1

CHAPTER 11

• Gases and their Properties

2

Density Comparison

• The density of gases is much less than that of solids or liquids:

compound

Solid density (g/mL)

Liquid density (g/mL)

Gas density (g/mL)

H2O 0.917 0.998 0.000588

CCl4 1.70 1.59 0.00503

Gas molecules are extremely far apart compared to liquids and solids

3

Pressure

force per unit area (N/m2)

Atmospheric pressure is measured using a barometer

– Measures of standard pressure:• 760.0 mm Hg• 760.0 torr• 1.000 atmosphere• 101.3 kPa (1 Pa = 1 N/m2)

Hg density = 13.6 g/mL

4

Boyle’s Law

Relates the compressibility of gases to pressure and volume at constant temperature

• For a gas:– P 1/V at constant temperature and # of moles of gas– P1V1 = c1 for gas at one pressure and volume– P2V2 = c2 for gas at a 2nd pressure and volume– c1 = c2 for the same gas at the same T

• Boyle’s Law: P1V1 = P2V2 • (constant mole of gas and constant temperature)

• Note: temperature should be measured in Kelvin

5

Boyle’s Law:

• Example: At 25 oC a sample of He has a volume of 4.00 x 102 mL under a pressure of 7.60 x 102 torr. What volume would it occupy under a pressure of 2.00 atm at the same temperature?

6

Charles’ Law

T

V

T

V

2

2

1

1

Relates the compressibility of gases to temperature and volume at constant pressure

Note: temperature should be measured in Kelvin

7

Charles’ Law:

• Example: A sample of hydrogen, H2, occupies 1.00 x 102 mL at 25.0oC and 1.00 atm. What volume would it occupy at 50.0oC under the same pressure?

8

Standard Temperature and Pressure (STP)

It is a reference point for gas calculations

– Standard Pressure:– 1.00000 atm or 101.3 kPa

– Standard Temperature: 273.15 K or 0.00oC

9

The Combined Gas Law

2

22

1

11

21

22

221

1

11

2

2

1

12211

T

V P

T

V P

c c

cT

V P and c

T

V P

T

V

T

V VPVP

Note: temperature should be measured in Kelvin

Boyle’s Law Charles’ Law

Combined Gas Law

10

The Combined Gas Law Equation• Example: A sample of nitrogen gas, N2,

occupies 7.50 x 102 mL at 75.0 0C under a pressure of 8.10 x 102 torr. What volume would it occupy at STP?

2

22

1

11

T

V P

T

V P

11

Avogadro’s Lawtwo gases at the same temperature and pressure with

equal volumes, contain the same number of molecules (or moles) of gas

• If you set temperature & pressure for any gas to STP:– -one mole of that gas has a volume 22.414 L – -this is the standard molar volumestandard molar volume

– -V moles (n)

• Example: 11.2 L of a gas at STP is how many moles?

Example: 44.8 L of a gas at STP = ? moles

12

Avogadro’s Law

• Example: 1.00 mole of a gas occupies 36.5L and its density is 1.36 g/L at some unspecified temperature and pressure (a) What is its molar mass? (b) What is its density at STP?

13

The Ideal Gas Law

– Example: 1.0000 mole of a gas at STP (1.0000 atm, and 273.15 K), has a volume of 22.414 L. Find R- the gas constant.

PV = nRT

14

The Ideal Gas Law

• Example: What volume would 50.0 g of ethane, C2H6, occupy at 1.40 x 102 oC under a pressure of 1.82 x 103 torr?

PV = nRT

15

Dalton’s Law of Partial Pressures

• The pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases

Ptotal = PA + PB + PC + .....

16

Dalton’s Law of Partial Pressures

• Example: If 1.00 x 102 mL of hydrogen, measured at 25.0 oC and 3.00 atm pressure, and 1.00 x 102 mL of oxygen, measured at 25.0 oC and 2.00 atm pressure. The hydrogen gas was forced into the container of oxygen gas at 25.0 oC. What would be the pressure of the mixture of gases?

17

Gas Laws and Chemical Reactions

2 mol KClO3 2 mol KCl 3 mol O2

or 2(122.5g/mol) 2 (74.6g/mol)

3(32.0g/mol)

3 moles of O2 can also be thought of as:3(22.4L) or 67.2 L at STP

g)(2(s)&MnO

(s)3 O 3 + KCl 2KClO 2 2

18

• Example: What volume of oxygen measured at STP, that can be produced by the thermal decomposition of 120.0 g of KClO3?

• 122.5g/mol 74.6g/mol 32.0g/mol

g)(2(s)&MnO

(s)3 O 3 + KCl 2KClO 2 2

Gas Laws and Chemical Reactions

19

Diffusion and Effusion of Gases• Diffusion: the intermingling (mixing) of

gases

• Effusion: the escape of gases through tiny holes