1. Chemistry Chapter 5 Gases Dr. Daniel Schuerch

2. Gas Pressure Gas pressure is the result of simultaneous collisions of billions of rapidly moving particles in a gas with an object –An empty place with no particles and no pressure is called a vacuum Atmospheric pressure results from the collisions of atoms and molecules in the air with objects –Decreases with increasing altitude Barometers are instruments used to measure atmospheric pressure The SI unit of pressure is the pascal (Pa) –Other units of pressure are the atmosphere (atm) and millimeters mercury (mm Hg) 1 atm = 760 mm Hg or Torr = 101.3 KPa = 14.69 psi

3. Properties of Gases Compressibility –A measure of how much the volume of matter decreases under pressure Gases are highly compressible –Due to the large spaces between particles of gas Gas pressure increases as a gas is compressed Factors affecting gas pressure –Amount of gas Increased gas at constant volume and temperature = increased pressure –Volume Decreased volume at constant amount of gas and temperature = increased pressure –Temperature Increased temperature at constant amount of gas and volume = increased pressure –Four common variables are used to describe gases are pressure (P) in atmospheres (atm), volume (V) in liters (L), and temperature (T) in kelvins (K), and the number of moles (n)

4. The Gas Laws: Boyle’s Law Pressure and Volume Plot of V vs. 1/P gives a strait line

5. The Gas Laws: Boyle’s Law Pressure and Volume Question: 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 temperature remains constant.

6. The Gas Laws: Boyle’s Law Pressure and Volume In a study to see how closely gaseous ammonia obeys Boyle’s law, several volume measurements were made at various pressures, using 1.0 mol NH 3 gas at a temperature of 0°C. Using the results listed below, calculate the Boyle’s law constant for NH 3 at the various pressures. ExperimentPressure (atm)Volume (L) 10.1300172.1 20.250089.28 30.300074.35 40.500044.49 50.750029.55 61.00022.08

7. The Gas Laws: Charles’s Law Temperature and Volume

8. Question: A balloon inflated in a room at 24ºC has a volume 4.0 L. The balloon is then heated to a temperature of 58ºC. What is the new volume if the pressure remains constant?

9. The Gas Laws: Gay-Lussac’s Law Pressure and Temperature

10. Question: The gas in a used aerosol can is at a pressure of 103 kPa at 25ºC. If the can is thrown into a fire, what will the pressure be when the temperature reaches 928ºC?

11. Gas Laws: Avogadro’s Law Volume and Moles Volume 1 / moles 1 = Volume 2 / moles 2

12. Gas Laws: Avogadro’s Law Volume and Moles Question: A 12.2 L sample containing 0.5 moles of O 2 gas at a pressure of 1 atm and temperature of 25 ºC converts to ozone O 3 at the same pressure and temperature. What will be the volume of ozone formed?

13. The Gas Laws: The Combined Gas Law The combined gas law describes the relationship among the pressure, temperature, and volume of an enclosed gas –The combined gas law allows you to do calculations for situations in which only the amount of gas is constant Question: 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? P 2 x V 2 T2T2 = T1T1 P 1 x V 1

14. Ideal Gases Ideal gas law P x V = n x R x T –P is pressure in atmospheres (atm) –V is volume in Liters (L) –n is the number of moles (n) –R is a constant equal to 0.08206(L·atm)/(K·mol) –T is the temperature in kelvin The ideal gas law allows the calculation of the number of moles of a contained gas at conditions that differ from standard temperature and pressure

15. Use the ideal gas law to find the amount of gas A deep underground cavern contains 2.24x10 6 L of methane gas (CH 4 ) at a pressure of 1.50x10 3 kPa and a temperature of 315 K. How many kilograms of CH 4 does the cavern contain? P x V = n x R x T

16. Use the ideal gas law to solve 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 1.89x10 3 kPa. How many moles of helium does the sphere contain? P x V = n x R x T

17. Use the ideal gas law to solve A sample containing 0.35 mol argon gas at a temperature of 13°C and a pressure of 568 torr is heated to 56°C and a pressure of 897 torr. Calculate the change in volume that occurs.

18. Ideal Gases and Real Gases Gases are not ideal Real gases differ most from an ideal gas at low temperatures and high pressures

19. Gas Stoichiometry The volumes of one mole of different liquids and solids are different The volumes of different gases at the same pressure and temperature contain an equal number of particles— Avogadro’s Hypothesis At standard temperature and pressure (STP) of one mole (6.02x10 23 particles) of any gas has a volume of 22.4 liters –Standard temperature is 0 ºC –Standard pressure is 1 ATM or 101.3 PA The density of a gas at STP is easily found by dividing the molar mass of the gas by 22.4 liters –Units for the density of a gas is g/L

20. Gas Stoichiometry 1.A container contains thirty liters (30.0L) of argon gas at STP. How many moles of argon are in the container? Volume  Moles 2. A container contains 1.34 moles of argon gas at STP. What is the volume of this container in liters? Moles  Volume 3.What is the density of argon gas at STP?

21. Gas Stoichiometry

22. Molar Mass of Gas

23. The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. What is the molar mass of the gas?

24. Daltons Law of Partial Pressure

25. For a particular dive, 46L Helium at 25°C and 1.0 atm and 12 L oxygen at 25°C and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25°C.

26. Daltons Law of Partial Pressure The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O 2 present.

27. Daltons Law of Partial Pressure The mole fraction of nitrogen in the air is 0.7808. Calculate the partial pressure of N 2 in the air when the atmospheric pressure 760 torr.

28. Daltons Law of Partial Pressure

29. The Nature of Gases Kinetic Theory and a Model for Gases –Kinetic energy is the energy of motion –Kinetic theory states that all matter consist of tiny particles that are in constant motion. –Principles of Kinetic Theory and the Model for Gases 1.Gas particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible. 2.The particles are in constant motion. The collisions of particles with the walls of the container are the cause of the pressure exerted by the gas. 3.The particles are assumed to exert no forces on each other. 4.The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

30. Average Kinetic Energy and Kelvin Temperature The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of a substance –A substance at 200K has twice the average kinetic energy of the same substance at 100K Temperature Energy

31. The meaning of temperature

32. Kinetic Energy and Temperature When heated, particles absorb energy, of which some is stored as potential energy in the particle and does not raise temperature of the substance The remaining energy speeds up particles increasing their kinetic energy Average Kinetic Energy is the kinetic energy somewhere in the middle range of a mass of molecules at a given temperature Kinetic Energy

33. Root Mean Square Velocity

35. Gases: Mixtures and Movement Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout Effusion is the movement of a gas through a tiny hole in its container Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass Graham’s Law of effusion –The rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass Rates of Effusion of two gases Rate A Rate B = Molar mass B Molar mass A

36. Effusion Rate Problem Calculate the ration of the effusion rates of hydrogen gas (H 2 ) and uranium hexafluoride (UF 6 ).

37. Real Gases Ideal gas law only works for gases at low pressures and high temperatures because –As pressure increases: the volume actually available to a given gas molecule decreases attractive interactions (Vander walls forces) between molecules of gasses increases –As temperature decreases: Van der Waals forces between molecules of gasses become significant compared to the kinetic energy of the gas molecules

38. Van der Waals equation for real gases P obs is pressure observed a is a proportionality constant (must be given to you problem) n is number of moles of gas V volume of the container b is an empirical constant determined by experimentation (must be given to you in problem) R is the gas constant 0.08206 L·atm/K·mol T is the temperature in Kelvin Corrected Pressure Corrected Volume P ideal V ideal