1. Gas Laws By: Ms. Buroker

2. Gas Laws Gas Laws explores the relationships between: Volume, V … Liters Temperature, T … Kelvin Amount, n … moles Pressure, P … atm

3. Pressure Measured in mmHg (often called the torr) 1atm = 760mmHg = 760 torr = 101,325Pa Pressure = Force Area

4. Devices Used to Measure Pressure Mercury Barometer: The atmospheric pressure pushes the mercury column up 760mm, before the weight (Force) of the column down per unit area is equal to the upward pressure (Note the vacuum above the Hg column in the tube) 1mmHg = 1torr Pressure Units Summary: 1atm = 760mmHg (torr) = 101,300Pa = 101.3kPa (also 29.92”Hg, 1.013bar, 14.7psi)

5. Open End Manometer

6. Boyle’s Law “Think Pressure and Volume” The volume is inversely proportional to the pressure Gases that strictly obey Boyle’s Law are called ideal gases P 1 V 1 = P 2 V 2 *Temperature is held constant

7. Let’s Practice! SO 2 gas, which plays a central role in acid rain, is found in the exhaust of automobiles and power plants. Consider a 1.53L sample of gaseous SO 2 at a pressure of 5.6 x 10 3 Pa. If the pressure is changed to 1.5 x 10 4 Pa at a constant temperature, what will the new volume of gas be? Answer = 0.57L (Does this make sense?) V = 1.53L V = ? 5.6 x 10 3 Pa 1.5 x 10 4 Pa

8. Charles’s Law “Think Volume and Temperature” Temperature and volume are directly proportional V 1 = V 2 T 1 T 2 *Pressure is held constant

9. Let’s Practice A sample of gas at 15 ○ C and 1atm has a volume of 2.58L. What volume will this gas occupy at 38 ○ C and 1atm? Answer: 2.79L

10. Avogadro’s Law STP … 1 mol of any gas at standard temperature and pressure occupies 22.4L!!

11. Ideal Gas Law Boyle’s Law Charles’s Law Avogadro’s Law PV = nRT The ideal gas law is an equation of state for a gas, where the state of the gas is its condition at a given time. We must recognize that the ideal gas law is an empirical equation – it is based in experimental measurements of the properties of gases. Universal Gas Constant 0.08206 L. atm/mol. K This law expresses the behavior that real gases approach at low pressures and high temperatures …. therefore, it is hypothetical.

12. Let’s Practice! A sample of hydrogen gas (H 2 ) has a volume of 8.56L at a temperature of 0 ○ C and a pressure of 1.5atm. Calculate the moles of H 2 molecules present in this gas sample. Answer = 0.57mol The reaction of Zn with HCl produces bubbles of H 2 gas.

13. Let’s Practice Again! Suppose we have a sample of ammonia gas with a volume of 7.0mL at a pressure of 1.68atm; the gas is compressed to a volume of 2.7mL at a constant temperature. Use the ideal gas law to calculate the final pressure. A sample of methane gas that has volume of 3.8L at 5 ○ C is heated to 86 ○ C at constant pressure. Calculate its new volume.

14. One More … I promise! A sample containing 0.35mol argon gas at a temperature of 13 ○ C and a pressure of 568torr is heated is heated to 56 ○ C and a pressure of 897torr. Calculate the change in volume that occurs.

15. Let’s Re-visit …STP “Standard Temperature Pressure” 1 mole of any gas at STP (273K and 1atm) occupies 22.42L. This volume of 22.42 liters is the MOLAR VOLUME if an ideal gas

16. Gas Stoichiometry 1 A sample of nitrogen gas has a volume of 1.75L at STP. How many moles of N 2 are present? 1.75L N 2 X 1 mol N 2 = 0.0781mol N 2 22.42L N 2

17. Gas Stoichiometry 2 Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate (CaCO 3 ). Calculate the volume of CO 2 at STP produced from the decomposition of 152g CaCO 3 by the reaction CaCO 3(s)  CaO (s) + CO 2(g) Answer = 34.1 L CO 2 at STP

18. Gas Stoichiometry 3 A sample of methane gas having a volume of 2.80L at 25 ○ C and 1.65atm was mixed with a sample of oxygen gas having a volume of 35.0L at 31 ○ C and 1.25atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO 2 formed at a pressure of 2.50atm and a temperature of 125 ○ C.

19. Molar Mass of a Gas It is possible to calculate the molar mass of a gas from its density. Molar Mass = dRT P The density of a gas was measured at a 1.50atm and 27 ○ C and found to be 1.95 g/L. Calculate the molar mass of the gas.

20. Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone. P Total = P 1 + P 2 + P 3 + ….. Thus, for a mixture of ideal gases, it is the total number of moles of particles that is important, not the identity or composition of the involved gas particles.

21. NOTE!!!!!! The fact that pressure exerted by an ideal gas is not affected by the identity of the gas particles reveals two things about ideal gases: 1.) The volume of the individual gas particle must not be important. 2.) The forces among the particles must not be important.

22. Practice Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent “the bends.” For a particular dive, 46L He at 25 ○ C and 1.0atm and 12L O 2 at 25 ○ C and 1.0atm were pumped into a tank with a volume of 5.0L. Calculate the partial pressure of each gas and the total pressure in the tank at 25 ○ C. Answer: P He = 9.3atm, P O 2 = 2.4atm, P Total = 11.7atm

23. Collecting a Gas Over Water A gas which is not soluble (or only slightly soluble) in water can be collected over water. E.g.: H 2 and O 2soluble A tube from the flask which is giving off the gas is placed under water. A test tube full of water is placed upside down above the end of the tube to collect the gas.

24. When gases are collected by water displacement, some of the water “vaporizes” at the given temperature so that the total pressure inside the container is the sum of the collected sample gas and the vapor pressure due to water Water vapor pressure is a function of temperature and must be looked up Collecting a Gas Over Water

25. Practice A sample of solid potassium chlorate was heated in a test tube and decomposed by the following reaction: 2KClO 3(s)  2KCl (s) + 3O 2(g) The oxygen produced was collected by displacement of water at 22 ○ C at a total pressure of 754torr. The volume of gas collected was 0.650L, and the vapor pressure of water at 22 ○ C is 21torr. Calculate the partial pressure of O 2 in the gas collected and the mass of KClO 3 in the sample that was decomposed.

26. Kinetic Molecular Theory

27. Effusion and Diffusion Diffusion is the term used to describe the mixing of gases. Effusion is the movement of gas through a tiny opening in a container into another container where the pressure is very low.

28. Effusion

29. Practice Calculate the ratio of effusion rates of H 2 and uranium hexafluoride (UF 6 ), a gas used in the enrichment process to produce fuel for nuclear reactors.

30. Practice #2 A gas takes 3.50 times longer to effuse than helium. Determine the molar mass of the gas. MM = 4.00(3.50) 2 Molar mass of unknown gas is 49.0g/mol

31. Real Gases An ideal gas is a hypothetical concept. No gas exactly follows the ideal gas law, although many gases come very close at low pressures and/or high temperatures. Thus ideal gas behavior can best be thought of as the behavior approached by real gases under certain conditions.