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Chapter 5 : Gases

Chapter 5 : Gases. Outline Pressure The Simple Gas Laws The Ideal Gas Law Applications of the Gas Law Mixtures of Gases Gases in Chemical Reactions Kinetic Molecular Theory “Real” Gases. Concept of Pressure. 50 Lb. 50 Lb. Pressure. Gases Pushing.

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Chapter 5 : Gases

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  1. Chapter 5 : Gases • Outline • Pressure • The Simple Gas Laws • The Ideal Gas Law • Applications of the Gas Law • Mixtures of Gases • Gases in Chemical Reactions • Kinetic Molecular Theory • “Real” Gases

  2. Concept of Pressure 50 Lb 50 Lb Pressure

  3. Gases Pushing • gas molecules are constantly in motion • as they move and strike a surface, they push on that surface • 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 Pressure

  4. The Pressure of a Gas • result of the constant movement of the gas molecules and their collisions with the surfaces around them • the pressure of a gas depends on several factors Pressure

  5. Measuring Pressure It’s difficult to measure the total force exerted by a gas. Need an indirect method to measure gas pressure. Measuring the pressure of a liquid is much easier. h The pressure of a liquid is proportional to its height Pressure

  6. A device that uses the height of a liquid to measure the barometric pressure is called a barometer. Usually, the liquid is mercury. The pressure exerted by 760 mm of mercury (mmHg) is called a standard atmosphere (atm). Pressure

  7. Why use Mercury ? Knowing that the density of mercury is 13.6 g/cm3, calculate the height of a column of water (d = 1.00 g/cm3) that exerts the same pressure as a 76.0 cm high column of Hg. If the pressure doubled, what would be the new height of the column of water ? Pressure

  8. Units of Pressure Lots of different units to measure pressure. = N m-2 = Pa Pressure

  9. Manometers Barometers are great for measuring the atmospheric (barometric) pressure. Not nearly so helpful for measuring the pressure of other gas pressures. Pressure

  10. Example The manometer pictured to the left is filled with Hg (d = 13.6 g cm-3). The barometric pressure is 748.2 mmHg and the difference in the mercury heights is 8.6 mm. What is the gas pressure, Pgas ? Pressure

  11. The Simple Gas Laws Pressure, temperature, volume and amount of a gas are all related. Some simple relationships were noted very early. Boyle’s Law For a fixed amount of gas at a constant temperature, gas volume is inversely proportional to gas pressure. OR Simple Gas Laws

  12. Simple Gas Laws

  13. Boyle’s Experiment • added Hg to a J-tube with air trapped inside • used length of air column as a measure of volume Simple Gas Laws

  14. Boyle’s Law and Diving • since water is denser than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atm • at 20 m the total pressure is 3 atm if your tank contained air at 1 atm pressure you would not be able to inhale it into your lungs Simple Gas Laws

  15. Application of Boyle’s Law One wants to determine the volume of the large, irregularly shaped tank shown above. The tank is initially evacuated (P=0) and then connected to a 50.0L cylinder of compressed air at a pressure of 21.5 atm. After filling the tank, the pressure of the cylinder is reduced to 1.55 atm. What is the tank’s volume ? Simple Gas Laws

  16. Charles’ Law For a fixed amount of gas at a constant pressure, the volume is directly proportional to the absolute temperature (Kelvin temperature). T(K) = T(oC) + 273.15 OR Simple Gas Laws

  17. As temperature increases, volume increases. Simple Gas Laws

  18. A Molecular View • the pressure of gas inside and outside the balloon are the same • at high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – causing the volume to become larger Simple Gas Laws

  19. Application of Charles’ Law Heat the gas…temperature goes up Simple Gas Laws

  20. Practice – The temperature inside a balloon is raised from 25.0°C to 250.0°C. If the volume of cold air was 10.0 L, what is the volume of hot air? Simple Gas Laws

  21. Avogadro’s Law For a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas. OR • count number of gas molecules by moles • equal volumes of gases contain equal numbers of molecules Simple Gas Laws

  22. The Ideal Gas Equation Recall the following relationships ; Combine all these proportionalities R = 0.082057 L atm mol-1 K-1 The Ideal Gas Equation

  23. The Ideal Gas Equation What is an “ideal gas” ? An “ideal gas” is a hypothetical gas where the gas’ atoms or molecules have no interaction with each other. R = 0.082057 L atm mol-1 K-1 Example : What is the volume occupied by 1.75 moles of Argon gas at a pressure of 700 torr and a temperature of 25oC ? The Ideal Gas Equation

  24. Predicting Changes with the I.G.E. “1” denotes initial conditions “2” denotes final conditions The Ideal Gas Equation

  25. Old Exam Question: The Ideal Gas Equation

  26. Using the IGE to identify an unknown gas Carbon monoxide (CO) is a toxic gas that causes rapid asphyxiation whereas carbon dioxide (CO2) is much less toxic. In a particular reaction, a gas is produced that is known to be either CO or CO2. In an effort to determine the identity of the gas the following experiment was performed. A glass vessel weighs 40.1305 g when clean, dry and completely evacuated. When completely filled with water it weighs 138.2410 g (density of water = 1.000 g/mL) and it weighs 40.2402 g when completely filled with the unknown gas (CO or CO2) at 740.3 mmHg and 24.0oC. What’s the identity of the gas ? The Ideal Gas Equation

  27. STP StandardTemperature and Pressure. Because gas properties depend on temperature and pressure, when comparing one gas to another it is important to choose a set of standard conditions. T = 0oC (273.15K) P = 1 atm (760 mmHg) The Ideal Gas Equation

  28. Molar Volume • solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L • 6.022 x 1023 molecules of gas • notice: the gas is immaterial • we call the volume of 1 mole of gas at STP the molar volume • it is important to recognize that one mole of different gases have different masses, even though they have the same volume Applications of the IGE

  29. Gas Densities Density is defined as mass divided by volume ; Mass equals molar mass, M, (g/mol) multiplied by number of moles, n. Replacing in the I.G.E., , gives Applications of the IGE

  30. General observations…. As the pressure increases, the density of a gas increases. The higher the molar mass, the larger the density of a gas. As temperature increases, the density of a gas decreases. Applications of the IGE

  31. Which of the following gases would be best suited for a hot-air balloon ? (H2, He, Ar) Hydrogen is very light, cheap, but extremely flammable. Argon is extremely inert, but heavy. Helium is inert and light. Much more expensive than H. Applications of the IGE

  32. Question on Gas Densities The “average” density of air is 29 g/mol. Which of these gases is lighter than air (at the same temperature and pressure) ? Applications of the IGE

  33. Mixtures of Gases • when ideal gases are mixed together, their molecules behave independent of each other • all the gases in the mixture have the same volume • all gases in the mixture are at the same temperature • Therefore the mixture can be thought of as one gas • we can measure the pressure, volume, and temperature of the mixture as if it were a pure substance • we can calculate the total moles of molecules in a mixture knowing P, V, and T, even though they are different molecules Mixtures of Gases

  34. Mixtures of Gases • the pressure of a single gas in a mixture of gases is called its partial pressure Dalton’s Law of Partial Pressures states that the total pressure of a mixture of gases is the sum of all the partial pressures of the components of the mixture Mixtures of Gases

  35. Starting with… Dalton’s Law From the I.G.E. The gases are at the same temperature and volume, so… Mixtures of Gases

  36. Rearranging the last equation The ratio of moles of “a” to the total moles is called the mole fraction, χa. These equations are also valid for more complicated mixtures of gases. Mixtures of Gases

  37. When working with gas mixtures, the I.G.E. can still be used but now n refers to the total number of moles. Example : What’s the total pressure of 78 moles of N2, 21 moles of O2 and 1 mole of Ar, confined to a volume of 100.0L and a temperature of 300K ? Mixtures of Gases

  38. Mixtures of Gases

  39. Collecting Gases • 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 • 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 • Table 5.4* Mixtures of Gases

  40. Mixtures of Gases

  41. Gases in Chemical Reactions Given the following reaction ; Δ NaN3 (s) 2 Na(l) + 3 N2 (g) How many grams of sodium azide (NaN3) are needed to generate 50.0L of N2 at 25.0oC and 800 mmHg ? Gases in Chemical Reactions

  42. Given the following reaction ; catalyst CO(g) + Cl2 (g) COCl2 (g) What volume of CO is required to completely react with 25.0 L of Cl2 if both gases are initially at the same temperature and pressure ? What mass of CO is required to completely react with 25.0 L of Cl2 at a temperature of 300oC and a pressure of 1.50 atm ?

  43. Kinetic Molecular Theory Basic postulates are ; 1. The size of a particle is very small. 2. The average kinetic energy of a particle is proportional to the temperature (in K). 3. All collisions are elastic. Can use these postulates to mathematically derive the Ideal Gas Equation (see text – page 216).

  44. According to KMT, particles of different masses must have the same average KE at a given temp. This requires that at a given temperature the lighter particles travel faster (on average) than the heavier ones. Avg. KE of one mole of gas particles Postulate 2 in KMT

  45. Ideal vs. Real Gases • Real gases often do not behave like ideal gases at high pressure or low temperature • Ideal gas laws assume • at low temperatures and high pressures these assumptions are not valid Real Gases

  46. Effect of Molecular Volume • at high pressure, the amount of space occupied by the molecules is a significant amount of the total volume • the molecular volume makes the real volume larger than the ideal gas law would predict Real Gases

  47. van der Waals modified the ideal gas equation to account for the molecular volume • b is called a van der Waals constant and is different for every gas because their molecules are different sizes Real Gases

  48. Effect of Molecular Interactions • at low temperature, the attractions between the molecules is significant • the intermolecular attractions makes the real pressure less than the ideal gas law would predict • van der Waals modified the ideal gas equation to account for the intermolecular attractions • a is called a van der Waals constant and is different for every gas because their molecules are different sizes Real Gases

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