**Chapter
9**

**The Gaseous
State**

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##

9-1 The Nature of Gases and the Kinetic Molecular
Theory

### l Describe the qualitative properties common
to all gases

### l List five common properties of all gases.

### l Apply the kinetic molecular theory of gases
to explain their common properties.

### l Apply Grahams Law to the relationship
between the average velocity of a gas and its molar mass.

9-2 The Pressure of a Gas

### l Distinguish between force and pressure

### l Convert among the various units used to
describe pressure.

9-3 Boyle’s Law

### l Apply Boyle’s Law
to calculate the effect of pressure changes on the volume

### l Describe the basis for Boyle’s law from
kinetic theory.

9-4 Charles’s Law and Gay-Lussac’s Law

### l Use Charles law
to calculate the effect of temperature changes on the volume

### l Calculate the effect
of a change of temperature on the pressure of a gas by application of Gay
Lussac’s law.

### l Apply Kinetic
theory to describe the basis of Charles’s Law and Gay-Lussac’s Law

### l Apply the
combined gas law.

9-5 Avagadro’s Law

### l Describe the
effect on the volume of a gas by adding a specified amount of gas

9-6 The Ideal Gas Law

### l Calculate a
milling variable (P, V, T) for a gas under two sets of conditions

### l Describe the
effect on the volume of a gas by adding a specified amount of gas.

### l Use the Ideal Gas
Law to calculate an unknown property of a sample of gas (P, V, T, or n) when
the other properties are known.

9-7 Dalton’s Law of Partial Pressures

### l Carry out gas law
calculations for a mixture of gases.

### l Convert between
moles of gas and volume at STP using the molar volume as a conversion factor

9-8 The Molar Volume and Density of a Gas

### l Calculate the
density of a gas at STP or other conditions

### l Apply the ideal
gas law or the molar volume relationship to stoichiometry problems involving
gases

__Importance__

## •
Gases
are all around us and are necessary for life

### l Greenhouse

### l Ozone Depletion

## •
Development
of Earth as an environment suitable for living

## •
They
can be harnessed to do work

### l Engines

### l Pneumatic devices

__Characteristics of Gases__

## •
Primarily made up of nonmetals

## •
Have low densities

## •
Diffuse rapidly and completely through each other

## •
Expand volume to completely fill container

## •
Compressible

## •
Exert pressure uniformly on container

__Kinetic Molecular Theory__

## •
Explains
the properties of gases

## •
Postulates

### l Gases consist of
small molecules that are in constant random motion.

### l The volumes of
all molecules of a gas are small compared to the space between molecules (A gas
is mostly empty space).

### l Intermolecular
forces between particles are negligible

### l Collisions
between molecules and with their container are perfectly elastic.

### l Ave. K.E. of the
molecules is proportional to absolute T.

__Temperature and Kinetic Energy__

_{•
}Average
k.e. = ª = 1/2mv_{2}

### l m = mass

### l v = velocity

## •
Ave K.E.
encompasses molecules that have varying speeds.

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__Graham’s Law__

## •
½m_{1}v_{1}^{2
= }½m_{2}v_{2}^{ 2
}rearranging gives

## •
r_{1}/r_{2}
=[*M*_{2}/*M*_{1}]^{1/2 }= v_{1}/v_{2}^{ }r = rate

## •
The rates of
diffusion (mixing) of two gases under identical conditions is inversely
proportional to the square root of their molar masses.

## •
lighter
molecules diffuse faster.

__Measuring Gases__

## •
In
order to describe a sample of gas completely four quantities have to be
addressed

### l Amount of gas (n)
- moles of gas n = __mass __

##
Molar Mass

### l Volume (V) - The
volume of a container holding a gas

### l Temperature (T)-
in Kelvin

### l Pressure (P)-
Force per unit area F/A (SI unit is Pascal)

__Atmospheric Pressure__

## •
Gravity
causes our atmospheric gases to exert force and therefore a pressure on the
Earth’s surface

### l A column of air 1
m2 has a mass of 10,000 kg

### l F=ma agravity=
9.8m/s2

### l 10,000 kg
(9.8m/s2) = 1 x105 kg-m/s2 = 1 x 105
Newtons (N)

## •
P=F/A

### = [1 x 10^{5 }N / 1 m^{2}]
= 1 x 10^{5} N/m^{2} = 1 x 10^{5} Pascal (Pa)

## •
Atmospheric
pressure depends on altitude and weather conditions

__ __

__ __

__ __

__ __

__Barometers__

## •
Used to Measure Atmospheric Pressure

## •
Made by inverting a glass tube containing mercury
into a dish containing mercury.

### l all air
evacuated.

### l Void space is
nearly a vacuum, only small amount of mercury vapor present.

## •
The mercury in the dish experiences atmospheric
pressure

### l As atmospheric
pressure changes the level of mercury in the tube will change

### l Standard
atmospheric pressure at sea level is = 760 mmHg = 760
torr = 1 atm = 101.3 kPa

__Boyle’s Law__

Pressure -Volume

## •
The
volume of a fixed quantity of gas maintained at constant temperature is
inversely proportional to the pressure.

### l V = constant
x 1/P or PV = constant

_{l }Therefore, P_{1}V_{1} = P_{2} V_{2}

## •
The
value of the constant depends on the temperature and the amount of gas in the
sample

### l Examples:

#### l Breathing

#### l scuba

#### l Cartesian
divers

__Charles Law__

Temperature - Volume

## •
The
volume of a fixed amount of gas maintained at constant pressure is directly
proportional to its absolute temperature.

### l V = constant x
T or
V/T = constant

_{l }Therefore, V_{1}/T_{1}
= V_{2}/T_{2}

## •
Based on Charles’ observation, Lord Kelvin
(William Thomson) noted that
extrapolation of volume temperature lines for all gases intersect the temp axis
at –273.15 ¢ªC, lead to the development of the absolute temperature scale. 0 K
corresponds to no translational motion.

__ __

__Guy Lussac’s Law__

Pressure-Temperature

## •
The pressure of a gas is directly proportional to
the Kelvin temperature at constant volume.

## •
P= kT

_{•
}__P___{1}
= __P___{2}

## T_{1} T_{2}

_{ }

__Combined Gas Law__

## •
Puts Charles, Boyles and Guy Lussac’s all together
in one law

## •
__PV__ = k

## T

_{•
}__P___{1}V_{1}
= __P___{2}V_{2}

## T_{1} T_{2}

_{•
}P_{1}V_{1 }T_{2} =
P_{2}V_{2 }T_{1}

__Avogadro’s Law__

## •
Equal
volumes of gases at the same temperature and pressure contain the same number
of molecules.

## •
The
volume of a gas is proportional to the number of molecules (moles) of gas present at constant pressure and
temperature

_{•
}V
= k*n* __V___{1} =
__V___{2}

## *n*_{1} *n*_{2}

__Molar Volume__

## •
Molar Volume – the volume of one mole of gas at
STP, 22.4 L.

## •
Because the particle size of gas molecules is so
small compared to the space between them all gas samples containing equal
numbers of particles at similar conditions will occupy the same volume.

__Ideal gas Law__

## •
Boyles law: V
= k_{1} 1/P (constant n,T)

## •
Charles law
V = k_{2} T (constant n,P)

## •
Avogadro’s law
V = k_{3} n (constant P, T)

## •
Combining the constants (k1, k2, k3) into a
proportionality constant R and combing the equations we get

## •
V= R[nT/P]
or PV = nRT

#

#

__Ideal Gas Law (Cont’d)__

## •
An ideal gas is a hypothetical gas whose pressure,
volume and temperature behavior is completely explained by the ideal gas
equation.

## •
R – is called the Universal Gas Constant

### l The value of R
depends on the units of P, V, n and T.

### l Most commonly R =
0.08206 L-atm/mol-K

__Dalton’s Law of Partial Pressures__

## •
The total pressure of a gas in a system is the sum
of the partial pressures of each component gas

## •
Partial Pressure - The pressure exerted by a
particular component in a mixture of gases.

## •
P_{T} = P_{1} + P_{2} + P_{3}
+ …

## •
P_{T} = n_{1}[RT/V] + n_{2}[RT/V]
+…

__Density of a Gas__

## •
Density = mass/volume

## •
Ideal Gas Law can be expressed as

### l N/V = P/RT

### l nM/V =PM/RT

### l M is molar mass

## •
Therefore density of a gas is

### l D = PM/RT
and

### l M = dRT/P