The Gaseous State of Matter Chapter 12 The Gaseous State of Matter

12.1 General Properties Least dense, most mobile of the three states Move at high velocities Large kinetic energy Example – Water 1 mol = 18mL @ liquid state 1 mol = 22.4L @ gas state

12.2 The Kinetic-Molecular Theory Boyle’s theory to explain behavior and properties of gases Ideal gasses (low P, high T) Consist of tiny particles Distance between particles is large, mostly empty space Particles have no attraction for each other Particles move in straight lines with frequent collisions with each other and container walls All collisions are perfectly elastic The average KE for all particles is the same for all gases at the same T, value is directly proportional to the T in Kelvin

12.2 Cont’d. KE = ½mv2 Diffusion – 2 or more gases mix spontaneously until they form a uniform mixture Effusion – process by which gas molecules pass through a small opening (from a container of high P to low P) Can use density in place of Molar Mass

12.3 Measurement of Pressure of Gases Pressure – force per unit area Atmospheric Pressure – pressure exerted by the atmosphere Barometer – instrument to measure pressure of gases in the atmosphere

Practice 12.1 A barometer reads 1.12 atm. Calculate the corresponding pressure in: Torr mmHg

12.4 Dependence of Pressure on Number of Molecules and Temperature Pressure is produced by gas molecules colliding with the walls of a container Number of collisions is dependent on the number of particles and temperature Double the number particles, double pressure Increase T, increase P

12.5 Boyle’s Law P1V1 = P2V2 @ constant T

Practice 12.2 A gas occupies a volume of 3.86L @ 0.750atm. At what pressure will the volume be 4.86L?

12.6 Charles’ Law V1/T1 = V2/T2 @ Constant P (T must be in K)

12.3 Practice A 4.50L container of nitrogen gas at 28.0*C is heated to 56.0*C. Assuming that the volume of the container can vary, what is the new volume of the gas?

12.7 Gay-Lussac’s Law P1/T1 = P2/T2 @ constant V (T must be in K) A gas cylinder contains 40.0L of a gas at 45.0*C and has a pressure of 650.torr. What will the pressure be if the temperature is changed to 100*C?

12.8 Combined Gas Law P1V1 = P2V2 STP – Standard Temperature and Pressure T1 T2 0*C and 1 atm (760 torr or 101.325 kPa) 15.00L of gas at 45.0*C and 800.torr are heated to 400.*C, and the pressure is changed to 300.torr. What is the new volume? To what temperature must 5.00L of oxygen at 50.*C and 600.torr be heated in order to have a volume of 10.0L and a pressure of 800.torr?

12.9 Dalton’s Law of Partial Pressures The total pressure of a mixture of gases is the sum of the partial pressures exerted by each of the gases in the mixture. Ptotal = P1 + P2 + P3 + … When a gas is collected over water, the pressure of the gas is found by: Pgas collected = Patm – PH2O

Practice 12.7 Hydrogen gas was collected by downward displacement of water. A volume of 600.0mL of gas was collected at 25.0*C and 740.0torr. What volume will the dry hydrogen gas occupy at STP?

12.10 Avogadro’s Law From Gay-Lussac’s Law  when measured at the same T and P, the ratios of volumes of reacting gases are small whole numbers, which leads to… Avogadro’s Law – Equal volumes of different gases at the same T and P contain the same number of molecules

12.10 Cont’d. Important because: It offered rational explanation of Gay-Lussac’s Law Provided a method for determining molar masses of gases and for comparing densities of gases of known molar masses Gave a firm foundation for the KMT

12.11 Mole-Mass-Volume Relationships of Gases Any mole of a gas will have the same volume as a mole of any other gas at the same temperature and pressure Molar Volume – 1 mole of gas occupies 22.4L @ STP

Practice 12.8 A gas with a mass of 86g occupies 5.00L at 25*C and 3.00atm pressure. What is the molar mass of the gas?

12.12 Density of Gases Density = mass/volume = g/L dSTP = (molar mass)(1mol/22.4L) Molar mass = (dSTP)/22.4L/1mol) These problems  basic unit conversion The molar mass of a gas is 20.g/mol. Calculate the density of the gas at STP.

12.13 Ideal Gas Law PV=nRT R=0.0821 L*atm/mol*K A 23.8L cylinder contains oxygen gas at 20.0*C and 732torr. How many moles of oxygen are in the cylinder? A 0.286g sample of a certain gas occupies 50.0mL at standard temperature and 76.0cmHg. Determine the molar mass of the gas.

12.4 Gas Stoichiometry For reacting gases at constant temperature and pressure, volume-volume relationships are the same mole-mole relationships.

Practice 12.13 What volume of oxygen will react with 15.0L of propane (C3H8) to form carbon dioxide and water? What volume of carbon dioxide will be formed? What volume of water will be formed? C3H8(g) + 5 O2(g)  3 CO2(g) + 4 H2O(g)

12.15 Real Gases Most gases behave according to the gas laws (ideally) over a wide range of temperatures and pressures When molecules become crowded (high P and/or low T) they deviate from ideal behavior Become liquids

Homework Required: 2-48 (even) Suggested: 1-47 (odd)