or volume to standard conditions (STP) Gas Laws Unit

  23. The Combined Gas Law • Formula: • Sample problem: • 2.00 L of a gas is collected at 25.0°C and 745.0 mmHg. What is the volume at STP? • Click for answer P1V1 P2V2 T1 T2 Gas Laws Unit

  24. The Combined Gas Continued • A sample of gas occupies a volume of 6.80 L at 790.0 mmHg and 300.0 K. What is the temperature of the gas when the volume is 7.00 L and the Pressure is 2.00 atm? Gas Laws Unit

  25. Ideal Gas Law • The Ideal gas law encorporates all three variables that we have been using plus it also incorporates molesinto the equation. This is the most common equation used in working with gases. • First written by Emil Clapeyron, and is sometimes (although rarely called the Clapeyron equation) • The formula is as follows: • PV = nRT • P = pressure, V = Volume, n = moles, R = Gas constant, T = temperature • R = 8.314 L * kPa or 0.0821 L * atm or 62.36 mmHg * L ----------- ----------- --------------- Mol * K mol * K mol * K Gas Laws Unit

  26. Ideal Gas Law • Example Problems • What is the pressure (in atm) exerted by a 0.500 mol sample of Nitrogen gas in a 10.0 L container at 298 K? • What mass would a sample of chlorine gas have if the pressure in a 10.0 L tank at 27 degrees Celsius is 3.50 atm? • Answers to Ideal Gas Law Problems Gas Laws Unit

  27. Dalton’s Law • This gas law was discovered by John Dalton. It deals with the partial pressures (The pressure of an individual gas in a mixture of gases) of a gas. It is primarily used for situations when a gas has been collected over water. • Go to the following web site for an explanation of Dalton’s Law: • http://www.fordhamprep.com/gcurran/sho/sho/lessons/lesson74.htm Gas Laws Unit

  28. Dalton’s Law • Formula • Pt = P1 + P2 + P3 + ….. + Pn (P = Pressure) • This formula can also be written as follows: • Patm = Pgas + PH2O (P=pressure, atm=atmosphere) • The second formula is the form which we will use the most often. This is the form of Dalton’s equation that allows us to correct for water vapor pressure(click to see water vapor chart)when a gas is collected over water. Gas Laws Unit

  29. Dalton’s Law • Example Problem: • 2.50 L of gas is collected over water at 25 degrees C and 795 mmHg. What is the volume of gas at STP? • Click for answer Gas Laws Unit

  30. Graham’s Law • Graham’s Law is used to give the rates of effusion and diffusion. • Effusion – Gas escapes a container through a small pin size hole. • Diffusion – Gradual mixing of two gases because of random motion of particles • Definition: The rates of effusion and diffusion are inversely proportional to the square roots of a gases molar mass. • Analogy – Big guy –vs- Small guy Gas Laws Unit

  31. Graham’s Law • Formula: • Rate A Square root (MB) -------- = ------------------- Rate B Square root (MA) • Sample Problem Gas Laws Unit

  32. The End Gas Laws Unit

  33. Temperature • The temperature of a substance is a measure of the average kinetic energy of that substances particles. • Think of this as the intensity of energy. • This is an intensive property – the measure of temperature does not depend on the amount of the sample of material. • This is different than heat Return Gas Laws Unit

  34. Heat • Heat is the measure of the total amount of energy transferred from an object of high temperature to one of low temperature • Think of this as the quantity of energy • This is an extensive property – the measure of heat depends on the amount of the sample of material. • It is always High  Low Return Gas Laws Unit

  35. Heating Curve(Chapter 2 – Page 44) • The picture to the right represents a heating curve for water. What is happening to the temperature when the substance is changing states? Gas Laws Unit Return

  36. Answers to Heat Capacity Problems • Problem #1: • First find mass: m = (1000 g / L)(4.0 L) = 4000 g • H=(4000g)(4.180 J/g* C)(21-87) = 1103520 J • Problem #2: • First find mass: m = (1000 g / L)(6.2 L) = 6200 g • 980 000 J = (6200g)(4.180 J/g* C)(Tf - 18 C) = 55.8 C Return Gas Laws Unit

  37. Barometer • The barometer The mercury barometer measures atmospheric pressure. It works this way.  Completely fill a long glass tube with mercury. Turn it upside down, and place the top below the surface of more mercury in an open basin. Rather than pouring out again, the mercury in the tube will only fall until the height of the column is about a meter. This is because the pressure of the air on the mercury in the basin is equal to the pressure of the mercury in the column. The gap at the top of the tube is not air but a vacuum. The difference in height between the top of the column and the top surface of the mercury in the basin is a measure of the weight of the air, which changesas the weather changes. • Weather can be predicted by this: • Low barometric pressure generally indicates stormy weather • High barometric pressure generally indicates good weather Return Gas Laws Unit

  38. Inverse Relationships Defined • An inverse relationship is when one of the variables is increased the other variable decreases. See the graph to the right for an illustration of this. Return Gas Laws Unit

  39. Direct Relationship defined • In a direct relationship when one of the variables gets bigger the other variable also gets bigger. See the graph to the right for an illustration of this. Return Gas Laws Unit

  40. Water Vapor Pressure • This is pressure in a container of gas that results from the water evaporating slightly as the gas is being collected over water. The amount of evaporation increases as the temperature increases. Return Gas Laws Unit

  41. Answer to Dalton’s Problem • 2.50 L of gas is collected over water at 25 degrees C and 795 mmHg. What is the volume of gas at STP? • You must use the combined gas law • 1st – Determine the pressure of the dry gas (vapor pressure chart) • 795 mmHg = Pg + 23.8 mmHg • Pg = 771.2 mmHg • 2nd – Use the combined gas law to solve. • (771.2 mmHg)(2.50L)/298K = (760 mmHg)V2/273K • V = 2.32 L Return Gas Laws Unit

  42. Answer to Combined GasLaw Problem • The data is organized to the left. Insert them into: • P1V1 / T1 = P2V2 / T2 • (745.0 mmHg)(2.00L) / 298K = ( 760.0 mmHg)(V2) / 273K V2 = 1.79 L Return Gas Laws Unit

  43. PV = nRT P(10.0L) = (0.500)(0.0821)(298K) P = 1.22 atm PV = nRT (3.50atm)(10.0L) = n(0.0821)(300K) n=1.42 moles * 70.90 g Cl2 ------------------------------------- = 101 grams 1 mole of Cl2 Answer to Ideal GasLaw Problem Return Gas Laws Unit

  44. Phase Diagrams Return Gas Laws Unit

  45. Combined Gas Law Graph Trace across the white area to see what happens as all three change. Trace across a colored area to see what happens when one variable is held constant. Return Gas Laws Unit

  46. Water Vapor Pressure Vapor Chart Notes Problem Gas Laws Unit

  47. Solids • In a solid: • The particles are packed very closely together. • The particles are very ordered • The particles vibrate about fixed postions. • The particles in a solid exhibit very strong Intermolecular Forces Back to State Changes Gas Laws Unit

  48. Liquids • Particles in a liquid: • Can slide/move past one another • Exhibit weaker Intermolecular Forces • Are arranged more randomly • Exhibit: • Surface Tension • Capillary Action Back To State Changes Gas Laws Unit

  49. Gases • Particles in a gas: • Are very spread out (lots of empty space between particle) • Move rapidly in random, straight paths • Don’t exhibit intermolecular forces • Are very compressible Back To State Changes Gas Laws Unit

  50. Surface Tension • Definition – The measure of a liquids tendency to decrease its surface area to a minimum. • What does this really mean? • Water spiders, capillary action, and water skiing are all illustrations of surface tension. Water Spider Picture Back To Liquids Gas Laws Unit

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