Mixture of gases. Mix 5 moles of CO 2 V = 40L 2 moles of N 2 T = 0 C 1 mole of Cl 2 What is P? Mary J. Bojan Chem 110

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1 Mixture of gases Mix 5 moles of CO 2 V = 40L 2 moles of N 2 T = 0 C 1 mole of Cl 2 What is P? 1

2 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: Χ I 2

3 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? What is the total pressure in the 10L vessel? 3

4 Sample Problem What is the partial pressure of O 2 in the vessel? torr torr torr torr 5. There is not enough data. 4

5 Composition of the atmosphere mole fraction: x i = moles of i total moles N 2 and O 2 represent > 99% of atm 5

6 Composition of the atmosphere For other components Eg. Neon use parts per million (ppm). ppm = x i 10 6 x Ne = Ne concentration = ppm If you know the barometric pressure, you can determine the partial pressure. P BAR = atm= P TOT P Ne = x Ne P TOT = ( atm) = atm 6

7 Collecting Gas over water Example: During a reaction, N 2 is collected over H 2 O. P bar = 742 torr (= P TOT ) V = 55.7 ml T = 23 C How much N 2 (moles) was collected? 7

8 Regions of Atmosphere 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 What is temperature? 8

9 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 If 5. Mean kinetic energy ε T(K). 9

10 T ε = 1/2 mu 2 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 10

11 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? 11

12 Why gases behave as they do Experimentally Observed Behavior V 1/P (n,t constant) As V increase V, P decreases WHY? 12

13 Kinetic Molecular Theory of Gases 3/2 RT = ½ Mu 2 different gases (at the same T) have different average speeds On average: lighter gases move faster heavier gases move slower 13

14 What is the rms speed (u) of N 2 at 20 C? 14

15 Motion of gases Effusion: leakage of gas through a small opening Usually we compare the rate of two gases Graham s Law Diffusion: spread of gas through space. Rate of effusion (diffusion) Heavy molecules effuse (diffuse) more slowly than lighter molecules. 15

16 Motion of Gases An unknown gas effuses at a rate 1.49 times as fast as Cl 2. What is the molecular weight of the gas? 16

17 Non-Ideal Gas Behavior PV=nRT for low P high T Real gases deviate from ideal behavior Reasons: 1. Molecules have finite size. 2. Molecules exert attractive forces. In general As P increases, non-ideality increases. As T decreases, non-ideality increases. 17

18 At high P, Postulate 2 in KMT not true As P increases PV/RT increases (H 2 ) V of container is not >> than V of gas use of ideal gas law leads to appearance of larger n. 18

19 At low T, postulate 3 in KMT not true As P increases PV/RT decreases (CO 2 ) attractive forces lead to the appearance of a smaller n (molecules stick together) Different gases behave differently Eg. CO 2 has stronger intermolecular forces than CH 4, or N 2, therefore it deviates more from ideality at low pressures. 19

20 Behavior at high T As T increase, effect if intermolecular forces is not as pronounced. One mole of the same gas at different temperatures. 20

21 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 = V cont V excluded = V nb b volume per mole of molecules a n V 2 (P + ) (V ) = nrt van der Waals Equation 21