Chapter 5 Gases Kim Shih Ph.D.. Gases Pushing Gas molecules are constantly in motion As they move and strike a surface, they push on that surface push.

Chapter 5Gases

Kim Shih Ph.D.

Gases Pushing• Gas molecules are constantly in

motion• As they move and strike a surface,

they push on that surface push = force

• If we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting pressure = force per unit area

The Effect of Gas Pressure• Gas flows from an area of high pressure to an

area of low pressurethe bigger the difference in pressure, the stronger

the flow of the gas• If there is something in the gas’s path, the gas

will try to push it along as the gas flows• Differences in air pressure result in weather and

wind patterns• The higher in the atmosphere you climb, the

lower the atmospheric pressure is around you

Pressure Imbalance in the Ear

If there is a differencein pressure acrossthe eardrum membrane,the membrane will bepushed out – what we commonly call a “popped eardrum”

The Pressure of a Gas

• Gas pressure is a result of the constant movement of the gas molecules and their collisions with the surfaces around them

• The pressure of a gas depends on several factorsnumber of gas particles in a given

volumevolume of the containeraverage speed of the gas particles

Gases and Gas Pressure

Manometer

for this sample, the gas has a larger pressure than the atmosphere, so

Manometer

Measuring Air Pressure

gravity

• We measure air pressure with a barometer

• Column of mercury supported by air pressure

• Force of the air on the surface of the mercury counter balances the force of gravity on the column of mercury

1. The height of the column increases because atmospheric pressure decreases with increasing altitude

2. The height of the column decreases because atmospheric pressure decreases with increasing altitude

3. The height of the column decreases because atmospheric pressure increases with increasing altitude

4. The height of the column increases because atmospheric pressure increases with increasing altitude

1. The height of the column increases because atmospheric pressure decreases with increasing altitude

2. The height of the column decreases because atmospheric pressure decreases with increasing altitude

3. The height of the column decreases because atmospheric pressure increases with increasing altitude

4. The height of the column increases because atmospheric pressure increases with increasing altitude

Practice – What happens to the height of the column of mercury in a mercury barometer as you

climb to the top of a mountain?

Common Units of Pressure

Brain Exercises

A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg?

Convert 45.5 psi into kPa

Manometers• The pressure of a gas trapped in a container can be

measured with an instrument called a manometer• Manometers are U-shaped tubes, partially filled with a

liquid, connected to the gas sample on one side and open to the air on the other

• A competition is established between the pressures of the atmosphere and the gas

• The difference in the liquid levels is a measure of the difference in pressure between the gas and the atmosphere

The Gas LawsIdeal Gas: A gas whose behavior follows the gas laws exactly.

The physical properties of a gas can be defined by four variables:

P pressure

T temperature

V volume

n number of moles

The Gas Laws ---- Boyle’s Law

Boyle’s Law

constant n and T

PV = k

Pressure of a gas is inversely proportional to its volume

Boyle’s Law

PinitialVinitial = PfinalVfinal

Boyle’s Law: A Molecular View• Pressure is caused by the molecules striking the sides

of the container• When you decrease the volume of the container with

the same number of molecules in the container, more molecules will hit the wall at the same instant

• This results in increasing the pressure

Boyle’s Law and Diving

Scuba tanks have a regulator so that the air from the tank is delivered at the same pressure as the water surrounding you.This allows you to take in air even when the outside pressure is large.

• Because water is more dense than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atm at 20 m the total pressure is 3

atm• If your tank contained air at 1

atm of pressure, you would not be able to inhale it into your lungs you can only generate enough

force to overcome about 1.06 atm

• If a diver holds her breath and rises to the surface quickly, the outside pressure drops to 1 atm

• According to Boyle’s law, what should happen to the volume of air in the lungs?

• Because the pressure is decreasing by a factor of 3, the volume will expand by a factor of 3, causing damage to internal organs. Always Exhale When Rising!!

Boyle’s Law and Diving

The Gas Laws ---- Charles’ Law

Charles’ Law

V α T

constant n and P

= kTV

Volume is directly proportional to temperature

= Tfinal

Vfinal

Tinitial

Vinitial

Charles’ Law

If the lines are extrapolated back to a volume of “0,” they all show the same temperature, −273.15 °C, called absolute zero

If you plot volume vs. temperature for any gas at constant pressure, the points will all fall on a straight line

• The pressure of gas inside and outside the balloon are the same

• At high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – causing the volume to become larger

• The pressure of gas inside and outside the balloon are the same

• At low temperatures, the gas molecules are not moving as fast, so they don’t hit the sides of the balloon as hard – therefore the volume is small

Charles’s Law – A Molecular View

The Gas Laws ---- Avogadro’s Law

Avogadro’s Law

constant T and P

= knV

= nfinal

Vfinal

ninitial

Vinitial

V α n

Volume directly proportional to the number of gas molecules

The Gas Laws

=Avogadro’s Law:

PinitialVinitial = PfinalVfinalBoyle’s Law:

nfinal

Vfinal

ninitial

Vinitial

Charles’ Law: = Tfinal

Vfinal

Tinitial

Vinitial

Summary

The General Gas Law

Avogadro’s Law:

PV = nRT = kBoyle’s Law:

Charles’ Law:

= kP

RTnV

=

= kP

nRTV

= (n and P are constant)

(P and T are constant)

(n and T are constant)

General Gas law: = nfinalTfinal

PfinalVfinal

ninitialTinitial

PinitialVinitial

The Ideal Gas Law

Standard Temperature and Pressure (STP) for

Gases

Ideal Gas Law: PV = nRT

P = 1 atm

T = 0 °C (273.15 K)

R is the gas constant and is the same for all gases.

R = 0.082058 K molL atm

The Ideal Gas LawWhat is the volume of 1 mol of gas at STP?

= 22.414 LV = PnRT

= (1 atm)

(1 mol)0.082058 K molL atm

(273.15 K)

Brain Exercises

A gas occupies 10.0 L at 44.1 psi and 57 °F. What volume will it occupy at standard conditions?

Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 x 104 mmHg and –23 °C

Density of Gas

PM=DRT

PV=nRT

PV=(Mass/M.W.)RT

P x M.W. = (Mass/V) RT

Density is directly proportional to molar mass

Density & Pressure

• Pressure is the result of the constant movement of the gas molecules and their collisions with the surfaces around them

• When more molecules are added, more molecules hit the container at any one instant, resulting in higher pressurealso higher density

Calculate the density of a gas at 775 torr and 27 °C if 0.250 moles weighs 9.988 g

Calculate the density of N2 at 125°C and 755 mmHg

Molar Mass of a Gas

• One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law

Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55°C and 886 mmHg

What is the molar mass of a gas if 12.0 g occupies 197 L at 380 torr and 127 °C?

Mixtures of Gases

• When gases are mixed together, their molecules behave independent of each other– all the gases in the mixture have the same volume

• all completely fill the container each gas’s volume = the volume of the container

– all gases in the mixture are at the same temperature• therefore they have the same average kinetic energy

• Therefore, in certain applications, the mixture can be thought of as one gas– even though air is a mixture, we can measure the pressure, volume,

and temperature of air as if it were a pure substance– we can calculate the total moles of molecules in an air sample,

knowing P, V, and T, even though they are different molecules

Partial Pressure and Dalton’s Law

Ptotal = P1 + P2 + … + PN

Mole Fraction (X) =

Dalton’s Law of Partial Pressures: The total pressure exerted by a mixture of gases in a container at constant V and T is equal to the sum of the pressures of each individual gas in the container.

Xi = Ptotal

PiXi = ntotal

ni or

Total moles in mixture

Moles of component

Lake Nyos

Brain Exercises

Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe

Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O2 at 298 K

Collecting Gases• Gases are often collected by having them

displace water from a container• The problem is that because water

evaporates, there is also water vapor in the collected gas

• The partial pressure of the water vapor, called the vapor pressure, depends only on the temperature so you can use a table to find out the partial pressure of the water

vapor in the gas you collect if you collect a gas sample with a total pressure of 758.2 mmHg* at 25

°C, the partial pressure of the water vapor will be 23.78 mmHg – so the partial pressure of the dry gas will be 734.4 mmHg Table 5.4*

Collecting Gas by Water Displacement

Vapor Pressure of Water

1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find mass O2.

0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.

Stoichiometric Relationships with Gases

2Na(s) + 3N2(g)2NaN3(s)

The reaction used in the deployment of automobile airbags is the high-temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0 °C are produced by decomposition of 45.0 g NaN3?

P, V, T of Gas A mole A mole B P, V, T of Gas B

Kim’s LawIf you don’t know where to start,

always start with mole number

Stoichiometric Relationships with Gases

2Na(s) + 3N2(g)2NaN3(s)

45.0 g NaN3

65.0 g NaN3

1 mol NaN3

2 mol NaN3

3 mol N2x x

Volume of N2 produced:

= 1.04 mol N2

Moles of N2 produced:

= 22.5 LV = PnRT

= (1.15 atm)

(1.04 mol)0.082058 K molL atm

(303.2 K)

Brain Exercises

How many liters of O2 @ STP can be made from the decomposition of 100.0 g of PbO2?2 PbO2(s) → 2 PbO(s) + O2(g) (PbO2 = 239.2, O2 = 32.00)

What volume of H2 is needed to make 35.7 g of CH3OH at 738 mmHg and 355 K?CO(g) + 2 H2(g) → CH3OH(g)

What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO?2 HgO(s) 2 Hg(l) + O2(g) MWHgO = 216.59 g/mol

The Kinetic-Molecular Theory of Gases1. A gas consists of tiny particles, either atoms or

molecules, moving about at random.2. The volume of the particles themselves is negligible

compared with the total volume of the gas; most of the volume of a gas is empty space.

3. The gas particles act independently of one another; there are no attractive or repulsive forces between particles.

4. Collisions of the gas particles, either with other particles or with the walls of a container, are elastic (constant temperature).

5. The average kinetic energy of the gas particles is proportional to the Kelvin temperature of the sample.

Kinetic Energy and Molecular Velocities

• Average kinetic energy of the gas molecules depends on the average mass and velocity– KE = ½mv2

• Gases in the same container have the same temperature, therefore they have the same average kinetic energy

• If they have different masses, the only way for them to have the same kinetic energy is to have different average velocities– lighter particles will have a faster average velocity than more

massive particles

The Kinetic-Molecular Theory of Gases

Molecular Speed vs. Molar Mass• To have the same average kinetic energy,

heavier molecules must have a slower average speed

averagespeed

molarmass

Temperature and Molecular Velocities _• KEavg = ½NAmu2

– NA is Avogadro’s number• KEavg = 1.5RT– R is the gas constant in energy units, 8.314 J/mol K∙• 1 J = 1 kg m∙ 2/s2

• Equating and solving we get– NA mass = molar mass in kg/mol∙

• As temperature increases, the average velocity increases

Molecular Velocities• All the gas molecules in a sample can travel at different

speeds• However, the distribution of speeds follows a statistical

pattern called a Boltzman distribution• We talk about the “average velocity” of the molecules,

but there are different ways to take this kind of average

• The method of choice for our average velocity is called the root-mean-square method, where the rms average velocity, urms, is the square root of the average of the sum of the squares of all the molecule velocities

Boltzman DistributionDistribution Function

Molecular Speed

Fra

ctio

n of

Mol

ecul

es

O2 @ 300 K

Calculate the velocity of O2 at 25 °C

T = 25 + 273 = 298K MM of O2 = 32g/mol

Calculate the rms velocity of CH4 (MM 16.04) at 25 °C

Mean Free Path

• Molecules in a gas travel in straight lines until they collide with another molecule or the container

• The average distance a molecule travels between collisions is called the mean free path

• Mean free path decreases as the pressure increases

Diffusion and Effusion• The process of a collection of molecules spreading out

from high concentration to low concentration is called diffusion

• The process by which a collection of molecules escapes through a small hole into a vacuum is called effusion

• The rates of diffusion and effusion of a gas are both related to its rms average velocity

• For gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of its molar mass

Graham’s Law: Diffusion and Effusion of Gases

Graham’s Law of Effusion

• For two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

Thomas Graham (1805–1869)

Calculate the molar mass of a gas that effuses at a rate 0.462 times N2

Calculate the ratio of rate of effusion for oxygen to hydrogen

Ideal vs. Real Gases• Real gases often do not behave like ideal gases at high

pressure or low temperature• Ideal gas laws assume

1. no attractions between gas molecules2. gas molecules do not take up space

based on the kinetic-molecular theory• At low temperatures and high pressures these

assumptions are not valid

Real Gas Behavior

• Because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures

The Behavior of Real GasesThe volume of a real gas is larger than predicted by the ideal gas law.

Real Gas Behavior

• Because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures

The Behavior of Real Gases

Attractive forces between particles become more important at higher pressures.

van der Waals’ Equation

• Combining the equations to account for molecular volume and intermolecular attractions we get the following equation– used for real gases

PV/RT Plots

Structure of the Atmosphere• The atmosphere shows several

layers, each with its own characteristics

• The troposphere is the layer closest to the Earth’s surface

Pollution added to the troposphere has a direct effect on human health and the materials we use because we come in contact with it• The stratosphere is the next layer

up(ozone layer)– less air mixingand weather in the

stratosphere means that pollutants last longer before “washing” out

• The boundary between the troposphere and stratosphere is called the tropopause

Pollutant Gases, SOx

• SO2 and SO3, oxides of sulfur, come from coal combustion in power plants and metal refining– as well as volcanoes

• Lung and eye irritants• Major contributors to acid rain

2 SO2 + O2 + 2 H2O 2 H2SO4

SO3 + H2O H2SO4

Pollutant Gases, NOx

• NO and NO2, oxides of nitrogen, come from burning of fossil fuels in cars, trucks, and power plants– as well as lightning storms

• NO2 causes the brown haze seen in some cities• Lung and eye irritants• Strong oxidizers• Major contributors to acid rain

4 NO + 3 O2 + 2 H2O 4 HNO3

4 NO2 + O2 + 2 H2O 4 HNO3

Stratospheric Ozone

• Ozone occurs naturally in the stratosphere• Stratospheric ozone protects the surface of the

earth from over-exposure to UV light from the SunO3(g) + UV light O2(g) + O(g)

• Normally the reverse reaction occurs quickly, but the energy is not UV light

O2(g) + O(g) O3(g)

Ozone Depletion• Chlorofluorocarbons became popular as aerosol

propellants and refrigerants in the 1960s• CFCs pass through the tropopause into the stratosphere• There, CFCs can be decomposed by UV light, releasing

Cl atomsCF2Cl2 + UV light CF2Cl + Cl

• Cl atoms catalyze O3 decomposition and remove O atoms so that O3 cannot be regenerated– NO2 also catalyzes O3 destruction

Cl + O3 ClO + O2

O3 + UV light O2 + O

ClO + O O2 + Cl