Gases © 2012 Pearson Education, Inc. Gases Made up of particles that have (relatively) large amounts of ____ No definite _ or_________ Due

Gases

© 2012 Pearson Education, Inc.

Gases

• Made up of particles that have (relatively) large amounts of ________

• No definite _______ or___________

• Due to a large amount of empty space, gases are easily __________

Gases


Gases

• Made up of particles that have (relatively) large amounts of _energy__

• No definite _shape_ or___volume__

• Due to a large amount of empty space, gases are easily _compressed_____

Gases


4 Quantities to define the state of a gas

• Quantity-moles

• Temperature in Kelvin

• Volume in liters

• Pressure in atmosphere.

Gases


• Pressure is the amount of force applied to an area:

Pressure

• Atmospheric pressure is the weight of air per unit of area.

P =FA

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Pressure

• A pressure is exerted when gas particles collide with the walls of any container it is held in.

Units

• 1.00 atm=

• 760. mm Hg=

• 760. torr=

• 1.01 x 105 Pa=

• 101.325 kPa

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Units of Pressure

• mmHg or torr– These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury.

• Atmosphere1.00 atm = 760 torr

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Manometer

The manometer is used to measure the pressure of a gas in a container.

Gases


Standard Pressure

• Normal atmospheric pressure at sea level is referred to as standard pressure.

• It is equal to– 1.00 atm

– 760 torr (760 mmHg)– 101.325 kPa

Gases


Exercise 1

• The pressure of a gas is measured at 49 torr. Represent this pressure in both atmospheres, mm Hg and pascals: (6.4 x

102 atm, 6.7x 105 Pa)

Gases


Kinetic-Molecular Theory

This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

Gases


Main Tenets of Kinetic-Molecular Theory

1.Gases consist of large numbers of tiny particles that are in constant, random motion.

Gases



2. Collisions between particles are elastic (the average kinetic energy is remains constant following a collision)

This seems to explain the observation that gases, when left alone in a container, don’t seems to lose energy, and don’t spontaneously convert to a liquid.

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Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

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3. The Attractive and repulsive intermolecular forces between gas molecules are very weak, and are nearly negligible, except when they collide.

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4.The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

. This seems to explain why gases are compressible.

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5. Average kinetic energy of molecules is proportional to its Kelvin Temperature.

ALL CALCULATIONS INVOLVING TEMPERATURE OF GASES MUST BE CONVERTED TO KELVIN TEMPERATURE

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• The pressure of the gas is caused by the collision of the molecules with the walls of the cylinder. The magnitude of the pressure depends on the frequency and the force of the collisions.

• The temperature of the gas depends on the average kinetic energy of the molecules

Gases


Boyle’s LawThe volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. P1V1

= k or P1V1 = P2 V2

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P and V are Inversely Proportional

A plot of V versus P results in a curve.Since

V = k (1/P)This means a plot of V versus 1/P will be a straight line.

PV = k

Gases


Exercise 1 Boyles Law

• SO2 is a gas that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider 1.53 L of SO2 at a pressure of 5.6 x 103 Pa. If the pressure is changed to 1.5 x 10 6 PA, what is the new volume of the gas?

Gases


Exercise 2

• If a 1.23 L sample of a gas at 53.0 torr is put under pressure up to a value of 240. torr at a constant temperature, what is the new volume?

Gases


Charles’s Law

• The volume of a fixed amount of gas at constant pressure is directly proportional to its absolyute temperature IN KELVIN!.

Gases


Charles’s Law

• So,

• It is a direct proportion. A plot of V versus T will be a straight line.

VT

= k

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Gay Lussac

• P1 T2 = P2 T1

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Combined Gas Law

• P1 V1T2 = P2V2 T1

• Notice the , laws are alphabetical (Boyle P and V, Charles V and T and Gay Lussac T and P (missing variable is held constant

Gases


The Quantity-Volume Relationship

• Gay-Lussacs Law of combining volumes- at a given temperature and pressure, the volumes of gases that react with each other are ratios of small whole numbers

• Avogadro’s law-equal volumes of gases at the same temp and press contan the same number of molecules!!

Gases


Avogadro’s Law• The volume of a gas at constant temperature

and pressure is directly proportional to the number of moles of the gas.

• Mathematically, this means V = kn

Gases


Example 1

If we have a 17.5 L container which holds 0.60 mol of O2 gas at

a pressure of 1 atm and a temperature of 25 C, and all of the O2 is converted to O3, what is the

volume of the ozone?

Gases


• If 2.11 g Ne gas occupies a volume of 12.0 L at 28.0 C. What volume will 6.58 g of Neon occupy under the same conditions?

Gases


Ideal-Gas Equation

V 1/P (Boyle’s law)V T (Charles’s law)V n (Avogadro’s law)

• So far we’ve seen that

• Combining these, we get

V nTP

Gases


Ideal-Gas Equation

The constant of proportionality is known as R, the gas constant.

Gases


Ideal-Gas Equation

The relationship

then becomes

nTP

V

nTP

V = R

or

PV = nRT

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Ideal gas law

• Most useful when gases are behaving ideally (under conditions that the molecules will not be attracted to each other. This occurs at :

• High temperatures and low pressure

Gases


Ideal gas Law Example 1

• A sample of nitrogen gas (N2) has a volume of 9.95 L at a temperature of 1.00 C and 1.75 atm.

• Calculate moles of N2 in this sample

• Calculate molecules N2 in this sample

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Other Gas Laws

Example 1.• A sample of methane gas has a pressure

of 455 torr at a temperature of -7.5 C and a volume of 2.25 L. If the conditions are changed so that the temperature rises to 21.0 C and and the pressure increases to 437 torr, what will be the new volume of the sample?

•

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Other Gas Laws

• Example 2

A sample of helium gas has a volume of 16.2 L and a pressure of 1.81 atm. The gas is compressed to a volume of 8.1 L. Calculate the final pressure of the gas (assume constant temperature)

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• Example 3

• Calculate the volume of 1 mole of a gas at STP.

• This is the molar volume of a gas at STP!!! Very good to know!!

Gases


Densities of Gases

If we divide both sides of the ideal-gas equation by V and by RT, we get

nV

PRT

=

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• We know that– Moles molecular mass = mass

Densities of Gases

• So multiplying both sides by the molecular mass () gives

n = m

PRT

mV

=

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Gases


Molecular Mass

We can manipulate the density equation (in g/L) to enable us to find the molecular mass of a gas:

becomes

PRT

d =

dRTP =

Gases


Density of gases

• The molar mass of air is approximately 29 g/mol at STP. What is its density?

Gases


Gas density/Molar Mass• The density of a gas was measured at

1.50 atm and 27 C and found to be 1.95 g/L. Calculate the molar mass of the gas.

Gases


The density of air at room temperature (22C) and 1 atm pressure is 1.19 g/L. What is the molar mass of air?

Gases


Gases


3 gases less dense than air

Neon, hydrogen, methane, ammonia, helium,

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3 gases more dense than air

CO2, O2 , propane

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• The density of a gas was measured at 1.50 atm and 27 C and found to be 1.95 g/L. Is this gas, carbon dioxide, oxygen, or neon?

Gases


Dalton’s Law ofPartial Pressures

• In a mixture of gases, the total pressure exerted by the mixture is equal to the sum of the individual partial pressures of each gas.

• In other words,

Ptotal = P1 + P2 + P3 + …

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Partial Pressures

• When one collects a gas over water, there is water vapor mixed in with the gas.

• To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

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Partial Pressures

The total pressure at constant T and V is determined by the total number of moles of gas present, it is not important if it is just

one gas or a mixture of many gases.

• .

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Partial Pressures

Assuming ideal gas behavior, the pressure in a mixture of gases is Ptotal = ntotal (RT/V)

• .

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• Calculate the number of moles of hydrogen present, in a 0.641 L mixture of Hydrogen and water vapor, at 21.0 C, that has a total pressure of 750. torr, given that the vapor pressure of water at this temperature is 20.0 torr.

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• Example 2

• 3.00 liters of carbon monoxide gas at a pressure of 199 kPa and 1.00L of carbon dioxide gas at a pressure of 300 kPa are injected into a 1.25 L container. Assuming no reaction between the two gases, what is the total pressure of the container?

Gases


Example 3The partial pressure of a gas was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of this gas.

Gases


Dalton’s Law II The partial pressure was observed to be 156 torr

in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction

• Moles of gas and pressure are directly proportional. Pressure fraction will equal mole fraction.

• 156 torr/743 torr= mole fraction=.210

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Gases


• A sample of solid potassium chlorate (KClO3) was heated in a test tube and decomposed by the following reaction: 2 KClO3 2 KCl + 3 O2 The oxygen produced was collected by displacement of water at 22 C at a total pressure of 754 torr. The volume of gas collected was 0.650 L, and the vapor pressure of water at 22 C is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the

sample that was decomposed.

Gases


• Example 2

• A sample of propane (C3H8) having a volume of 3.25 L at 22 C and a pressure of 1.33 at, was mixed with a sample of oxygen gas having a volume of 15.5 L at 25 C and 1.25 atm. The mixture was then ignites to form CO2 and water. Calculate the volume of CO2 formed at a pressure of 1.50 atm and a temperature of 125 C.

Gases



The average kinetic energy of the molecules is proportional to the absolute temperature. Changing the temp changes the shape of the curve, but not the area beneath it

Gases


Gases


Root Mean Square Velocity

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Root Mean Squared Velocity

• The square root of the avergages of the squares of the speeds of all of the particles in a gas sample at a particular temperature

• R- 8.31 T- Kelvin temperature

• M-molar mass gas

Gases


Exercise 19: Root Mean Square Velocity

• Calculate the rms velocity for the following gases at 25 C, and at 50C– He

– O2

– Rn

Gases


• Quantitatively, what can be said about the rms speed as it relates to the molar mass of a gas and the temperature of the gas

Gases


Diffusion

Diffusion is the spread of one substance throughout a space or throughout a second substance.

Gases


Graham’s Law of Effusion and Diffusion

Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Gases


Effusion

The difference in the rates of effusion for helium and nitrogen, for example, explains why a helium balloon would deflate faster.

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Graham's Law

KE1 KE2=

1/2 m1v12 1/2 m2v2

2=

=m1

m2

v22

v12

m1

m2

v22

v12

=v2

v1

=

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Rate of effusion gas 1 = M2

Rate of effusion gas 2 M 1

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Exercise 20 Calculate the ratio of effusion rates of H2 and UF6

• Rate H2 =

Rate UF6

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Real Gases

In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

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Real Gases

Even the same gas will show wildly different behavior under high pressure at different temperatures.

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Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

Gases


Corrections for Nonideal Behavior

• The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account.

• The corrected ideal-gas equation is known as the van der Waals equation.

Gases


The van der Waals Equation

) (V − nb) = nRTn2aV2(P +

Documents

Gases © 2012 Pearson Education, Inc. Gases Made up of particles that have (relatively) large amounts of ________ No definite _______ or___________ Due

Gases © 2012 Pearson Education, Inc. Gases Made up of particles that have (relatively) large amounts of ____ No definite _ or_________ Due