Lecture 22: W 10/12 Lecture 23: F 10/14 (Special lecture by Dr. Ben Lear) Lecture 24: M 10/17

Transcription

1 Week 8: Lectures Lecture 22: W 10/12 Lecture 23: F 10/14 (Special lecture by Dr. Ben Lear) Lecture 24: M 10/17 Reading: BLB Ch Homework: BLB 10: 23, 30, 45, 5, 71, 75, 82, 83, 84; Supp 10: 1 15 Reminder: No Angel Quiz on Thur 10/13 ALEKS Objective 8 due on Tue 10/18 Angel Quiz 8 due on Thur 10/20 Jensen Office Hour: 501 Chemistry Building Thursday 10/13: cancelled Tuesday 10/18: 10:30 11:30 am Gas Molecules Characteristics! Gas molecules are constantly moving expand in whatever volume is available mix completely with one another! They are far apart (10 times as far as they are big) can be easily compressed! They move in straight lines! They collide with each other! They collide with walls: pressure! Higher temperature yields faster motion! Lower temperature yields slower motion and eventually condensation Gases are described in terms of: pressure (P), temperature (T), volume (V), # moles (n) All gases behave similarly at low pressure Gases will mix in all proportions with other gases to form homogeneous mixtures Jensen Chem 110 Chap 10 Page: 1 Jensen Chem 110 Chap 10 Page: 2

2 Pressure Pressure: force per unit area Force: Kg m s 2, or Newton (N); Unit area: m 2 SI unit for pressure: 1 N m 2 = 1 Pa (Pascal) Standard Atmospheric Pressure**: 1 atm = x 10 5 Pa 1 atm = 760 torr (or mm Hg) [1 atm = 14.7 lb/in 2 ] Measuring Pressure Barometer used to measure P atm The key idea is balance force on area P atm = P Hg P atm = F atm /A P Hg = F l /A = gd l h so, d l = density of liquid (here: Hg) g = gravitational constant P atm = constant x h P atm P Hg P atm " height (h) of column of liquid Measure P in terms of height of Hg 1 atm = 760 torr = 760 mm Hg [know this conversion!] Jensen Chem 110 Chap 10 Page: 3 Jensen Chem 110 Chap 10 Page: 4

3 Mercury Manometer Used to measure the difference in pressure between open or closed end and that of a gas in a vessel. Closed Ended: P g = h (mm Hg) Open Ended: Which P is greater? Example: The height of the column of mercury in the open-ended manometer shown is found to be 65 mm. If the external pressure is 1.06 atm, what is the gas pressure inside the bulb? A atm B atm C atm D atm E. The pressure cannot be determined from the information given. P gas = P atm P h P gas = P atm P h Jensen Chem 110 Chap 10 Page: 5 Jensen Chem 110 Chap 10 Page: 6

4 Understanding Gases State of gas is described by: n = moles of gas P = pressure V = volume of container T = (absolute) temperature (K = C )! Boyle s Law (volume & pressure) V of a fixed amount of gas at constant T is inversely proportional to P V " 1/P or PV = constant (T,n fixed) STP: standard temperature & pressure (T = K; P = 1 atm) Three foundational relationships:! Boyle!s Law (P and V)! Charles! Law (V and T)! Avogadro!s Law (V and moles) Combining these three to one equation The ideal Gas Law (P, V, T, and moles): P V = n R T! Charle s Law (volume & temperature) V of fixed amount of gas at constant P is proportional to the absolute temperature V " T or V/T = constant (P,n fixed) Note: T in absolute temperature (K)! K = C Jensen Chem 110 Chap 10 Page: 7 Jensen Chem 110 Chap 10 Page: 8

5 ! Avogadro s Law (volume & moles) V of gas at constant T and P is proportional to the number of moles of gas: V " n or V/n = constant (P,T fixed) V n Using Ideal Gas Law: P V = n R T! Given 3 quantities, solve for the 4th Example: What is the volume occupied by 1 mol of gas at exactly 0 C and 1atm (STP)? So far: V! 1/P (Boyle!s law) V! T (Charles!s law) V! n (Avogadro!s law) Combining these three to one equation: Ideal Gas Law: P V = n R T Units of R (gas constant) are very important! Jensen Chem 110 Chap 10 Page: 9 Jensen Chem 110 Chap 10 Page: 10

6 Practice Example: How many molecules comprise one breath of air with a volume of 2.5 L at body temperature (37 ºC) and a pressure of 750 mm Hg? A. 5.8 x B. 4.4 x C. 6.2 x D. 6.7 x E. 6.0 x 10 23! Changes in P, V, T Given: initial conditions of P i, V i, T i final conditions of any two quantities Find: Value for the third final value Example: A sample of gas at 25 C and 1.0 atm in a 2.5 L vessel is allowed to expand until the pressure is 0.85 atm and the temperature is 15 C. What is the final volume of the gas? Jensen Chem 110 Chap 10 Page: 11 Jensen Chem 110 Chap 10 Page: 12

7 Practice Example: At 27 C and 1.00 atm, a sample of He gas (2.35 mol) occupies 57.9 L. What is the volume of this sample at 150 C and 1.00 atm? Summary: Ideal Gas Law PV = nrt A L B L C L D L E L At STP (What T and P? ), 1mol of any gas has molar volume V STP = L. Jensen Chem 110 Chap 10 Page: 13 Jensen Chem 110 Chap 10 Page: 14

8 Application of the Ideal Gas Law: Density and Molar Mass Density and Molar Mass At the same T and P, density is to molar mass. Example: Which of these gases has a density of 3.42 g/l at 30 C and 1.2 atm? Ideal Gas Law: P V = n R T A. He B. Cl 2 C. F 2 D. Kr E. Xe Jensen Chem 110 Chap 10 Page: 15 Jensen Chem 110 Chap 10 Page: 16

9 Practice Example: What is the density of ammonia (NH 3 ) gas in a 4.32 L container at 837 torr and 45 C? A g/l B g/l C g/l D g/l E x 10 2 g/l Gas Mixtures: Partial and Total 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 of the gas mixture is equal to the sum of partial pressures Mole fraction: dimensionless & must sum to 1 Partial pressure: Jensen Chem 110 Chap 10 Page: 17 Jensen Chem 110 Chap 10 Page: 18

10 Example: 3.0 L 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? Practice Example: What is the partial pressure of O 2 in the vessel below? P tot = 756 torr Gas Mole fraction T = C Ar V TOT =5.00 L N CO Ne O 2? What is the total pressure in the 10 L vessel? A torr B. 242 torr C. 380 torr D. 680 torr E. 756 torr How many moles of CO 2 are in this vessel? Jensen Chem 110 Chap 10 Page: 19 Jensen Chem 110 Chap 10 Page: 20

11 Collecting gases over water P total = P gas + P H2O barometric pressure vapor pressure Example: A student collected 201 ml of H 2 over water at 27 o C and a barometric pressure of 733 torr. The vapor pressure of water at 27 o C is torr. How many grams of H 2 were collected? A g B x 10!2 g C. 130 g D x 10!3 g E x 10!2 g If you know the barometric pressure, you can determine the partial pressure of gas by using the vapor pressure of H 2 O (Appendix B, P vap of H 2 O) Jensen Chem 110 Chap 10 Page: 21 Jensen Chem 110 Chap 10 Page: 22

12 Kinetic Molecular Theory (KMT) Temperature and Molecular Speed KMT explains why gases behave the way they do; look at gases on a molecular level The 5 key postulates of KMT 1. Molecules move in straight lines; but their directions are. # = average kinetic energy of molecule u = average (root mean square) speed of molecule m = mass of molecule (in kg) 2. Molecules are small (The volume they occupy is small compared to the total volume) they have volume. 3. There are intermolecular forces (molecules do not attract or repel each other). 4. Molecules experience elastic collisions 5. Mean kinetic energy # " T (in K) " Distribution of molecular speeds: Some molecules move more slowly; some move faster. " When T increases, less molecules move, more molecules move, so the average molecular speed. Jensen Chem 110 Chap 10 Page: 23 Jensen Chem 110 Chap 10 Page: 24

13 KMT explains the behaviors of ideal gases At constant n and V; P increases as T increases. Average Molecular Speed, Molar Mass, and Temperature T increases, #, u ; more collisions per unit time & harder collisions so P increases At constant n and T, P decreases as V increases. " At the same T, different gases have average kinetic energy (#). Constant T means constant # & u. longer distances between collisions & fewer collisions per unit time with walls so P decreases (Boyle!s Law) " At the same T, different gases have average speeds (u) " At a given temperature, the a gas is, the its average molecular speed will be. Jensen Chem 110 Chap 10 Page: 25 Jensen Chem 110 Chap 10 Page: 26

14 Average Molecular Speed and Molar Mass Practice Example: All three gas containers below have V = 1 L and T = 25 C. Which of the following statements is/are true? Example: What is the average speed of O 2 at 20 C? Note: use R = 8.314J/(mol K) and M in kg/mol. 1. The average molecular speed is the same in all three samples. 2. The pressure is the same for all three samples. 3. The average molecular kinetic energy is the same in all three samples. A. 1 only B. 2 only C. 3 only D. 1 and 2 E. 2 and 3 Jensen Chem 110 Chap 10 Page: 27 Jensen Chem 110 Chap 10 Page: 28

15 Other Properties of Gases Effusion Rate and Molar Mass Example: An unknown gas effuses at a rate of times H2 gas at 25 C. What is the molar mass of the gas? Effusion: leakage of gas through a small opening Diffusion: spread of gas through space or second substance. Rate of effusion (or diffusion) " 1 M Usually we compare the effusion (or diffusion) rate of two gases: Graham!s law: $ Heavy molecules effuse (diffuse) more slowly than lighter molecules Jensen Chem 110 Chap 10 Page: 29 Jensen Chem 110 Chap 10 Page: 30

16 Practice Example: A sample of N 2 gas (2.0 mmol) effused through a pinhole in 5.5 s. How long will it take for the same amount of CH 4 to effuse under the same conditions? A. 7.3 s B. 5.5 s C. 3.1 s D. 4.2 s E. 9.6 s Collisions and Diffusion " At STP molecules collide ~10 10 times per second. N 2 speed = 500 m/s but in 1 s it collides times " This means that although molecular speeds are high at STP, molecules don t go very far net distance traveled << (speed x time) " Mean free path (MFP): distance between collisions. MFP is ~6x10-8 m at 1 atm for air molecules What happens to the MFP as density and P decrease? Jensen Chem 110 Chap 10 Page: 31 Jensen Chem 110 Chap 10 Page: 32