The Behavior of Gases

Review of KMT of Gases Assumptions Gases consist of tiny particles far apart from one another Collision between gas particles are elastic, with no loss of KE Gas particles are in constant, rapid motion. No forces of attraction or repulsion exist between gas particles Average KE of particles depends on absolute temperature of the gas

Review of Pressure Pressure is force per unit area SI unit of force is the Newton (N) SI unit of pressure is the pascal 1Pa = 1N/m2

14.1 Properties of Gases Compressibility Factors affecting Gas Pressure Amount of gas (n) number of particles, i.e. moles of gas Volume (V) space occupied by the gas Temperature (T, absolute temperature) Recall TK = TC + 273

14.2 The Gas Laws The gas laws describe the relationship of the 4 important variables that describe gas behavior Pressure (P) Moles (n) Volume (V) Temperature (T in Kelvins)

Boyle’s Law: Pressure & Volume Volume is inversely related to Pressure When Pressure increases, Volume decreases If temperature and moles are constant

Practice Problems page 419 Given a volume of 2.50 L, if the pressure of N2O (an anesthetic) decreases from 105 kPa to 40.5 kPa, what is its new volume? (assume n & T are constant) If 4.00 L of NH3 at 205 kPa is allowed to expand to 12.0L, what is the new pressure if T and n remain constant?

Charles’ Law: Volume and Temperature Volume is directly proportional to absolute temperature When temperature of an enclosed gas increases, its volume increases If pressure is constant

Sample Problems page 421 If a sample of CO2 occupies a volume of 6.80 L at 325ºC, what will its volume be at 25ºC if the pressure does not change? Exactly 5.00 L of air at -50.0ºC is warmed to 100.0ºC. What is the new volume if pressure remains constant?

Gay-Lussac Law: Pressure and Temperature Pressure is directly proportional to absolute temperature As the temperature of an enclosed gas increases, its pressure increases if volume is constant

Gay-Lussac Law

Sample Problems page 423 A sample of N2 gas has a pressure of 6.58 kPa at 539K. If the volume does not change, what will the pressure be at 211K? The pressure in a car tire is 198 kPa at 27ºC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire?

The Combined Gas Law: Pressure, Volume and Temperature Combines Boyle’s, Charles’, and Gay-Lussac’s Laws Relates pressure, volume and temperature

Sample Problems page 424 A gas at 155 kPa and 25ºC has an initial volume of 1.00L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125ºC. What is the new volume? A 5.00 L sample of air has a pressure of 107 kPa at 50.0ºC. If the temperature is raised to 102ºC and the volume expands to 7.00 L, what will the new pressure be?

14.3 Ideal Gases Gases at ordinary temperatures and pressures comply with the assumptions of the KMT of gases These are called ideal gases Gases at extremely low temperatures and/or extremely high pressures do not These are called real gases

Avagadro’s Law: Moles & Volume The volume of a confined gas is directly proportional to moles of a gas If the moles of gas increases, the volume of the gas increases If temperature and pressure are constant n = kV n/V = k n1/V1 = n2/V2

Practice Problem A cylinder of gas with a moveable piston contains 2.00 mol N2 with a volume of 11.0 L. What is the new volume if 1.50 mol of CO2 is injected into the cylinder? Assume that pressure and temperature are unchanged and that the N2 and CO2 do not react with one another. 19.3 L

Molar Volume of Gases: Remember This! At STP, the standard molar volume of any gas is 22.4L One mole of a gas has a volume of 22.4L at STP Use this as a conversion factor when solving stoichiometry problems involving gases

Practice Problems A chemical reaction produces 0.0680 mol of oxygen gas. What is the volume of the gas at STP? A reaction produced 98.0 mL of SO2 gas at STP. a. How many moles of SO2 were produced? b. What was the mass in grams of the gas? c. What is the density of the gas?

14.3 Ideal Gas Law: Pressure, Volume, Moles, Temperature A single law that relates pressure, volume, moles, and temperature of a gas PV=nRT n is number of moles of gas R is the ideal gas constant Value of R varies depending on units used for pressure and volume

The Ideal Gas Constant

Sample Problems A rigid hollow sphere containing 685 L He has a temperature of 621K and a pressure of 1.89 x 103 kPa. How many moles of He are in the sphere? (251 mol) What volume will 12.0 g of methane gas (CH4) occupy at a temperature of 25ºC and pressure of 0.52 atm? A gaseous product of a reaction is collected in a 30.0 L container at 25ºC. The measured pressure of the gas was 150 kPa. The mass of gas produced was about 116 g. What is the molar mass of the gas?

Ideal Gases and Real Gases Ideal gases are real gases which comply with the ideal gas equation Real gases deviate from the ideal gas equation at low temperatures and high pressures This is because the assumptions of KMT are no longer valid at low T and high P

Real Gases Deviate from the Ideal

14.4 Gas Mixtures and Movements Very often gases are mixtures Pure substances Homogeneous mixtures Solutions The total pressure of a mixture of gases is the sum of the pressures of each individual gas (component gas) in the mixture

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases is the sum of the partial pressure of each component of the mixture Partial pressure is the pressure of each gas within a mixture of gases

Example of Dalton’s Law If you mix 2 moles O2 at 0.12 atm with 2 moles of N2 at 0.12 atm, the total pressure is the sum of the partial pressures. Do Problem 32, p. 434

Mole Fraction can be used to calculate partial pressures The mole fraction of a gas is the moles of a gas divided by the total moles of gas in a mixture X = moles x/ total moles In a mixture of 200 moles of O2 and 500 moles N2, what is the mole fraction of O2? XO2 = 200 mol O2/700 mol = 0.29 Suppose this mixture had a total pressure of 600 kPa. What is the PO2? PO2 = XO2 · Ptotal = 0.29 x 600 kPa = 174 kPa

Graham’s Law of Effusion Diffusion Movement of molecules from an area of higher concentration to lower concentration

Effusion Effusion Rate of effusion Movement of gas molecules through a pinhole Rate of effusion How much gas effuses per second Sometimes velocity is used

Graham’s Law of Effusion At a given temperature, lower mass molecules diffuse and effuse faster than greater mass molecules This is because they have the same KE KE = ½ mv2