# Gases - PowerPoint PPT Presentation

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Unit 8. 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

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Gases

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Unit 8

## Gases

### Overview

• Characteristics of Gas

• Pressure

• Partial Pressures

• Mole Fractions

• Gas Laws

• Boyles Law

• Charles 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

### Pressure

• A force that acts on a given area

Pressure =

Force

Area

### 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

### The Gas Laws

Robert Boyle

Joseph Louis Gay-Lussac

Jacques Charles

### 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

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

… 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 37.0C 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