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### Gases

Overview

- Characteristics of Gas
- Pressure
- Partial Pressures
- Mole Fractions

- Gas Laws
- Boyles Law
- Charles Law
- Avogadro’s Law
- Guy-Lussac’s Law
- Ideal Gas Law

- Ideal Gases

- Real Gases
- Density of Gases
- Volumes of Gases
- Standard molar volume
- Gas stoichiometry

- Effusion/Diffusion
- Graham’s Law

Characteristics of Gases

- Expansion– gases expand to fill their containers
- Compression– gases can be compressed
- Fluids – gas particles flow past each other
- Density – gases have low density
- 1/1000 the density of the equivalent liquid or solid

- Gases effuse and diffuse

Kinetic Molecular Theory

- Gases consist of large numbers of tiny particles that are far apart relative to their size.
- Collisions between gas particles and between particles and container walls are elastic.
- Elastic collision – collision in which there is no net loss of kinetic energy

- Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy.
- There are no forces of attraction between gas particles.
- The temperature of a gas depends on the average kinetic energy of the particles of the gas.

Kinetic Energy of Gas Particles

- At the same conditions of temperature, all gases have the same average kinetic energy

m = mass

v = velocity

At the same temperature, small molecules move FASTER than large molecules

Speed of Molecules

- V = velocity of molecules
- M = molar mass
- R = gas constant
- T = temperature

Measuring Pressure

- The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century
- Called a barometer

- The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high

Units of Pressure

- 1 atmosphere (atm)
- 760 mm Hg (millimeters of mercury)
- 760 torr
- 1.013 bar
- 101300 Pa (pascals)
- 101.3 kPa (kilopascals)
- 14.7 psi (pounds per square inch)

STP

- Standard Temperature and Pressure (STP)
- 1 atmosphere
- 273 K

Dalton’s Law of Partial Pressures

- Partial pressure – pressure exerted by particular component in a mixture of gases
- Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of the component gases
Pt = P1 + P2 + P3+…

Mole Fraction

- Mole fraction – expresses the ratio of the number of moles of one component to the total number of moles in the mixture
P1 = Pt or P1 = X1Pt

X1 = mole fraction of gas 1

Example: The mole fraction of N2 in air is 0.78 (78% of air is nitrogen). What is the partial pressure of nitrogen in mmHg?

PN2 = (0.78)(760 mmHg) = 590 mmHg

Collecting Gas Over Water

- Gas collected by water displacement is always mixed with a small amount of water vapor
- Must account for the vapor pressure of the water molecules
Ptotal = Pgas + PH2O

Note: The vapor pressure of water varies with temperature

Boyles Law

Pressure is inversely proportional to volume when temperature is held constant.

Charles Law

- The volume of a gas is directly proportional to temperature.
(P = constant)

Temperature MUST be in KELVINS!

Gay-Lussac’s Law

The pressure and temperature of a gas are

directly related, provided that the volume

remains constant.

Temperature MUST be in KELVINS!

Combined Gas Law

Expresses the relationship between pressure, volume and temperature of a fixed amount of gas

Avogadro’s Law

For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).

V = constant ×n

V = volume of the gas

n = number of moles of gas

For example, doubling the moles will double the volume of a gas

Ideal Gases

- Imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory

Ideal Gas Law

PV = nRT

- P = pressure
- V = volume
- n = moles
- R = ideal gas constant
- T = temperature (Kelvin)

Note: 1 J = 1 Pa∙m3

Standard Volume

- STP of 1 mole of gas = 1 atm and 273K
PV = nRT

(1atm)(V) = (1mol)(.0821)(273)

V = 22.4 L

- Volume of 1 mole of gas at STP = 22.4 liters

Real Gases

- Real Gas – does not behave completely according to the assumptions of the kinetic molecular theory
- At high pressure (smaller volume) and low temperature gases deviate from ideal behavior
- Particles will be closer together so there is insufficient kinetic energy to overcome attractive forces

Real Gases

- The Van der Waals Equation adjusts for non-ideal behavior of gases (p. 423 of book)

corrected pressure

corrected volume

Pideal

Videal

Density of Gases

… so at STP…

Density of Gases

- Combine density with the ideal gas law
- (V = p/RT)

M = Molar Mass

P = Pressure

R = Gas Constant

T = Temperature in Kelvins

Gas Stoichiometry #1

If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.

3 H2(g) + N2(g) 2NH3(g)

3moles H2 +1mole N2 2moles NH3

3liters H2 + 1liter N2 2liters NH3

Gas Stoichiometry #2

How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?

3 H2(g) + N2(g) 2NH3(g)

12 L H2

2

L NH3

= L NH3

8.0

3

L H2

Gas Stoichiometry #3

How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?

2 KClO3(s) 2 KCl(s) + 3 O2(g)

50.0 g KClO3

1 mol KClO3

3 mol O2

22.4 L O2

122.55 g KClO3

2 mol KClO3

1 mol O2

= 13.7 L O2

Stoichiometry #4

How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?

2KClO3(s) 2KCl(s) + 3O2(g)

50.0 g KClO3

1 mol KClO3

3mol O2

0.612

=

mol O2

122.55 g KClO3

2mol KClO3

= 16.7 L

Diffusion

- Spontaneous mixing of two substances caused by the random motion of particles
- The rate of diffusion is the rate of gas mixing
- The rate of diffusion increases withtemperature
- Small molecules diffuse faster than large molecules

Effusion

- Process by which gas particles pass through a tiny opening

Graham’s Law of Effusion

- Rate of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

M1 = Molar Mass of gas 1

M2 = Molar Mass of gas 2

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