The Nature of Gases

Transcript The Nature of Gases

Fall 1999 Chapter 7

Gases and Gas Laws

Some Gases in Our Lives Air: oxygen O argon Ar 2 nitrogen N 2 carbon dioxide CO 2 Noble gases : ozone O water H 2 3 O helium He neon Ne krypton Kr xenon Xe fluorine F 2 methane CH 4 Other gases: chlorine Cl 2 ammonia NH 3 carbon monoxide CO

Properties of a Gas • Volume V L, mL, cc • Temperature T  C , K • Moles • Pressure n g/mole P mmHg, atm, torr 4

Units of Pressure One atmosphere (1 atm)



Is the average pressure of the atmosphere at sea level



Is a standard of pressure



P = Force Area 1.00 atm = 760 mm Hg = 760 torr

atm pressure Measuring Pressure Barometers 760 mmHg Hg

Learning Check A. What is 475 mm Hg expressed in atm?

1) 475 atm 2) 0.625 atm 3) 361000 atm B. The pressure of a tire is measured as 29.4 psi.

What is this pressure in mm Hg?

1) 2.00 mm Hg 2) 1520 mm Hg 3) 22 300 mm Hg

Solution A. What is 475 mm Hg expressed in atm?

475 mm Hg x 1 atm = 0.625 atm (2) 760 mm Hg B. The pressure of a tire is measured as 29.4 psi.

What is this pressure in mm Hg?

29.4 psi x 1.00 atm x 760 mmHg = 1520 mmHg 14.7 psi 1.00 atm (2)

Pressure and Altitude • As altitude increases, atmospheric pressure decreases 10

Pressure and Boiling Point • As P atm decreases, water boils at lower temperatures and foods cook more slowly 11

Boyle’s Law

Pressure and Volume

1 2 3 4 Pressure and Volume Experiment Pressure Volume P x V (atm) (L) (atm x L) 8.0 2.0 16 4.0

4.0

_____ 2.0

1.0

8.0

16 _____ _____

Boyle's Law P x V = k (constant) when T,n remain constant 13

P and V Changes P 1 V 1

V 2

2 14

Boyle's Law



The pressure of a gas is inversely related to the volume when T,n does not change



The PV product remains constant P 1 V 1 = P 2 V 2 P 1 V 1 = 8.0 atm x 2.0 L = 16 atm L P 2 V 2 = 4.0 atm x 4.0 L = 16 atm L

PV Calculation What is the new volume (L) of a 1.6 L sample of Freon gas initially at 50. mm Hg after its pressure is changed to 200. mm Hg?

( T and n are constant)

HINT • The pressure goes from 50. mmHg to 200. mmHg. Is that an increase or decrease in pressure ? • What will happen to the volume?

P V

Finding the New Volume

Take the old volume and multiply by a factor of pressures to make the result bigger.

Solution 1.6 L x 200 mmHg = 6.4 L 50 mmHg • Factor greater than 1; answer is larger 19

Learning Check A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T and n constant) Explain.

1) 3.2 L 2) 6.4 L 3) 12.8 L

Solution A sample of nitrogen gas is 6.4 L at a pressure of 0.70 atm. What will the new volume be if the pressure is changed to 1.40 atm? (T and n constant) 6.4 L x 0.70 atm = 3.2 L (1) 1.40 atm Volume must decrease to cause an increase in the pressure

Learning Check A sample of helium gas has a volume of 12.0 L at 600. mm Hg. What new pressure is needed to change the volume to 36.0 L?

(T and n constant) Explain.

Solution A sample of helium gas has a volume of 12.0 L at 600. mm Hg. What new pressure is needed to change the volume to 36.0 L? (T constant) Explain.

600. mm Hg x 12.0 L = 200. mmHg (1) 36.0 L Pressure decrease when volume increases.

Worksheet 7-1 • Do the problems from Worksheet 7-1 • You can work these problems alone or with others around you. • You may use your notes and textbook. • When you have finished, compare answers with someone else.

Charles’ Law T = 273 K T = 546 K Observe the V and T of the balloons. How does volume change with a temperature increase ?

Charles’ Law: V and T At constant pressure, the volume of a gas is directly related to its absolute (K) temperature V 1 T 1 = V T 2 2 1. If final T is higher than initial T, final V is ( greater, or less ) than the initial V.

2. If final V is less than initial V, final T is ( higher, or lower ) than the initial T.

2. If final V is less than initial V, final T is ( lower ) than the initial T.

V and T Calculation A balloon has a volume of 785 mL when the temperature is 21 °C. As the balloon rises, the gas cools to 0 °C. What is the new volume of the balloon?

Think about what happens to T;always use K !!!

Solution 785 mL x 273 K =729 mL 294 K Factor less than 1; answer is smaller 29

Learning Check A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. What temperature (in °C) is needed to change the volume to 640 mL?

1) 443 °C 2) 170 °C 3) - 82°C

Solution A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. What temperature (in °C) is needed to change the volume to 640 mL?

T 2 = 291 K x 640 mL = 443 K 420 mL = 443 K - 273 K = 170 °C (2)

P (mm Hg) 936 761 691 P and T T ( °C) 100 25 0 When temperature decreases, the pressure of a gas ( decreases or increases ).

When temperature increases, the pressure of a gas (decreases or increases ).

Gay Lussac’s Law • Pressure and Absolute temperature are directly proportional

T P

P and T Calculation A gas has a pressure at 2.0 atm at 18 °C. What will be the new pressure if the temperature rises to 62 °C? (V,n constant) T = 18 °C T = 62°C

Solution 2.0

atm x 335 K =2.3 atm 291 K Factor more than 1; answer is larger 35

Learning Check Answer with 1) Increases 2) Decreases 3) Does not change A. Pressure _________, when V decreases B. When T decreases, V __________ C. Pressure ____________ when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume _______when T changes from 15.0 °C to 45.0°C (constant P and n )

Solution Answer with 1) Increases 2) Decreases 3) Does not change A. Pressure 1) Increases , when V decreases B. When T decreases, V 2) Decreases C. Pressure 2) Decreases when V changes from 12.0 L to 24.0 L (constant n and T) D. Volume 1) Increases when T changes from 15.0 °C to 45.0°C (constant P and n )

Worksheet 7-2 • Do the problems from Worksheet 7-2. • You can work these problems alone or with others around you. • You may use your notes and textbook. • When you have finished, compare answers with someone else.

C

ombined

G

L

• CGL

gives the result of changing 2 properties P 1 V 1 T 1 = P 2 V 2 T 2 39

Problem • Oxygen gas has a pressure of 0.15 atm when the volume is 15. L and the temperature is 27º C . What will the new volume be if T becomes 127 º C and the pressure becomes 900. mmHg ?

Answer Change T to Kelvin: 27  C +273 = 300 K,127  C +273 = 400 K Change mmHg to atm: 900. mmHg x 1 atm = 1.18 atm 760 mmHg 41

Algebraic solution 15. L x 0.15 atm x 400 K = 1.2 L 300 K 1.18 atm 42

Alternate solution 15 L x 0.15 atm x 400 K = 1.2 L 1.18 atm 300 K

P V T V

Worksheet 7-3 • Do the problems from Worksheet 7-3. • You can work these problems alone or with others around you. • You may use your notes and textbook. • When you have finished, compare answers with someone else.

Avogadro’s Law • Volume is directly related to the number of moles of gas 45

Avogadro’s Law 0.60 moles of O 2 gas has a volume of 50.L. What is the volume when 1.0 moles of O 2 added? is 46

Does a balloon get bigger or smaller when air is added?

•Add air 47

Does a balloon get bigger or smaller when air is added?

Add air 48

Solution 50 L x 1.6 moles = 133 L 0.6 moles Factor more than 1; answer is larger 49

STP

• Standard temperature 0  C or 273 K • Standard pressure 760 mmHg or 1 atm 50

Molar Volume

• At STP, 1 mole of gas has a volume of 22.4 L.

1 mole = 22.4 L (at STP) 51

Problem • What is the mass of 50. L of CO 2 gas at STP? Hint: find moles first 52

• 50. L x 1 mole x 22.4 L 44.0 g = 98. g 1 mole 53

• What is the volume of 100. g of nitrogen gas N 2 at STP?

100.g x 1 mole x 22.4 L = 28.0 g 1 mole 80.0 L 55

Worksheet 7-4 • Do the problems from Worksheet 7-4. • You can work these problems alone or with others around you. • You may use your notes and textbook. • When you have finished, compare answers with someone else.

Dalton’s Law

• Total pressure is the sum of all the partial pressures • P total =P 1 + P 2 + P 3 +

……..

• What is the total pressure in a container with 0.112 atm of oxygen and 450. mmHg of nitrogen? Give answer in mmHg.

ANSWER •

0.112 atm x 760 mmHg = 85 mmHg 1 atm

•

P t = P 1 + P 2 = 85 +450. = 535 mmHg

Nature of Gases



Gases fill a container completely and uniformly



Gases exert a uniform pressure on all inner surfaces of their containers

Kinetic Theory of Gases The particles in gases

•

Are very far apart

•

Move very fast in straight lines until they collide

•

Have no attraction (or repulsion)

•

Move faster at higher temperatures

Question • Use the KMT to explain why increasing the temperature of a gas increases the pressure. (n and V are constant) 62

• T 1

O O O O O O

< T 2