Unit 8
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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

Unit 8

Gases


Overview

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

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

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

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

Speed of Molecules

  • V = velocity of molecules

  • M = molar mass

  • R = gas constant

  • T = temperature


Pressure

Pressure

  • A force that acts on a given area

    Pressure =

Force

Area


Measuring pressure

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

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)


Temperature

Temperature


Gases

STP

  • Standard Temperature and Pressure (STP)

    • 1 atmosphere

    • 273 K


Dalton s law of partial pressures

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

  • 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

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

The Gas Laws

Robert Boyle

Amadeo Avogadro

Joseph Louis Gay-Lussac

Jacques Charles


Boyles law

Boyles Law

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


Charles law

Charles Law

  • The volume of a gas is directly proportional to temperature.

    (P = constant)

Temperature MUST be in KELVINS!


Gay lussac s law

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

Combined Gas Law

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


Avogadro s law

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

Ideal Gases

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


Ideal gas law

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

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 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 gases1

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

Density of Gases

… so at STP…


Density of gases1

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

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

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

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

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

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

Effusion

  • Process by which gas particles pass through a tiny opening


Graham s law of effusion

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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