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Elements that exist as gases at 250C and 1 atmosphere

• Gases assume the volume and shape of their containers.

• Gases are the most compressible state of matter.

• Gases will mix evenly and completely when confined to the same container.

• Gases have much lower densities than liquids and solids.

Physical Characteristics of Gases

Units of Pressure

1 pascal (Pa) = 1 N/m2

1 atm = 760 mm Hg = 760 torr

= 101,325 Pa = 14.7 psi = 29.92 in. Hg

Barometer

Pressure = ForceArea

(force = mass x acceleration)

Measures atmosphericpressure

Sea level 1 atm

4 miles 0.5 atm

10 miles 0.2 atm

Atmospheric Pressure Varies with Altitude

Boyle’s LawBoyle’s LawPV = PV = kkThis means Pressure and This means Pressure and

Volume are Volume are INVERSELYINVERSELY PROPORTIONALPROPORTIONAL if moles if moles and temperature are and temperature are constant (do not change). constant (do not change). For example, P goes up as V For example, P goes up as V goes down.goes down.

PP11VV11 = P = P22 V V22 Used for changingconditions.

Robert Boyle

Charles’s LawCharles’s LawIf n and P are If n and P are

constant, constant, then V then V αα T T

V and T are V and T are directlydirectly proportionalproportional..

VV11 V V22

==

TT11 T T22

• If one temperature goes up, If one temperature goes up,

the volume goes up!the volume goes up!

Jacques Charles

Gay-Lussac’s LawGay-Lussac’s LawIf n and V are If n and V are

constant, constant, then P then P αα T T

P and T are P and T are directly directly proportionalproportional..

PP11 P P22

==

TT11 T T22 If one temperature goes If one temperature goes

up, the pressure goes up, the pressure goes up!up!

Combined Gas Law• The good news is that you don’t

have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 P2 V2

= T1 T2

Avogadro’s Law

Amedeo Avogadro

•For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas.•Obeyed by gases at low pressure.

2

2

nV

=nV

1

1

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 deg C (273 K)

STP allows us to compare amounts of gases between different pressures and temperatures

STP allows us to compare amounts of gases between different pressures and temperatures

Ideal Gas Law

Charles’ law: V T(at constant n and P)

Avogadro’s law: V n(at constant P and T)

Boyle’s law: V (at constant n and T)1P

V = constant x = RnT

P

nT

PR is the gas constant

PV = nRT

These relationships can be combined as follows:

More familiar form of the Ideal Gas Law

Remember the conditions 0 0C and 1 atm are called standard temperature and pressure (STP).

PV = nRT

R = PVnT

=(1 atm)(22.414L)

(1 mol)(273.15 K)

R = 0.082057 L • atm / (mol • K)

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

The gas constant, R, has this value when using pressure is in atm and V is in liters.

•The ideal gas law is best regarded as a limiting law – it expresses behavior that real gases approach at low pressures and high temperatures.

•Therefore, an ideal gas is a hypothetical substance.

•Most gases obey the ideal gas law closely enough at pressures below 1 atm that only minimal errors result from assuming ideal behavior.

d = density of gas T = temperature in Kelvin P = pressure of gas R = universal gas constant

Molar Mass of a

Gas

g L atmK

gL mol K = = atm mol

Molar mass =

dRT

P

•The ideal gas law can be used to calculate the molar mass of a gas from its measured density.

Gas Stoichiometry

What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction:

C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)

g C6H12O6 mol C6H12O6 mol CO2 V CO2

5.60 g C6H12O6

1 mol C6H12O6

180 g C6H12O6

x6 mol CO2

1 mol C6H12O6

x = 0.187 mol CO2

V = nRT

P

0.187 mol x 0.0821 x 310.15 KL•atmmol•K

1.00 atm= = 4.76 L

Dalton’s Law of Partial Pressures

V and T are constant

P1 P2 Ptotal = P1 + P2

The symbols P1 and P2 represent each partial pressure, the pressure that a particular gas would exert if it were alone in the container.

•For a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone.

PTOTAL = P1 + P2 + P3 + …….

•The symbols P1, P2, P3, and so on represent the partial pressure.

Mole fraction: the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture.

...Χ

+n+nn

=n

n=

TOTAL 21

11

Since the mole fraction of each component in a mixture of ideal gases is directly related to its partial pressure:

TOTALTOTAL PP

=n

n= 11

1Χcan be rearranged

TOTAL11 PxΧ=P

Thus, the partial pressure of a particular component of a gaseous mixture is the mole fraction of that component times the total pressure.

A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?

P1 = X1 PT

Xpropane = 0.116

8.24 + 0.421 + 0.116

PT = 1.37 atm

= 0.0132

Ppropane = 0.0132 x 1.37 atm = 0.0181 atm

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

Bottle full of oxygen gas and water vapor

PT = PO + PH O2 2

A mixture of gases results whenever a gas is collected by displacement of water. In this situation, the gas in the bottle is a mixture of water vapor and the oxygen being collected.

Water vapor is present because molecules of water escape from the surface of the liquid and collect in the space above the liquid.

Kinetic Molecular Theory of Gases

1. The particles are so small compared with distances between them that the volume of the individual particles can be assumed to be negligible (zero).

2. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

3. Gas molecules exert neither attractive nor repulsive forces on one another.

4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. Any two gases at the same temperature will have the same average kinetic energy.

Simple model that attempts to explain the properties of an ideal gas.

Kinetic theory of gases and …

• Compressibility of Gases (decreasing the volume)

• Boyle’s Law (volume is decreased, pressure is increased)

decrease in volume = gas particles hit the walls more often = increase pressure

• Charles’ Law (at constant pressure, volume and temperature are directly proportional)

higher temperature = speeds of molecules increase and hit walls more often and with more force = if pressure is kept constant volume must increase

Kinetic theory of gases and …

• Avogadro’s Law (gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas)

increase in number of particles = volume must increase to keep pressure and temperature constant

• Dalton’s Law of Partial Pressures

Molecules do not attract or repel one another

P exerted by one type of molecule is unaffected by the presence of another gas

Ptotal = Pi

Velocity of a Gas•Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds, i.e. they exhibit a DISTRIBUTION of speeds; some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same.•At the same temperature, lighter gases move, on average, faster than heavier gases.

urms = 3RTM

To into account the distribution of speeds we use the root mean square velocity to determine the average velocity of gases.

R = 8.3145 J/K mol (molar gas constant)∙T = temperature in KelvinM = mass of a mole in kilograms

Remember J = kg m∙ 2/s2

Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.

NH3

17 g/molHCl36 g/mol

NH4Cl

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

•Effusion – term used to describe the passage of a gas through a tiny orifice into an evacuated chamber.

Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.

•Rate of effusion measures the speed at which the gas is transferred into the chamber.

•Rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.

•Graham’s Law of Effusion

•Where M1 and M2 represent the molar masses of the gases.

1

2

21

MM

=gasforeffusionofRategasforeffusionofRate

• We must correct for non-ideal gas behavior when:– Pressure of the gas is high.– Temperature is low.

• Under these conditions: – Concentration of gas particles is high.– Attractive forces become important.

Van der Waals equationnonideal gas

P + (V – nb) = nRTan2

V2( )

}

correctedpressure

}

correctedvolume

Correction to ideal gas law to account for real gas behavior.

Real gases occupy volume so correction is made to volume.

Real gases have attractive forces so pressure must be corrected to account for gas particles hitting walls of container less often.