GasesUnit 8

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

1. Gases consist of large numbers of tiny particles that are far apart relative to their size.

2. 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

3. Gas particles are in continuous, rapid, random motion. They therefore possess kinetic energy.

4. There are no forces of attraction between gas particles.

5. 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

2

2

1mvKE

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 = ForceArea

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)

Temperature

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

Joseph Louis Gay-LussacAmadeo Avogadro

Robert Boyle

Jacques Charles

Boyles Law

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

2211 VPVP

Charles Law

The volume of a gas is directly proportional to temperature.

(P = constant)

Temperature MUST be in KELVINS!

2

2

1

1

T

V

T

V

Gay-Lussac’s Law

The pressure and temperature of a gas aredirectly related, provided that the volume remains constant.

2

2

1

1

T

P

T

P

Temperature MUST be in KELVINS!

Combined Gas Law

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

2

22

1

11

T

VP

T

VP

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 gasn = 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)

Numerical Value of R Units

0.0821 (atm∙L)/(mol∙K)

8.314 J/(mol∙K)

62.4 (mmHg∙L)/(mol∙K)

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

2

( )obs

nP a x V nb nRT

V

Density of Gases

… so at STP…

molar mass

molar volume

massDensity

volume

molar mass

22.4 LDensity

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

MPD

RT

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)

3 moles H2 + 1 mole N2 2 moles NH3 3 liters H2 + 1 liter N2 2 liters 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

L H2

= L NH3 L NH3

3

28.0

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

122.55 g KClO3

3 mol O2

2 mol KClO3

22.4 L O2

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?

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

50.0 g KClO3 1 mol KClO3

122.55 g KClO3

3 mol O2

2 mol KClO3

= mol O2

= 16.7 LP

nRTV

atm0.930

K))(310Kmol

atmL1mol)(0.082(0.612

0.612

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 with temperature

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