Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2008, Prentice Hall Chemistry: A...

Roy KennedyMassachusetts Bay Community College

Wellesley Hills, MA2008, Prentice Hall

Chemistry: A Molecular Approach, 1st Ed.

Nivaldo Tro

Mixtures of Gaseswhen gases are mixed together, their

molecules behave independent of each other

therefore, in certain applications, the mixture can be thought of as one gas

Tro, Chemistry: A Molecular Approach 2

Partial Pressurethe pressure of a single gas in a mixture of

gases is called its partial pressure

we can calculate the partial pressure of a gas if

the sum of the partial pressures of all the gases in the mixture equals the total pressureDalton’s Law of Partial Pressuresbecause the gases behave independently


Composition of Dry Air



V

T x R x n P P P

n n n

same theare mixture in the

everything of volumeand re temperatutheV

T x R x n P

V

T x R x n P

togethermixed B, andA gases, for two

totalBAtotal

BAtotal

BB

AA

ExamplePHe=341 mmHg, PNe=112 mmHg, Ptot =

662 mmHg, V = 1.00 L, T=298 K

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.


the fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes

total

A

total

A

n

n

P

P

the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction,

for gases, = volume % / 100%

total

AA n

n

the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure

totalAA PP

Deep Sea Divers & Partial Pressure

its also possible to have too much O2, a condition called oxygen toxicityPO2 > 1.4 atmoxygen toxicity can lead to muscle spasms, tunnel vision,

and convulsionsits also possible to have too much N2, a condition

called nitrogen narcosisalso known as Rapture of the Deep

when diving deep, the pressure of the air divers breathe increases – so the partial pressure of the oxygen increasesat a depth of 55 m the partial pressure of O2 is 1.4 atmdivers that go below 50 m use a mixture of He and O2

called heliox that contains a lower percentage of O2 than air



Mountain Climbing & Partial Pressureour bodies are adapted to breathe

O2 at a partial pressure of 0.21 atmSherpa, people native to the Himalaya

mountains, are adapted to the much lower partial pressure of oxygen in their air

partial pressures of O2 lower than 0.1 atm will lead to hypoxiaunconsciousness or death

climbers of Mt Everest carry O2 in cylinders to prevent hypoxiaon top of Mt Everest, Pair = 0.311 atm,

so PO2 = 0.065 atm

ExampleFind 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

A diver breathes a heliox mixture with an oxygen mole fraction of 0.050. What must the total pressure be for the partial pressure of oxygen to be 0.21 atm?

Collecting Gasesgases are often collected by having them

displace water from a containerthe problem is that since water evaporates,

there is also water vapor in the collected gasthe partial pressure of the water vapor,

called the vapor pressure, depends only on the temperature

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*


Vapor Pressure of Water


Examples1.02 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.


Reactions Involving Gasesthe principles of reaction stoichiometry

from Chapter 4 can be combined with the gas laws for reactions involving gases

in reactions of gases, the amount of a gas is often given as a volume

the ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio

when gases are at STP, use 1 mol = 22.4 L

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

ExamplesHow many grams of H2O form when 1.24

L H2 reacts completely with O2 at STP?O2(g) + 2 H2(g) → 2 H2O(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)


Properties of Gasesexpand to completely fill their containertake the shape of their containerlow density

much less than solid or liquid statecompressiblemixtures of gases are always homogeneousfluid


Kinetic Molecular Theorythe particles of the gas (either

atoms or molecules) are constantly moving

the attraction between particles is negligible

when the moving particles hit another particle or the container, they do not stick; but they bounce off and continue moving in another directionlike billiard balls


Kinetic Molecular Theorythere is a lot of empty space

between the particlescompared to the size of the

particlesthe average kinetic energy of the

particles is directly proportional to the Kelvin temperatureas you raise the temperature of the

gas, the average speed of the particles increases


Because the gasmolecules have enough kineticenergy to overcomeattractions, theykeep moving aroundand spreading outuntil they fill the container.

As a result, gasestake the shape andthe volume of thecontainer they are in.


Because there is a lot of unoccupied space in the structureof a gas, the gas molecules can be squeezed closer together


Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density


Density & Pressure 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


Gas Laws Explained – Dalton’s Law of Partial Pressures

Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures

kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact

therefore the molecules behave independent of each other, each gas contributing its own collisions to the container with the same average kinetic energy

since the average kinetic energy is the same, the total pressure of the collisions is the same


Dalton’s Law & Pressuresince the gas

molecules are not sticking together, each gas molecule contributes its own force to the total force on the side


Calculating Gas Pressure


Kinetic Energy and Molecular Velocitiesaverage kinetic energy of the gas molecules

depends on the average mass and velocityKE = ½mv2

gases in the same container have the same temperature, 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 velocitieslighter particles will have a faster average velocity

than more massive particles


Molecular Speed vs. Molar Massin order to have the same average kinetic

energy, heavier molecules must have a slower average speed


Temperature vs. Molecular Speedas the absolute

temperature increases, the average velocity increasesthe distribution

function “spreads out,” resulting in more molecules with faster speeds


Mean Free Pathmolecules 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 Effusionthe 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

both the rates of diffusion and effusion of a gas are 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 the molar mass

MM

1 rate


Effusion


Graham’s Law of Effusionfor two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

A gas

B gas

B gas

A gas

MassMolar

MassMolar

rate

rate

35

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

gases at high pressure or low temperature

Ideal gas laws assume1) 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


The Effect of Molecular Volumeat high pressure, the amount of space

occupied by the molecules is a significant amount of the total volume

the molecular volume makes the real volume larger than the ideal gas law would predict

van der Waals modified the ideal gas equation to account for the molecular volumeb is called a van der Waals constant and is

different for every gas because their molecules are different sizes

bnP

nRTV


Real Gas Behaviorbecause 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 Effect of Intermolecular Attractionsat low temperature, the attractions between

the molecules is significantthe intermolecular attractions makes the real

pressure less than the ideal gas law would predict

van der Waals modified the ideal gas equation to account for the intermolecular attractionsa is called a van der Waals constant and is

different for every gas because their molecules are different sizes 2

V

n

V

nRTP

a


Real Gas Behaviorbecause real

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


Van der Waals’ Equationcombining the equations to

account for molecular volume and intermolecular attractions we get the following equationused for real gasesa and b are called van der Waal

constants and are different for each gas

nRTn-VV

nP

2

ba


Real Gasesa plot of PV/RT vs. P for 1 mole of a gas shows

the difference between real and ideal gasesit reveals a curve that shows the PV/RT ratio

for a real gas is generally lower than ideality for “low” pressures – meaning the most important factor is the intermolecular attractions

it reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideality for “high” pressures – meaning the most important factor is the molecular volume


PV/RT Plots

Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2008, Prentice Hall Chemistry: A...

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