Gases. What are the four variables needed to describe a gas?

Transcription

1 Gases What are the four variables needed to describe a gas? 1

2 Gases The simplest state of matter K.E. >> intermolecular forces Random motion Predictable behavior 2

3 Gases at STP Few Elements: H 2 N 2 O 2 O 3 F 2 Cl 2 Noble Gases Few Molecules: HF HCl HBr HI CO CO 2 NH 3 NO NO 2 N 2 O SO 2 H 2 S No ionic compounds; WHY? 3

4 KMT of Gases 1. Gas particles (atoms or molecules): Hard spheres Insignificant volume (ignore particle volume) Far apart 4

5 KMT of Gases 2. Particles motion: Straight paths until collision Random motion Fill container 5

6 KMT of Gases 3.Gas particles have no attractions (IM forces) between them. (not quite true) 6

7 KMT of Gases 4. Collisions are perfectly elastic. no energy lost during collision KE before = KE after 7

8 Pressure What is pressure? Collisions of gas particles with the walls of the container impart a force (f) P = force area 8

9 Atmospheric Pressure 9

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11 Gas Variables Four macroscopic variables are needed to describe a gas. P = pressure V = volume T = temperature n = number of moles Interrelated 11

12 You Predict (and Why?) How to increase P? n V T add gas smaller V higher T P = f A 12

13 Gas Laws Boyle s Law Charles Law Avogadro s Law P & V V & T V & n The other two variables are constant. 13

14 Boyle s Law (T,n constant) Relationship of P & V 14

15 P = k 1 V Boyle s Law (T,n constant) P when V or PV = k P 1/V 15

16 Boyle s Law (T,n constant) Condition #1: P 1 V 1 = k same Condition #2: P 2 V 2 = k P 1 V 1 = P 2 V 2 before after 16

17 P 1 V 1 = P 2 V 2 A balloon is filled with 30. L of He at 1.0 atm. What is the new volume of the balloon if it rises to where P = 0.25 atm? 17

18 P 1 V 1 = P 2 V 2 Boyle s law is how your lungs work!! 18

19 Charles Law What happens to the volume of a balloon if temperature is increased? 19

20 Charles Law (P,n constant) T then V V = k T V/T = k (T in Kelvin) before V 1 T 1 = V 2 T 2 after 20

21 Charles Law V/T = k V o C T ( o C) 21

22 Charles Law V 1 /T 1 = V 2 /T 2 A sample of CO occupies 3.20 L at 125 o C. Calculate the temperature at which it will occupy 1.54 L. 22

23 Avogadro s Law: At constant P & T, V a n independent of gas type! Thus any two gas samples with the same P, V, & T will have the same number of particles! 23

24 Kinetic Molecular Theory Explain: Boyle s Law Charles Law Avogadro s Law In terms of KMT (what are the particles doing?) 24

25 Help!!! How are you suppose to remember all these equations? 25

26 Ideal Gas Law: constant V a 1/P V a T V a n V = R nt P PV = nrt pivnert R = universal gas constant Independent of type of gas!! 26

27 PV = nrt Knowing 1 mole of ideal gas occupies 22.4 L at STP, what is the value of R? (units?) R = L atm mol K 27

28 PV = nrt How many moles of N 2 are in a 2.00 L tank at 25 o C and 20. atm? How many grams? 28

29 PV = nrt R = L atm mol K Units must be consistent with R First convert from P in atm. V in liters n in moles T in K kpa, mmhg ml, cm 3 g, kg, #particles o C 29

30 PV = nrt What is the P in a 4.0 L fire extinguisher that contains 260 g CO 2 at T = 30 o C? 30

31 What if conditions of a gas change? R = P 1V 1 n 1 T 1 before change R = P 2V 2 n 2 T 2 after change P 1 V 1 n 1 T 1 = P 2V 2 n 2 T 2 31

32 P 1 V 1 n 1 T 1 = P 2 V 2 n 2 T 2 This can replace Boyle s, Charles, etc. laws. 32

33 P 1 V 1 T 1 = P 2 V 2 T 2 P 1 V 1 = P 2 V 2 Show that the combined gas law reduces to Boyle s law if T and n are constant. 33

34 P 1 V 1 T 1 = P 2 V 2 T 2 Let s step through a problem. The volume of a balloon is 30. L at 40 o C and 150 kpa. What is its volume at STP? P 1 = 150 kpa V 1 = 30. L T 1 = 40 o C = 313 K P 2 = kpa V 2 =? T 2 = 273 K 34

35 P 1 V 1 T 1 = P 2 V 2 T 2 Substitute values. Use same units for all pairs; T in K. (150 kpa)(30.l) (101.3 kpa)v 2 = 313 K 273 K V 2 = 39 L 35

36 Try a Problem!!! Before a long road trip, a car tire has P = 3.1 atm at T = -12 o C. After driving the tire T rises to 45 o C. What is the new P in the tire? 36

37 A 2.1 ml bubble rises from the bottom of a lake where T = 8 o C and P = 6.4 atm to the lake surface where T = 25 o C and P = 1.0 atm. What is new V of the bubble? Try another. 37

38 Which Equation to Use? Use: PV = nrt If conditions don t change. Not on Regents Chart. R = L atm/mol K Units Use P 1 V 1 T 1 = P 2V 2 T 2 Units: T in K If conditions do change. Table T 38

39 What is an Ideal Gas? Ideal gases obey all the assumptions of KMT. Ideal gases obey PV = nrt Most gases under normal T & P behave like ideal gases. 39

40 Real Gases Unlike the statements of KMT: particles do have volume Particles do have IM forces Under what conditions of T & P is a real gas most like an ideal gas? Why? high T & low P 40

41 Dalton s Law of Partial Pressures Every gas in a mixture of gases (for example, air) adds to the total pressure as if it were the only gas in the container! 41

42 Dalton s Law Mixture of gases A, B, C confined in a volume V. P A = n ART V and P total = P A + P B + P C Partial pressure of gas A 42

43 Air: a Mixture of Gases Air is mostly a mixture of N 2 and O 2. What is partial pressure of O 2 if: P total P N2 = kpa = 79.1 kpa P total = P O2 + P N = P O2 P = 22.2 kpa O2 43

44 Graham s Law of Diffusion Perfume spreads throughout a room by diffusion, a mixing process controlled molecular collisions. How fast a gas diffuses is related to its velocity. (start demo) 44

45 Graham s Law of Diffusion Compare the kinetic energy (KE) of 2 gases at the same T. 1 KE A = m A v 2 2 A KE B = m B v 2 B 1 2 mass velocity Since T s are the same: 1 m A v 2 = 1 2 A m B v 2 B 2 45

46 Graham s Law of Diffusion 1 m A v 2 = 1 2 A m B v 2 B 2 v A 2 v B 2 = m B m A v A v B = m B m A Diff.Rate A Diff.Rate B = molar mass B molar mass A 46

47 Graham s Law of Diffusion NH 3 (g) + HCl(g) NH 4 Cl(s) What is equation for this combination reaction? NH 3 HCl Which gas diffuses faster? By how much? Carry answer to 3 sig figs. 47

48 Graham s Law of Diffusion Diff.Rate A Diff.Rate B = molar mass B molar mass A Which gas effuses out of a balloon faster, N 2 or He? By how much? (Hint: let gas A have the smaller molar mass.) 48

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50 Warm-up What are the four macroscopic variables that describe a gas? 50

51 Warm-up A gas at 3.3 atm in a 2.7 L container is transferred to an empty 8.6 L container. What is the new pressure? 51

52 Warm-up What is Charles law? What assumptions does Charles law make? Explain, on the molecular level. If a gas has a volume of 4.7 L at 120 o C, what volume does it have at 450 o C? 52

53 Warm-up Explain using KMT why the gas pressure in a container increases if the temperature is raised. 53

54 Warm-up How many grams of O 2 gas are in a 42 L container at 370kPa at 58 o C? 54

55 Warm-up P 1 V 1 T 1 = P 2 V 2 T 2 Show that the combined gas law on Table T reduces to Charles law. 55

56 Warm-up How many grams of dintrogen pentoxide are in a 3.7 L balloon at STP? 56

57 Warm-up A rigid container containing nitrogen gas at STP is designed to withstand a maximum pressure of 320 kpa. At what temperature (in o C) will the container burst? 57

58 Warm-up How many grams of CO 2 are in a 3700 ml flask at 25 o C and 670 kpa? A 2.7 L balloon on the ground at STP rises to the upper atmosphere where T = -12 o C and P = 18 kpa. How big is the balloon? 58