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Fall 1999Chapter 7

Gases and Gas Laws

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Some Gases in Our Lives

Air:

oxygen O2 nitrogen N2 ozone O3

argon Ar carbon dioxide CO2 water H2O

Noble gases:

helium He neon Ne krypton Kr xenon Xe

Other gases:

fluorine F2 chlorine Cl2 ammonia NH3

methane CH4 carbon monoxide CO

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Properties of a Gas

• Volume V L, mL, cc

• Temperature T C , K

• Moles n g/mole

• Pressure P mmHg, atm, torr

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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

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Measuring Pressure Barometers

760 mmHg

atm

pressure

Hg

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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

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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)

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Pressure and Altitude

• As altitude increases,

atmospheric pressure decreases

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Pressure and Boiling Point

• As P atm decreases, water boils at

lower temperatures and foods cook

more slowly

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Boyle’s Law

Pressure and Volume

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Pressure and VolumeExperiment Pressure Volume P x V

(atm) (L) (atm x L)

1 8.0 2.0 16

2 4.0 4.0 _____

3 2.0 8.0 _____

4 1.0 16 _____

Boyle's Law P x V = k (constant) when

T,n remain constant

P1V1= 8.0 atm x 2.0 L = 16 atm L

P2V2= 4.0 atm x 4.0 L = 16 atm L

P1V1 = P2V2 = k

Use this equation to calculate how a volume changes when pressure changes, or how pressure changes when volume changes.

new vol. old vol. x Pfactor new P old P x Vfactor

V2 = V1 x P1 P2 = P1 x V1

P2 V2

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P and V Changes

P1

P2

V1 V2

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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

P1V1 = P2V2

P1V1= 8.0 atm x 2.0 L = 16 atm L

P2V2= 4.0 atm x 4.0 L = 16 atm L

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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)

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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

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Finding the New Volume

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

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Solution

1.6 L x 200 mmHg = 6.4 L 50 mmHg

• Factor greater than 1; answer is larger

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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

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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

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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.

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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.

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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.

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Charles’ Law

T = 273 K T = 546 K

Observe the V and T of the balloons. How does volume change with a temperature increase ?

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Charles’ Law: V and T

At constant pressure, the volume of a gas is

directly related to its absolute (K) temperature

V1 = V2

T1 T2

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.

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Charles’ Law: V and T

At constant pressure, the volume of a gas is

directly related to its absolute (K) temperature

V1 = V2

T1 T2

1. If final T is higher than initial T, final V

is (greater) than the initial V.

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

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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 !!!

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Solution

785 mL x 273 K =729 mL

294 K

Factor less than 1; answer is smaller

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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

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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?

T2 = 291 K x 640 mL = 443 K

420 mL

= 443 K - 273 K = 170°C (2)

170°C 3) - 82°C

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P and T

P (mm Hg) T (°C)

936 100

761 25

691 0

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

When temperature increases, the pressure

of a gas (decreases or increases).

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Gay-Lussac’s Law

• Pressure and Absolute temperature are directly proportional

T P

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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

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Solution

2.0 atm x 335 K =2.3 atm

291 K

Factor more than 1; answer is larger

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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)

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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)

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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.

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Combined Gas Law

• CGL gives the result of changing 2 properties

P1V1 P2V2

=

T1 T2

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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?

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Answer

Change T to Kelvin:

27C +273 = 300 K,127C +273 = 400 K

Change mmHg to atm:

900. mmHg x 1 atm = 1.18 atm

760 mmHg

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Algebraic solution

15. L x 0.15 atm x 400 K = 1.2 L

300 K 1.18 atm

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Alternate solution

15 L x 0.15 atm x 400 K = 1.2 L

1.18 atm 300 K

P V T V

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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.

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Avogadro’s Law

• Volume is directly related to the number of moles of gas

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Avogadro’s Law

0.60 moles of O2 gas has a volume of 50.L. What is the volume when 1.0 moles of O2 is added?

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

•Add air

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

Add air

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Solution

50 L x 1.6 moles = 133 L

0.6 moles

Factor more than 1; answer is larger

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STP• Standard temperature

0 C or 273 K• Standard pressure

760 mmHg or 1 atm

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Molar Volume • At STP, 1 mole of gas

has a volume of 22.4 L.

1 mole = 22.4 L (at STP)

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Problem

• What is the mass of 50. L of CO2 gas at STP? Hint: find moles first

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• 50. L x 1 mole x

22.4 L

44.0 g = 98. g

1 mole

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• What is the volume of 100. g of nitrogen gas N2 at STP?

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

80.0 L

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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.

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Dalton’s Law

• Total pressure is the sum

of all the partial pressures

• Ptotal =P1 + P2 + P3 + ……..

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

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ANSWER

• 0.112 atm x 760 mmHg = 85 mmHg

1 atm

• Pt = P1 + P2 = 85 +450. = 535 mmHg

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Nature of Gases

Gases fill a container completely and uniformly

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

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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

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Question

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

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• T1 < T2

O O O

O O O

OO O O

OO

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The End