Mary J. Bojan Chem 110 Mixture of gases Mix 5 moles of CO2 V = 40L 2 moles of N2 T = 0°C 1 mole of Cl2 What is P ? 1Mary J. Bojan Chem 110 Partial Pressure Partial pressure: the pressure a gas would have if it was the only gas in the container. Dalton’s Law of Partial Pressures Total pressure is equal to the sum of partial pressures. The fraction of the total pressure contributed by each gas is equal to its mole fraction: ΧI 2Mary J. Bojan Chem 110 Sample Problem 3.0L of He at 5.0 atm and 25°C is combined with 4.5 L of Ne at 2.0 atm and 25°C at constant T into a 10L vessel. What is the partial pressure of the He in the 10L vessel? 3 What is the total pressure in the 10L vessel?Mary J. Bojan Chem 110 Sample Problem What is the partial pressure of O2 in the vessel? 1. 75.6 torr 2. 378 torr 3. 680 torr 4. 756 torr 5. There is not enough data. 4Mary J. Bojan Chem 110 Composition of the atmosphere mole fraction: N2 and O2 represent > 99% of atm 5 € xi=moles of itotal molesMary J. Bojan Chem 110 Composition of the atmosphere Eg. Neon xNe = 0.00001818 Ne concentration = 18.18 ppm For other components use parts per million (ppm). ppm = xi × 106 6 If you know the barometric pressure, you can determine the partial pressure. PBAR = 0.987 atm= PTOT PNe = xNe PTOT = 18.18×10-6 ( 0.987 atm) = 17.94×10-6 atmMary J. Bojan Chem 110 Collecting Gas over water Example: During a reaction, N2 is collected over H2O. Pbar = 742 torr (= PTOT) V = 55.7 ml T = 23°C 7 How much N2 (moles) was collected?Mary J. Bojan Chem 110 Temperature Profile Thermosphere: High energy radiation is absorbed Ions formed. Mesosphere: Density of gases is small. Stratosphere: Warming caused by ozone cycle Ultraviolet light absorbed Troposphere: Life: where we live! – weather – planes 8 Regions of Atmosphere What is temperature?Mary J. Bojan Chem 110 KINETIC MOLECULAR THEORY • gives a view of gases on a molecular level • 5 key postulates 1. Molecules move in straight lines; their direction is random. 2. Molecules are small. (The volume they occupy is small compared to the total V.) 3. Molecules do not attract or repel each other (no intermolecular forces). 4. Elastic collisions 5. Mean kinetic energy ε ∝ T(K). 9 IfMary J. Bojan Chem 110 T ∝ ε = 1/2 mu2 ε = average kinetic energy of molecule u = (root mean square) speed of molecule m = mass of molecule (in kg) When T increases: • less molecules move slowly • more molecules move quickly • average speed is greater 10Mary J. Bojan Chem 110 Kinetic Molecular Theory provides explanations for why gases behave as they do. Experimentally Observed Behavior P∝T (n,V fixed) As T increase; P increases. WHY? 11Mary J. Bojan Chem 110 Why gases behave as they do Experimentally Observed Behavior V∝1/P (n,T constant) As V increase V, P decreases WHY? 12Mary J. Bojan Chem 110 Kinetic Molecular Theory of Gases 3/2 RT = ½ Mu2 • different gases (at the same T) have different average speeds • On average: lighter gases move faster heavier gases move slower 13Mary J. Bojan Chem 110 What is the rms speed (u) of N2 at 20°C? 14Mary J. Bojan Chem 110 Motion of gases Effusion: leakage of gas through a small opening Rate of effusion (diffusion) Diffusion: spread of gas through space. Usually we compare the rate of two gases Graham’s Law Heavy molecules effuse (diffuse) more slowly than lighter molecules. 15Mary J. Bojan Chem 110 Motion of Gases An unknown gas effuses at a rate 1.49 times as fast as Cl2. What is the molecular weight of the gas? 16Mary J. Bojan Chem 110 Non-Ideal Gas Behavior PV=nRT for low P high T Real gases deviate from ideal behavior 2. Molecules exert attractive forces. In general As P increases, non-ideality increases. As T decreases, non-ideality increases. 17 Reasons: 1. Molecules have finite size.Mary J. Bojan Chem 110 At high P, Postulate 2 in KMT not true • As P increases PV/RT increases (H2) V of container is not >> than V of gas use of ideal gas law leads to appearance of larger n. 18Mary J. Bojan Chem 110 At low T, postulate 3 in KMT not true • As P increases PV/RT decreases (CO2) attractive forces lead to the appearance of a smaller n (molecules stick together) 19 Different gases behave differently Eg. CO2 has stronger intermolecular forces than CH4, or N2, therefore it deviates more from ideality at low pressures.Mary J. Bojan Chem 110 Behavior at high T As T increase, effect if intermolecular forces is not as pronounced. 20 One mole of the same gas at different temperatures.Mary J. Bojan Chem 110 Correcting the ideal gas law • at intermediate pressures, P is too small. deviation is related to: size of attractive interactions (a) frequency of collisions • at high pressure, V is too large actual V = Vcont − Vexcluded = V − nb b ⇒ volume per mole of molecules (P + ) (V − ) = nRT van der Waals Equation 21 € a nV⎛ ⎝ ⎜ ⎞ ⎠ ⎟
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