Chapter 12 - Gases

Foundations of College Chemistry, 14th _Ed. Morris Hein and Susan Arena

Air in a hot air balloon expands upon heating. Some air escapes from the top, lowering the air density, making the balloon buoyant.

12 The Gaseous State of Matter

Properties of Gases

•

_{Gases have an indefinite shape}

•

_{Gases expand to fill their containers uniformly}

•

_{Gases are compressible}

•

_{Gases have low densities}

– _{air 0.0013 g/mL} – _{water 1.00 g/mL} – _{iron 7.9 g/mL}

•

_{Gases diffuse uniformly throughout their containers}

to form homogeneous mixtures.

3

Properties of Gases

• _{Gases are described in terms of four properties:}

Common units of pressure

101.325 kPa

= 760 mm Hg

= 760 torr

= 1 atm

= 30 in Hg

= 14.7psi

Measuring Pressure

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Pressure: Force per unit area

Pressure = areaforce

Pressure results from gas molecule collisions with the container walls.

Pressure depends on:

1) The number of gas molecules 2) Gas temperature

3) Volume occupied by the gas

Barometer

A barometer

• _{measures the pressure exerted}

by the gases in the atmosphere

• _{indicates atmospheric pressure}

Atmospheric Pressure

© 2014 John Wiley & Sons, Inc. All rights reserved.

Definition: total pressure exerted by gases in the atmosphere

Due to the mass of the atmospheric gases pressing downward on the Earth’s surface.

Altitude and Atmospheric Pressure

Atmospheric pressure

• _{depends on the altitude and}

the weather

• _{is lower at high altitudes}

where the density of air is less

Examples

•

_{Convert 740. mm Hg to atm and kPa. 101.3}

kPa = 760 mm Hg

•

_{The atmospheric pressure at the summit of}

Mt. McKinley (Denali) is 606 mm Hg on a

certain day. What is the pressure in

1) On the Number of Molecules

Pressure (P ) is directly proportional to the number of gas molecules present (n ) at constant

temperature (T ) and volume (V ).

Increasing n creates more frequent collisions with the container walls, increasing the pressure

V = 22.4 L T = 25.0 °C

Pressure Dependence

© 2014 John Wiley & Sons, Inc. All rights reserved.

Pressure is directly proportional to temperature when moles (n ) and volume (V ) are held constant.

Increasing T causes: a) more frequent and

b) higher energy collisions

0.1 mol of gas in a 1L container

T = 0 °C T = 100 °C 2.24 atm 3.06 atm

Boyle’s Law

Boyle’s law states that

• _{the pressure of a gas is}

inversely related to its volume when T and n are constant

• _{if the pressure (P) increases,}

then the volume decreases

• _{can be stated as}

P₁V₁ = P₂V₂

13

P

and

V

in Inhalation

During inhalation,

• _{the lungs expand} • _{the pressure in the}

lungs decreases

• _{air flows toward the}

P

and

V

in Exhalation

During exhalation,

• _{lung volume decreases} • _{pressure within the}

lungs increases

• _{air flows from the}

15

Learning Check

A sample of helium gas in a balloon has a volume of 6.4 L at a pressure of 0.70 atm. At 1.40 atm (T and n

17

Freon-12, CCl₂F₂, is used in refrigeration systems. What is the new volume (L) of an 8.0-L sample of Freon gas initially at 550 mmHg after its pressure is changed to 2200 mmHg at constant T?

STEP 1 Organize the data in a table of initial and final conditions. Conditions 1 Conditions 2 Know Predict

P₁ = 550 mmHg P₂ = 2200 mmHg P increases

V₁ = 8.0 L V₂ = ? V decreases

STEP 2 Rearrange the gas law for the unknown.

Solve Boyle’s law for V₂. When pressure increases, volume decreases.

P₁V₁ = P₂V₂ V₂ = V₁P₁

P₂

STEP 3 Substitute values into the gas law to solve for the unknown.

V₂ = 8.0 L x 550 mmHg = 2.0 L 2200 mmHg

19

Learning Check

1. If the helium in a cylinder has a volume of 120 mL and a pressure of 850 mmHg, what is the new volume if the pressure changes to 425 mmHg inside the cylinder?

1. A sample of Ne gas occupies 250. mL at 880.

torr. Calculate the

P

if the volume is

increased to 1.0 L, assuming constant

temperature. (Note: Convert mL to L.)

2. 3. A sample of oxygen gas has a volume of

12.0 L at 600. mmHg. What is the new

Kelvin Temperature Scale

Derived from the relationship between temperature and volume of a gas.

As a gas is cooled by 1 ºC increments,

the gas volume decreases in increments of 1/273.

All gases are expected to have zero volume if cooled to −273 ºC.

V -T relationship of methane (CH₄) with extrapolation (---) to absolute zero.

Temperature in Gas Law Problems

This temperature (−273 ºC) is referred to as absolute zero.

Absolute zero is the temperature (0 K) when the volume of an ideal gas becomes zero.

All gas law problems use the Kelvin temperature scale!

T_K = T_°C + 273 Celsius temperature

23

Charles’s Law

V &T

In Charles’s law,

• _{the Kelvin temperature of a gas is}

directly related to the volume

• _{P and n are constant}

• when the temperature of a gas increases, its volume increases

• _{Charles’s law is written}

25

A balloon has a volume of 785 mL at 21°C. If the

temperature drops to 0 °C, what is the new volume of the balloon (P constant)?

STEP 1 Organize the data in a table of initial and final conditions.

Conditions 1 Conditions 2 Know Predict V₁ = 785 mL V₂ = ? V decreases

T₁ = 21 °C T₂ = 0 °C

= 294 K = 273 K T decreases

Be sure to use the Kelvin (K) temperature in gas calculations.

Calculations Using Charles's Law (continued)

STEP 2 Rearrange the gas law for the unknown.

Solve Charles's law for V₂

V₁ = V₂

T1 T2

V₂ = V₁T₂

T₁

STEP 3 Substitute values into the gas law to solve for the unknown.

27

1. A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)?

2. 3.0 L of H₂ gas at −15 ºC is allowed to warm to 27 ºC at constant pressure. What is the gas volume at 27 ºC? ANS: 3.5L

3. A gas has a volume of 3.00 L at 10.0 ºC. What is the temperature of the gas if it expands to 6.00 L, assuming constant pressure? ANS: 566 K

Gay-Lussac’s Law:

P

and

T

In Gay-Lussac’s law,

• _{the pressure exerted by a gas is directly} related to the Kelvin temperature

• _{Warm days are high pressure} • _{V and n are constant}

Gay-Lussac’s Law

Temperature is proportional to pressure

A gas has a pressure at 2.0 atm at 18 °C. What is the new pressure when the temperature is 62 °C (V and

n constant)?

STEP 1 Organize the data in a table of initial and final conditions.

Conditions 1 Conditions 2 Know Predict

P₁ = 2.0 atm P₂ = ? P increases

T₁ = 18 °C + 273 T₂ = 62 °C + 273 T increases = 291 K = 335 K

31

Example of Using Gay-Lussac’s Law

(continued)

STEP 2 Rearrange the gas law for the unknown.

Solve Gay-Lussac’s law for P₂.

P₁ = P₂

T₁ T₂

P₂ = P₁T₂

T₁

STEP 3 Substitute values into the gas law to solve for the unknown.

P₂ = 2.0 atm x 335 K = 2.3 atm 291 K

Learning Check

A gas has a pressure of 645 mmHg at 128 °C. What is the temperature in Celsius if the pressure increases to 1.50 atm (n and V remain constant)?

Answer: 436 °C

33

Vapor Pressure and Boiling Point

Vapor pressure

• _{is the pressure above water at}

equilibrium in a closed container

• _{at the boiling point is equal to the}

external pressure

• _{Must be equal or higher than atm}

Boiling Point of Water

The boiling point of water

• _{depends on the vapor}

pressure

• _{is lower at higher altitudes}

35

The combined gas law uses Boyle’s law, Charles’s law, and Gay-Lussac’s law (n is constant).

P₁ V₁ = P₂ V₂

T₁ T₂

37

A sample of helium gas has a volume of 0.180 L, a pressure

of 0.800 atm, and a temperature of 29 °C. At what

temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n constant)?

STEP 1 Organize the data in a table of initial and final conditions.

Conditions 1 Conditions 2

P₁ = 0.800 atm P₂ = 3.20 atm

V₁ = 0.180 L (180. mL) V₂ = 90.0 mL

T₁ = 29 °C + 273 = 302 K T₂ = ??

STEP 2 Rearrange the gas law for the unknown.

Solve the combined gas law for T₂.

P₁ V₁ =P₂ V₂

T₁ T₂

T₂ = T₁ P₂V₂

P₁V₁

STEP 3 Substitute values into the gas law to solve for the unknown.

T₂ = 302 K x 3.20 atm x 90.0 mL = 604 K

39

Avogadro's Law: Volume and Moles

Avogadro’s law states that

• the volume of a gas is directly

related to the number of moles(n) of gas

• T and P are constant

Avogadro’s Law

Volume is proportional to moles

Learning Check

If 0.75 mol of helium gas occupies a volume of 1.5 L, what volume will 1.2 mol of helium occupy at the same temperature and

pressure?

43

The volumes of gases can be compared at STP (standard

temperature and pressure) when they have

• _{the same temperature}

Standard temperature (T) = 0 °C or 273 K

• _{the same pressure}

Standard pressure (P) = 1 atm (760 mmHg)

Molar Volume

The molar volume of a gas

45

The molar volume at STP

• _{has about the same volume as}

three basketballs

• _{can be used to write conversion}

factors

22.4 L and 1 mol 1 mol 22.4 L

Molar Volume as a Conversion Factor

Example of Using Molar Volume

What is the volume occupied by 2.75 mol of N₂ gas at STP?

The Gas Laws

•

_{Boyles Law}

_pressure



-- volume



•

_{Charles Law}

_temperature



-- volume



•

_{Avogadros Law moles}

_

_{-- volume}

_

– _V  n

The Gas Laws

•

_{Boyles Law}

_pressure



-- volume



•

_{Charles Law}

_temperature



-- volume



•

_{Avogadros Law moles}

_

_{-- volume}

_

– _V  n