chapter 10 physical characteristics of gases. 10-1 the kinetic-molecular theory of matter ...

Chapter 10Chapter 10

Physical Characteristics of GasesPhysical Characteristics of Gases

10-1 The Kinetic-Molecular Theory 10-1 The Kinetic-Molecular Theory of Matterof Matter

Kinetic-molecular theory Kinetic-molecular theory is based on the is based on the idea that particles of matter are in constant idea that particles of matter are in constant motion. motion.

The theory can be used to explain the The theory can be used to explain the properties of solids, liquids and gases in properties of solids, liquids and gases in terms of the energy of particles and the terms of the energy of particles and the forces that act between them. forces that act between them.

10-1 The Kinetic-Molecular Theory 10-1 The Kinetic-Molecular Theory of Gasesof Gases

KMT provides a model KMT provides a model of an of an ideal gasideal gas. .

An ideal gas is an An ideal gas is an imaginary gas that imaginary gas that perfectly fits all the perfectly fits all the assumptions of KMT.assumptions of KMT.

10-1 The Kinetic-Molecular Theory 10-1 The Kinetic-Molecular Theory of Matter – Assumption 1of Matter – Assumption 1

Gases consist of a large number of tiny Gases consist of a large number of tiny particles that are far apart relative to their particles that are far apart relative to their size.size.– Most of the volume is empty space.Most of the volume is empty space.– Gases have low density.Gases have low density.– Gases are easily compressed.Gases are easily compressed.– Gas particles are considered point masses Gas particles are considered point masses

(have mass but no volume). (have mass but no volume).


Collisions between gas Collisions between gas particles and between particles and between particles and container particles and container walls are elastic collisions. walls are elastic collisions. – No net loss of energy. No net loss of energy. – Kinetic energy is transferred, Kinetic energy is transferred,

but total KE of 2 particles is but total KE of 2 particles is constant as long as constant as long as temperature is constant. temperature is constant.


Gas particles are in continuous, rapid, Gas particles are in continuous, rapid, random motion. random motion. – They possess kinetic energy. They possess kinetic energy. – Gas particles move in all directions. Gas particles move in all directions. – Gas particles move in straight line trajectories Gas particles move in straight line trajectories

until they collide and change directions. until they collide and change directions.


There are no forces of attraction or repulsion There are no forces of attraction or repulsion between gas particles. between gas particles. – Gas particles are too far apart to experience Gas particles are too far apart to experience

intermolecular forces. intermolecular forces. – When they collide, their kinetic energy is When they collide, their kinetic energy is

sufficient to overcome any attractive forces sufficient to overcome any attractive forces (they bounce apart like billiard balls).(they bounce apart like billiard balls).


The average kinetic The average kinetic energy of gas particles energy of gas particles depends on the depends on the temperature of the gas. temperature of the gas.

All particles in a gas All particles in a gas sample have the same sample have the same mass, so KE depends only mass, so KE depends only on speed.on speed.

Average speeds increase Average speeds increase with an increase in with an increase in temperature and decrease temperature and decrease with a decrease in with a decrease in temperature. temperature.

velocity

mass

Fraction of Particles v. Particle Fraction of Particles v. Particle Speed at Various TemperaturesSpeed at Various Temperatures

Speed distribution for the same gas molecules at various temperatures.

Speed distribution for various gases with different masses at same temperature.

10-1 The Kinetic-Molecular Theory 10-1 The Kinetic-Molecular Theory of Matter - Assumptionsof Matter - Assumptions

The behavior of real gases can be modeled The behavior of real gases can be modeled with KMT (ideal gas assumptions) except with KMT (ideal gas assumptions) except under special circumstances.under special circumstances.

Assumptions of KMT are not valid at Assumptions of KMT are not valid at extremely low temperatures and/or extremely low temperatures and/or extremely high pressures.extremely high pressures.

10-1 KMT and Gas Behavior: 10-1 KMT and Gas Behavior: ExpansionExpansion

Gases move rapidly in all Gases move rapidly in all directions (assumption directions (assumption 3) without significant 3) without significant attractive or repulsive attractive or repulsive forces between them forces between them (assumption 4). (assumption 4).

In this way, they expand In this way, they expand to fill the entire to fill the entire available volume. available volume.

10-1 KMT and Gas Behavior: Fluidity10-1 KMT and Gas Behavior: Fluidity

Attractive forces are insignificant between Attractive forces are insignificant between particles of an ideal gas. (assumption 4) particles of an ideal gas. (assumption 4) They easily glide past each other. They easily glide past each other.

Liquids and gases flow, and are therefore Liquids and gases flow, and are therefore referred to as referred to as fluidsfluids. .

10-1 KMT and Gas Behavior: Low 10-1 KMT and Gas Behavior: Low DensityDensity

Particles in the gaseous Particles in the gaseous state are very far apart. state are very far apart. (assumption 1)(assumption 1)

A small number of gas A small number of gas particles can therefore particles can therefore occupy a large volume. occupy a large volume.

The ratio of mass to The ratio of mass to volume is very low, about volume is very low, about 1/1000 the density of the 1/1000 the density of the same substance in liquid same substance in liquid or solid form. or solid form.

Because gas particles are so far apart Because gas particles are so far apart (assumption 1), it is possible to force (assumption 1), it is possible to force them closer together, reducing the them closer together, reducing the volume occupied by the gas. volume occupied by the gas.

10-1 KMT and Gas Behavior: 10-1 KMT and Gas Behavior: CompressibilityCompressibility

10-1 KMT and Gas Behavior: 10-1 KMT and Gas Behavior: Diffusion and EffusionDiffusion and Effusion

DiffusionDiffusion – the – the spontaneous mixing of the spontaneous mixing of the particles of two substances particles of two substances caused by their random caused by their random motion (assumption 3)motion (assumption 3)

EffusionEffusion – a process by – a process by which gas particles pass which gas particles pass through a tiny opening through a tiny opening because of their rapid because of their rapid random motion random motion (assumption 3)(assumption 3)

10-1 Deviation of Real Gases from 10-1 Deviation of Real Gases from Ideal BehaviorIdeal Behavior

A A real gasreal gas is a gas that does not is a gas that does not behave completely according to behave completely according to the assumptions of the kinetic-the assumptions of the kinetic-molecular theory. molecular theory.

In 1873, Johannes van der Waals In 1873, Johannes van der Waals accounted for these deviations by accounted for these deviations by explaining that real gases occupy explaining that real gases occupy space and exert attractive forces space and exert attractive forces on each other. on each other.

When gas particles are forced to When gas particles are forced to be close together, particle volume be close together, particle volume and attractive forces are no longer and attractive forces are no longer negligible. negligible.

extremely high pressureextremely high pressure extremely low temperature extremely low temperature

10-2 Pressure10-2 Pressure

Pressure is force per unit area. Pressure is force per unit area.

P = f/AP = f/A

5 m

5 m 5 m

15 m

300 N

300 N


Gas molecules exert pressure with any Gas molecules exert pressure with any surface with which they are in contact. surface with which they are in contact.

Pressure is caused by collisions. Pressure is caused by collisions. Pressure depends on volume, temperature Pressure depends on volume, temperature

and number of gas molecules present. and number of gas molecules present.


Earth’s atmosphere is an Earth’s atmosphere is an envelope of air that exerts envelope of air that exerts pressure on earth’s pressure on earth’s surface and all the objects surface and all the objects on it.on it.

Atmospheric pressure is Atmospheric pressure is the sum of the pressures the sum of the pressures exerted by all the gases exerted by all the gases that make up the that make up the atmosphere (nitrogen, atmosphere (nitrogen, oxygen, argon, carbon oxygen, argon, carbon dioxide, etc.) dioxide, etc.)

Earth’s atmosphere exerts Earth’s atmosphere exerts a pressure of a pressure of approximately 10.1 N/cmapproximately 10.1 N/cm22

How did this happen?

10-2 Measuring Pressure10-2 Measuring Pressure

A barometer is a device A barometer is a device used to measure used to measure atmospheric pressure. atmospheric pressure.

The first barometer was The first barometer was invented by Evangelista invented by Evangelista Torricelli in the 1600s. Torricelli in the 1600s.

The mercury falls until the The mercury falls until the pressure exerted by its pressure exerted by its weight is equal to the weight is equal to the pressure exerted by the pressure exerted by the atmosphere. atmosphere.

The average atmospheric The average atmospheric pressure at sea level is pressure at sea level is 760 mmHg. 760 mmHg.

10-2 Units of Pressure10-2 Units of Pressure

millimeters of mercury (mmHg)millimeters of mercury (mmHg) atmospheres (atm)atmospheres (atm) pascals (Pa) and kilopascals (kPa)pascals (Pa) and kilopascals (kPa) torr (torr)torr (torr)

760 mmHg = 101.325 kPa = 760 torr = 1 atm760 mmHg = 101.325 kPa = 760 torr = 1 atm

10-2 Units of Pressure10-2 Units of Pressure

Convert 0.97 atm to kPa.Convert 0.97 atm to kPa.

Convert 785 mmHg to atm.Convert 785 mmHg to atm.

Convert 120 kPa to mmHg.Convert 120 kPa to mmHg.

Convert 430 mmHg to kPa.Convert 430 mmHg to kPa.

10-2 STP10-2 STP

Standard Temperature and PressureStandard Temperature and Pressure– 00˚C˚C– 1 atm, 101.325 kPa, 760 mmHg1 atm, 101.325 kPa, 760 mmHg

10-3 Gas Laws!10-3 Gas Laws!

Gas laws are simple mathematical relationships Gas laws are simple mathematical relationships between the volume, temperature, pressure and between the volume, temperature, pressure and amount of a gas. amount of a gas.

Boyle’s LawBoyle’s Law relates pressure and volume. relates pressure and volume. Charles’s LawCharles’s Law relates volume and temperature. relates volume and temperature. Gay-Lussac’s LawGay-Lussac’s Law relates pressure and relates pressure and

temperature. temperature. The The combined gas lawcombined gas law relates pressure, relates pressure,

temperature and volume. temperature and volume.

10-3 Boyle’s Law: Pressure-Volume10-3 Boyle’s Law: Pressure-VolumeRelationshipRelationship

Decreasing the volume of a gas Decreasing the volume of a gas causes the pressure to causes the pressure to increase. increase.

Increasing the volume of a gas Increasing the volume of a gas causes the pressure to causes the pressure to decrease. decrease.

Pressure is caused by gas Pressure is caused by gas molecules hitting the walls of the molecules hitting the walls of the container. container.

Decreasing the volume means Decreasing the volume means there will be more molecules per there will be more molecules per unit volume. unit volume.

The number of collisions will The number of collisions will increase and the pressure will increase and the pressure will increase. increase.

10-3: Boyle’s Law10-3: Boyle’s Law

The volume of a fixed mass of gas varies The volume of a fixed mass of gas varies inversely with the pressure at constant inversely with the pressure at constant temperature. temperature.

Remember, two variables are inversely Remember, two variables are inversely proportional if their product is a constant.proportional if their product is a constant.

PV = kPV = k

10-3: Boyle’s Law10-3: Boyle’s Law

Boyle’s law is most often used to compare Boyle’s law is most often used to compare changing conditions for a gas. changing conditions for a gas.

If temperature and number of molecules remains If temperature and number of molecules remains constant, thenconstant, then

PP11VV11 = k AND P = k AND P22VV22 = k = k

So, PSo, P11VV11 = P = P22VV22

If three of these values are known, you can If three of these values are known, you can solve for the fourth. solve for the fourth.

10-3: Boyle’s Law10-3: Boyle’s LawSample ProblemSample Problem

A sample of oxygen gas has a volume of A sample of oxygen gas has a volume of 150 mL when its pressure is 0.947 atm. 150 mL when its pressure is 0.947 atm. What will the volume of the gas be at a What will the volume of the gas be at a pressure of 0.987 atm if the temperature pressure of 0.987 atm if the temperature remains constant?remains constant?

10-3: Boyle’s Law10-3: Boyle’s LawSample ProblemSample Problem

A gas has a pressure of 1.26 atm and A gas has a pressure of 1.26 atm and occupies a volume of 7.40 L. If the gas is occupies a volume of 7.40 L. If the gas is compressed to a volume of 2.93 L at a compressed to a volume of 2.93 L at a constant temperature, what will its pressure constant temperature, what will its pressure be?be?

10-3 Charles’ Law: Volume-10-3 Charles’ Law: Volume-Temperature RelationshipTemperature Relationship

At constant pressure, gases At constant pressure, gases expand when heated and expand when heated and contract when cooled.contract when cooled.

At higher temperatures, gas At higher temperatures, gas molecules move faster and molecules move faster and collide more often with their collide more often with their container and with greater force. container and with greater force.

In a flexible container like a In a flexible container like a balloon, this forces the walls balloon, this forces the walls outward. outward.

The increased volume means The increased volume means gas molecules must travel gas molecules must travel farther before colliding with their farther before colliding with their container. container.

The lower collision frequency is The lower collision frequency is offset by the greater collision offset by the greater collision force and the pressure remains force and the pressure remains constant. constant.

Hot air balloons use Charles’s Law.

10-3: Charles’s Law 10-3: Charles’s Law

The volume of a fixed mass of gas at The volume of a fixed mass of gas at constant pressure varies directly with the constant pressure varies directly with the Kelvin temperature. Kelvin temperature.

Two variables are directly proportional if Two variables are directly proportional if their quotient is a constant.their quotient is a constant.

V/T = kV/T = kWhy must the temperature be in degrees Kelvin?Why must the temperature be in degrees Kelvin?

10-3: Celsius to Kelvin Conversions10-3: Celsius to Kelvin Conversions

K = K = °C + 273°C + 273

10-3: Charles’s Law10-3: Charles’s Law

Charles’s Law is most often used to Charles’s Law is most often used to compare changing conditions for a gas. compare changing conditions for a gas.

If pressure and number of moles are If pressure and number of moles are constant, thenconstant, then

VV11/T/T11 = k AND V = k AND V22/T/T22 = k = k

So, VSo, V11/T/T11 = V = V22/T/T22

If three of these values are known, you If three of these values are known, you can solve for the fourth. can solve for the fourth.

10-3: Charles’s Law10-3: Charles’s LawSample ProblemSample Problem

A sample of neon gas occupies a volume of A sample of neon gas occupies a volume of 752 mL at 25752 mL at 25°C. What volume will the gas °C. What volume will the gas occupy at 50°C if the pressure remains occupy at 50°C if the pressure remains constant?constant?

10-3: Charles’s Law10-3: Charles’s LawSample ProblemSample Problem

A helium-filled balloon has a volume of A helium-filled balloon has a volume of 2.75L at 202.75L at 20°C. The volume of the balloon °C. The volume of the balloon decreases to 2.46L when it is placed outside decreases to 2.46L when it is placed outside on a cold day. What is the outside on a cold day. What is the outside temperature in K? in °C?temperature in K? in °C?

10-3: Gay-Lussac’s Law10-3: Gay-Lussac’s Law

What is the relationship between What is the relationship between temperature and pressure if volume and temperature and pressure if volume and number of moles are held constant?number of moles are held constant?

How can this observation be explained How can this observation be explained using kinetic molecular theory?using kinetic molecular theory?

10-3: Gay-Lussac’s Law10-3: Gay-Lussac’s Law

How can the relationship between pressure How can the relationship between pressure and temperature be expressed and temperature be expressed mathematically?mathematically?

What formula might you use to compare What formula might you use to compare changing conditions of temperature and changing conditions of temperature and pressure for a gas at constant volume?pressure for a gas at constant volume?

10-3: Gay-Lussac’s Law10-3: Gay-Lussac’s LawSample ProblemSample Problem

A sample of helium gas exerts a pressure of A sample of helium gas exerts a pressure of 3.2 atm at 503.2 atm at 50°C. If the container is cooled to °C. If the container is cooled to 25°C, what pressure will the gas exert?25°C, what pressure will the gas exert?

10-3: Gay-Lussac’s Law10-3: Gay-Lussac’s LawSample ProblemSample Problem

A gas canister is designed to withstand A gas canister is designed to withstand pressure up to 30 atm. The gas contained in pressure up to 30 atm. The gas contained in the canister exerts a pressure of 7.2 atm at the canister exerts a pressure of 7.2 atm at 2525°C. At what temperature will the canister °C. At what temperature will the canister explode?explode?

10-3: The Combined Gas Law10-3: The Combined Gas Law

Boyle’s Law: PBoyle’s Law: P11VV11 = P = P22VV22

Charles’s Law: VCharles’s Law: V11/T/T11 = V = V22/T/T22

Gay-Lussac’s Law: PGay-Lussac’s Law: P11/T/T11 = V = V22/T/T22

The combined gas law combines these The combined gas law combines these three laws. three laws.

10-3 Combined Gas Law10-3 Combined Gas Law

A sample of nitrogen gas exerts 1.5 atm of A sample of nitrogen gas exerts 1.5 atm of pressure and occupies a volume of 4.2 L at pressure and occupies a volume of 4.2 L at 2525°C. What volume will it occupy at STP?°C. What volume will it occupy at STP?

10-3: Dalton’s Law of Partial 10-3: Dalton’s Law of Partial PressuresPressures

John Dalton (Atomic John Dalton (Atomic Theory) discovered Theory) discovered that in the absence of that in the absence of a chemical reaction, a chemical reaction, the pressure of a gas the pressure of a gas mixture is the sum of mixture is the sum of the individual the individual pressures of each gas pressures of each gas alone. alone.


The pressure of each gas in a mixture is The pressure of each gas in a mixture is called the called the partial pressurepartial pressure of that gas. of that gas.

Dalton’s law of partial pressuresDalton’s law of partial pressures states states that the total pressure of a mixture of gases that the total pressure of a mixture of gases is equal to the sum of the partial pressures is equal to the sum of the partial pressures of the component gases. of the component gases.

PPTT = P = P11 + P + P22 + P + P33 + … + …

10-3: Gases Collected by Water 10-3: Gases Collected by Water DisplacementDisplacement

Gases produced in the Gases produced in the lab are often collected lab are often collected over water.over water.

Hydrogen gas can be Hydrogen gas can be produced by reacting produced by reacting an acid with certain an acid with certain metals, like zinc. metals, like zinc.

One apparatus for One apparatus for collecting the hydrogen collecting the hydrogen gas is shown.gas is shown.


A gas collected by A gas collected by water displacement is water displacement is always mixed with always mixed with water vaporwater vapor. It is . It is impossible to collect a impossible to collect a pure sample of gas pure sample of gas over water. over water.

Water molecules at the Water molecules at the surface evaporate and surface evaporate and mix with the gas. mix with the gas.


The vapor pressure of The vapor pressure of water varies with water varies with temperature. temperature.

As temperature increases, As temperature increases, more water molecules more water molecules have enough energy to have enough energy to break free of the surface break free of the surface and become vapor and become vapor particles. particles.

Water vapor pressure Water vapor pressure increases with increases with temperature. temperature.


If you wanted to If you wanted to determine the pressure of determine the pressure of the gas you collected the gas you collected over water, you would over water, you would need to correct for the need to correct for the pressure exerted by the pressure exerted by the water vapor. water vapor.

First, make sure the First, make sure the water level inside and water level inside and outside the collection outside the collection flask are equal. This flask are equal. This means the pressure means the pressure inside the flask and inside the flask and outside the flask are outside the flask are equal. equal.

Patm

Pgas + PH2O

Patm = Pgas + PH2O


Read the atmospheric pressure. Read the atmospheric pressure. Then, determine the temperature and look Then, determine the temperature and look

up the vapor pressure of water at that up the vapor pressure of water at that temperature. (Table A-8 in the appendix)temperature. (Table A-8 in the appendix)

Subtract the vapor pressure of water at the Subtract the vapor pressure of water at the given temperature from the atmospheric given temperature from the atmospheric pressure to determine the pressure of the pressure to determine the pressure of the dry gas. dry gas.


Oxygen gas from the decomposition of potassium chlorate, Oxygen gas from the decomposition of potassium chlorate, KClOKClO33, was collected by water displacement. The , was collected by water displacement. The

barometric pressure and the temperature during the barometric pressure and the temperature during the experiment were 731.0 torr and 20.0experiment were 731.0 torr and 20.0˚C, respectively. What ˚C, respectively. What was the partial pressure of the oxygen collected?was the partial pressure of the oxygen collected?


Some hydrogen gas is collected over water at 20.0Some hydrogen gas is collected over water at 20.0˚C. The ˚C. The levels of water inside and outside the gas collection bottle levels of water inside and outside the gas collection bottle are the same. The partial pressure of hydrogen is 742.5 are the same. The partial pressure of hydrogen is 742.5 torr. What is the barometric pressure at the time the gas is torr. What is the barometric pressure at the time the gas is collected?collected?


Helium gas is collected over water at 25Helium gas is collected over water at 25˚C. What is the ˚C. What is the partial pressure of the helium, given that the barometric partial pressure of the helium, given that the barometric pressure is 750.0 mmHg?pressure is 750.0 mmHg?

chapter 10 physical characteristics of gases. 10-1 the kinetic-molecular theory of matter ...

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gas molecules

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fraction of particles