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Chapter 5 Gases Kim Shih Ph.D.

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**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

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**The Effect of Gas Pressure**

Gas flows from an area of high pressure to an area of low pressure the 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

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**Pressure Imbalance in the Ear**

If there is a difference in pressure across the eardrum membrane, the membrane will be pushed out – what we commonly call a “popped eardrum”

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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 factors number of gas particles in a given volume volume of the container average speed of the gas particles

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Gases and Gas Pressure

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

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Manometer

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**Measuring Air Pressure**

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 gravity

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Practice – What happens to the height of the column of mercury in a mercury barometer as you climb to the top of a mountain? The height of the column increases because atmospheric pressure decreases with increasing altitude The height of the column decreases because atmospheric pressure decreases with increasing altitude The height of the column decreases because atmospheric pressure increases with increasing altitude The height of the column increases because atmospheric pressure increases with increasing altitude The height of the column increases because atmospheric pressure decreases with increasing altitude The height of the column decreases because atmospheric pressure decreases with increasing altitude The height of the column decreases because atmospheric pressure increases with increasing altitude The height of the column increases because atmospheric pressure increases with increasing altitude

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**Common Units of Pressure**

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Brain Exercises

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**A high-performance bicycle tire has a pressure of 132 psi**

A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg? Convert 45.5 psi into kPa

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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

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The Gas Laws Ideal 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

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**The Gas Laws ---- Boyle’s Law**

Pressure of a gas is inversely proportional to its volume Boyle’s Law PV = k constant n and T

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Boyle’s Law PinitialVinitial = PfinalVfinal

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**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

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Boyle’s Law and Diving 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 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.

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Boyle’s Law and Diving 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!!

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**Volume is directly proportional to temperature**

The Gas Laws ---- Charles’ Law Volume is directly proportional to temperature Charles’ Law V α T = k T V constant n and P

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Charles’ Law = Tfinal Vfinal Tinitial Vinitial

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If you plot volume vs. temperature for any gas at constant pressure, the points will all fall on a straight line If the lines are extrapolated back to a volume of “0,” they all show the same temperature, − °C, called absolute zero

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**Charles’s Law – A Molecular View**

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 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

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**The Gas Laws ---- Avogadro’s Law**

Volume directly proportional to the number of gas molecules Avogadro’s Law V α n = k n V = nfinal Vfinal ninitial Vinitial constant T and P

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**The Gas Laws Summary Boyle’s Law: PinitialVinitial = PfinalVfinal =**

Tfinal Vfinal Tinitial Vinitial Charles’ Law: ninitial Vinitial nfinal Vfinal Avogadro’s Law: =

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**The General Gas Law Boyle’s Law: PV = nRT = k (n and T are constant)**

Charles’ Law: (n and P are constant) = k P RT n V = Avogadro’s Law: (P and T are constant) = nfinalTfinal PfinalVfinal ninitialTinitial PinitialVinitial General Gas law:

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**The Ideal Gas Law Ideal Gas Law: PV = nRT**

R is the gas constant and is the same for all gases. R = K mol L atm T = 0 °C ( K) Standard Temperature and Pressure (STP) for Gases P = 1 atm

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**The Ideal Gas Law What is the volume of 1 mol of gas at STP?**

nRT = (1 atm) (1 mol) K mol L atm ( K)

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Brain Exercises

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**A gas occupies 10. 0 L at 44. 1 psi and 57 °F**

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

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**Density of Gas PV=nRT PV=(Mass/M.W.)RT P x M.W. = (Mass/V) RT PM=DRT**

Density is directly proportional to molar mass

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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 pressure also higher density

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**Calculate the density of a gas at 775 torr and 27 °C if 0**

Calculate the density of a gas at 775 torr and 27 °C if moles weighs g Calculate the density of N2 at 125°C and 755 mmHg

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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

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**Calculate the molar mass of a gas with mass 0**

Calculate the molar mass of a gas with mass g that has a volume of 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?

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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

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**Partial Pressure and Dalton’s Law**

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. Ptotal = P1 + P2 + … + PN Total moles in mixture Moles of component Mole Fraction (X) = Xi = ntotal ni Xi = Ptotal Pi or

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Lake Nyos

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Brain Exercises

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**Find the partial pressure of neon in a mixture with total pressure 3**

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

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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 mmHg* at 25 °C, the partial pressure of the water vapor will be mmHg – so the partial pressure of the dry gas will be mmHg Table 5.4*

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**Collecting Gas by Water Displacement**

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**Vapor Pressure of Water**

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**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.

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**Stoichiometric Relationships with Gases**

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? 2Na(s) + 3N2(g) 2NaN3(s) P, V, T of Gas A mole A mole B P, V, T of Gas B

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**If you don’t know where to start, always start with mole number**

Kim’s Law If you don’t know where to start, always start with mole number

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**Stoichiometric Relationships with Gases**

2Na(s) + 3N2(g) 2NaN3(s) Moles of N2 produced: 45.0 g NaN3 65.0 g NaN3 1 mol NaN3 2 mol NaN3 3 mol N2 x x = 1.04 mol N2 Volume of N2 produced: (1.15 atm) (1.04 mol) K mol L atm (303.2 K) P nRT V = = = 22.5 L

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Brain Exercises

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**How many liters of O2 @ STP can be made from the decomposition of 100**

How many liters of STP can be made from the decomposition of 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 atm and 313 K is generated by the thermolysis of 10.0 g of HgO? 2 HgO(s) 2 Hg(l) + O2(g) MWHgO = g/mol

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**The Kinetic-Molecular Theory of Gases**

A gas consists of tiny particles, either atoms or molecules, moving about at random. 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. The gas particles act independently of one another; there are no attractive or repulsive forces between particles. Collisions of the gas particles, either with other particles or with the walls of a container, are elastic (constant temperature). The average kinetic energy of the gas particles is proportional to the Kelvin temperature of the sample.

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**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

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**The Kinetic-Molecular Theory of Gases**

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**Molecular Speed vs. Molar Mass**

To have the same average kinetic energy, heavier molecules must have a slower average speed molar mass average speed

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**Temperature and Molecular Velocities**

_ KEavg = ½NAmu2 NA is Avogadro’s number KEavg = 1.5RT R is the gas constant in energy units, J/mol∙K 1 J = 1 kg∙m2/s2 Equating and solving we get NA∙mass = molar mass in kg/mol As temperature increases, the average velocity increases

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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

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**Boltzman Distribution**

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**Calculate the velocity of O2 at 25 °C**

T = = 298K MM of O2 = 32g/mol Calculate the rms velocity of CH4 (MM 16.04) at 25 °C

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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

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**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

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**Graham’s Law: Diffusion and Effusion of Gases**

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**Graham’s Law of Effusion**

Thomas Graham (1805–1869) For two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

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**Calculate the molar mass of a gas that effuses at a rate 0**

Calculate the molar mass of a gas that effuses at a rate times N2 Calculate the ratio of rate of effusion for oxygen to hydrogen

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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 molecules 2. gas molecules do not take up space based on the kinetic-molecular theory At low temperatures and high pressures these assumptions are not valid

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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

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**The Behavior of Real Gases**

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

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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

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**The Behavior of Real Gases**

Attractive forces between particles become more important at higher pressures.

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**van der Waals’ Equation**

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

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PV/RT Plots

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**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

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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

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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

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**O3(g) + UV light O2(g) + O(g)**

Stratospheric Ozone Ozone occurs naturally in the stratosphere Stratospheric ozone protects the surface of the earth from over-exposure to UV light from the Sun O3(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)

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**CF2Cl2 + UV light CF2Cl + Cl**

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 atoms CF2Cl2 + 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

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The Gas Laws You can predict how pressure, volume, temperature, and number of gas particles are related to each other based on the molecular model of a.

The Gas Laws You can predict how pressure, volume, temperature, and number of gas particles are related to each other based on the molecular model of a.

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