Chapter 10 Chapter 10 Gas LawsGas Laws

Objectives: Objectives: Understand the characteristics of gases, Understand the characteristics of gases, real and Ideal. real and Ideal. Understand the gas law Understand the gas law

Physical characteristics Physical characteristics of gasesof gases

The Kinetic-Molecular Theory of GasesThe Kinetic-Molecular Theory of Gases The Kinetic molecular theory is based on the The Kinetic molecular theory is based on the

idea that particles of matter are always in idea that particles of matter are always in motion.motion.

Ideal Vs. Real GasesIdeal Vs. Real Gases

Ideal gases Vs. Real gasesIdeal gases Vs. Real gases An ideal gas is an imaginary gas that perfectly fits all An ideal gas is an imaginary gas that perfectly fits all

the assumptions of the kinetic-molecular theory.the assumptions of the kinetic-molecular theory. A real gas is will only have these characteristics at a A real gas is will only have these characteristics at a

certain (not to high) pressure and temperature (not certain (not to high) pressure and temperature (not to low)to low)

To better understand this concept think of an ideal To better understand this concept think of an ideal energy efficient car, this car would be 100 % energy efficient car, this car would be 100 % efficient, that would never really happen because it efficient, that would never really happen because it would always loss energy to heat and friction. would always loss energy to heat and friction.

Ideal vs. RealIdeal vs. Real

Most gases are real gases in that they do Most gases are real gases in that they do not behave completely according to the not behave completely according to the assumptions of the kinetic molecular assumptions of the kinetic molecular theory.theory.

Noble gases will behave most like ideal Noble gases will behave most like ideal gases. Other diatomic gases will as well, gases. Other diatomic gases will as well, due to the fact that these are nonpolar due to the fact that these are nonpolar gases and tend to bond only to gases and tend to bond only to themselves. themselves.

Kinetic-Molecular Theory Kinetic-Molecular Theory

Five assumptions of ideal gases:Five assumptions of ideal gases: 1. gases consist of large number of tiny particles that are far apart 1. gases consist of large number of tiny particles that are far apart

relative to their size. (most of the volume of gases is empty space)relative to their size. (most of the volume of gases is empty space) 2. Collision between gas particles and between particles and 2. Collision between gas particles and between particles and

container walls are elastic collisions. an elastic collision is one in container walls are elastic collisions. an elastic collision is one in which there is no net loss of kinetic energy.which there is no net loss of kinetic energy.

3. Gas particles are in constant, rapid, random motion. They 3. Gas particles are in constant, rapid, random motion. They therefore possess kinetic energy, which is energy of motion. therefore possess kinetic energy, which is energy of motion.

4. THERE ARE NO FORCES OF ATTRACTION OR REPULSION 4. THERE ARE NO FORCES OF ATTRACTION OR REPULSION BETWEEN GAS PARTICLES. (THEY COLLID BUT DO NOT BETWEEN GAS PARTICLES. (THEY COLLID BUT DO NOT STICK TOGETHER)STICK TOGETHER)

5. The average kinetic energy of gas particles depends on the 5. The average kinetic energy of gas particles depends on the temperature of the gas. temperature of the gas.

Kinetic Energy an Kinetic Energy an TemperatureTemperature

Assumption five, the average kinetic energy of Assumption five, the average kinetic energy of gas particles depends on the temperature of gas particles depends on the temperature of the gas. the gas.

Equation: KE = ½ mvEquation: KE = ½ mv22

M = mass, v = speedM = mass, v = speed Gas of the same sub will have the same mass, Gas of the same sub will have the same mass,

therefore their KE depends only of speed. therefore their KE depends only of speed. (speed increases with temp increase)(speed increases with temp increase)

All gases at the same temperature have the All gases at the same temperature have the same KE. Therefore lighter gases have higher same KE. Therefore lighter gases have higher speeds. speeds.

Physical Properties of Physical Properties of gasesgases

Expansion : Completely fill the container.Expansion : Completely fill the container. (3/4) move in all directions and no attraction (3/4) move in all directions and no attraction

Fluidity: Flow past one another (4)Fluidity: Flow past one another (4) Low density: (density in gas is 1/1000 that of Low density: (density in gas is 1/1000 that of

the liquid state) (1 – the gaseous state is the liquid state) (1 – the gaseous state is farther apart)farther apart)

Compressibility: With pressure we can Compressibility: With pressure we can decrease the volume.decrease the volume.

Diffusion and Effusion: gases spread out and Diffusion and Effusion: gases spread out and mix with one another.mix with one another.

Diffusion and EffusionDiffusion and Effusion

Diffusion: Diffusion: Spontaneous mixing of the particles of two Spontaneous mixing of the particles of two

substances caused by their random motionsubstances caused by their random motion

Effusion:Effusion: Is a process by which gas particles under Is a process by which gas particles under

pressure pass through a tiny opening. pressure pass through a tiny opening.

Combine Gas LawCombine Gas Law

Recall that only Ideal gases can be Recall that only Ideal gases can be determined by the combined gas law.determined by the combined gas law.

PP11VV1 1 = = PP22VV22

TT1 1 TT22

P P = Pressure= Pressure

T T = Temperature = Temperature

V V = volume = volume

PressurePressure

Pressure = force per unit area on a surface.Pressure = force per unit area on a surface.

Pressure = Force / AreaPressure = Force / Area

SI Unit for force is a Newton, N. SI Unit for force is a Newton, N. A Newton is the fore that will increase the A Newton is the fore that will increase the

speed of a one kilogram mass by one meter speed of a one kilogram mass by one meter per second each second it is applied.per second each second it is applied.

PressurePressure

At Earth’s surface, each kilogram of mass exerts 9.8 N At Earth’s surface, each kilogram of mass exerts 9.8 N of force, due to gravity.of force, due to gravity.

Lets look at the relationship of force and area = Lets look at the relationship of force and area = pressure. pressure.

If a ballerina has a force of 500 N and is standing flat If a ballerina has a force of 500 N and is standing flat on two feet (325cmon two feet (325cm22) the force is 1.5N. If the same ) the force is 1.5N. If the same ballerina stands on her toes the area decreases to ballerina stands on her toes the area decreases to (13cm(13cm22) the force increases to 38.5 N. If she sands on ) the force increases to 38.5 N. If she sands on one toe it increases to 77N. one toe it increases to 77N.

So we can see the if force is constant and area So we can see the if force is constant and area decrease the pressure will increase.decrease the pressure will increase.

Units of PressureUnits of Pressure

Pascal Pascal Pa Pa SI unitSI unit1Pa = 1N/m1Pa = 1N/m22

Millimeter Millimeter mm Hgmm Hg At sea level At sea level of mercuryof mercury 0C = 0C = 760mmHg760mmHg

Atmosphere Atmosphere atm atm 1atm=760mmHg1atm=760mmHg

=1.01325 X 10=1.01325 X 1055 Pa Pa= 101.325 kPa= 101.325 kPa

Torr Torr TorrTorr 1 torr = 1 mm Hg1 torr = 1 mm Hg

Standard Temperature Standard Temperature and Pressureand Pressure

STP = 1 atm of pressure at 0C.STP = 1 atm of pressure at 0C.

Pressure conversionsPressure conversions

The average pressure in Denver The average pressure in Denver Colorado is 0.830 atm. Express this Colorado is 0.830 atm. Express this pressure in mmHg?pressure in mmHg?

In kPa?In kPa?

Practice:Practice:

Covert a pressure of 1.75 atm to kPa?Covert a pressure of 1.75 atm to kPa? To mmHg?To mmHg?

Convert a pressure of 570. torr to Convert a pressure of 570. torr to atmospheres an to kPa?atmospheres an to kPa?

Gas LawsGas Laws

Objective: Be able to define the gas laws and use the Objective: Be able to define the gas laws and use the equation to solve gas law problems. equation to solve gas law problems. Understand the combined gas laws is all of the gas laws Understand the combined gas laws is all of the gas laws together.together.Be able to determine the gas laws from the combined gas Be able to determine the gas laws from the combined gas law. law.

Combined Gas LawCombined Gas Law

Recall that only Ideal gases can be determined by the Recall that only Ideal gases can be determined by the combined gas law.combined gas law.

Expresses the relationship between pressure, volume Expresses the relationship between pressure, volume and temperature of a fixed amount of gas.and temperature of a fixed amount of gas.

PP11VV1 1 = = PP22VV22

TT1 1 TT22

P P = Pressure= Pressure

T T = Temperature = Temperature

V V = volume = volume

Boyles Law: Pressure-Boyles Law: Pressure-Volume Volume

Boyles Law – volume of a fixed mass of Boyles Law – volume of a fixed mass of gas varies inversely with the pressure at gas varies inversely with the pressure at constant temperature. constant temperature. This means that when volume increases This means that when volume increases

pressure decreases by the same amount. pressure decreases by the same amount. Lets consider the kinetic-molecular theory, Lets consider the kinetic-molecular theory,

how can we explain this relationship.how can we explain this relationship.

Boyles LawBoyles Law

PV = kPV = k K is the constantK is the constant

PP11VV11 = P = P22VV22

Use this equation when comparing changing Use this equation when comparing changing conditions.conditions.

If given three of the four values, one can If given three of the four values, one can solve for what is missing.solve for what is missing.

Practice:Practice:

A sample of oxygen has a volume of 150 A sample of oxygen has a volume of 150 ml when its pressure is 0.97 atm. What ml when its pressure is 0.97 atm. What will the volume of the gas be at a 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?

Charles’s Law: Volume-Charles’s Law: Volume-Temperature Temperature RelationshipRelationship

The Kelvin temperature scale is a scale The Kelvin temperature scale is a scale that starts at a temperature that starts at a temperature corresponding to -273.15 C. That corresponding to -273.15 C. That temperature is the lowest possible. The temperature is the lowest possible. The temperature -273.15C is called absolute temperature -273.15C is called absolute zero and is given the value of aeroin the zero and is given the value of aeroin the Kelvin scale.Kelvin scale.

K=273.15 + CK=273.15 + C

Charles LawCharles Law

VV11 == V V22

TT11 TT22

If pressure is constant then the volume If pressure is constant then the volume changes 1/273 for each degree Celsius.changes 1/273 for each degree Celsius.

Charles’s Law states that the volume of a fixed Charles’s Law states that the volume of a fixed mass of gas at constant pressure varies mass of gas at constant pressure varies directly with the Kelvin temperaturedirectly with the Kelvin temperature

Charles LawCharles Law

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

Gay-Lussac’s LawGay-Lussac’s Law

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

Pressure is constantPressure is constant Pressure and Temperature are directly Pressure and Temperature are directly

proportional, this means as one doubles proportional, this means as one doubles so does the other.so does the other.

Gay-Lussac LawGay-Lussac Law

PP11 = = PP22

TT11 T T22

Temperature should be in Kelvin:Temperature should be in Kelvin:

C + 273 = KC + 273 = K

Gay Lussac’s LawGay Lussac’s Law

PracticePractice The gas in an aerosol can is at a The gas in an aerosol can is at a

pressure of 3.00 atm at 25C. Directions pressure of 3.00 atm at 25C. Directions on the can warn the user not to keep the on the can warn the user not to keep the can in a place where the temperature can in a place where the temperature exceeds 52C. What would the gas exceeds 52C. What would the gas pressure in the can be at 52C?pressure in the can be at 52C?

Combined Gas LawCombined Gas Law

We use the combine gas law when the We use the combine gas law when the three variables must be dealt with all at three variables must be dealt with all at once.once.

The Combine Gas Law expresses the The Combine Gas Law expresses the relationship between pressure, volume, relationship between pressure, volume, and temperature of a fixed amount of and temperature of a fixed amount of gas. gas.

Combined Gas LawCombined Gas Law

PP11VV11 = = PP22VV22

TT11 TT22

In this case nothing is constant!In this case nothing is constant!

Pressure units must be the samePressure units must be the same

Volume units must be the sameVolume units must be the same

Temperature must be in KelvinTemperature must be in Kelvin

Practice:Practice:

A helium-filled balloon has a volume of A helium-filled balloon has a volume of 50.0 L at 25C and 1.08 atm. What 50.0 L at 25C and 1.08 atm. What volume will it have at 0.855 atm and volume will it have at 0.855 atm and 10C?10C?

Partial PressurePartial Pressure

Daltons law of partial pressure – the total Daltons law of partial pressure – the total pressure of a mixture of gases is equal to pressure of a mixture of gases is equal to the sum of the partial pressure of the the sum of the partial pressure of the component gases. component gases.

PPt t = P= P11 + P + P2 ………..2 ………..

The total Pressure of a mixture of gases The total Pressure of a mixture of gases is equal to the pressures of all the is equal to the pressures of all the components combined.components combined.

Gases Collected over waterGases Collected over water

In lab most of the time gas is collected over In lab most of the time gas is collected over water. Gas collected this way is not pure, but water. Gas collected this way is not pure, but has water vapor mixed into it. has water vapor mixed into it.

We can use atmospheric pressure to We can use atmospheric pressure to determine the p of the water or the gas.determine the p of the water or the gas.

P atm = Pgas + PwaterP atm = Pgas + Pwater If you want to find the partial pressure of a dry If you want to find the partial pressure of a dry

gas we can subtract the water pressure (which gas we can subtract the water pressure (which can be a standard found on a chart) from the P can be a standard found on a chart) from the P atm. atm.

Practice:Practice:

Oxygen gas from decomposition of Oxygen gas from decomposition of potassium chlorate, KClOpotassium chlorate, KClO33, was collected , was collected

by water displacement. The barometric by water displacement. The barometric pressure and the temperature during the pressure and the temperature during the experiment were 731.0 Torr and 20C. experiment were 731.0 Torr and 20C. What was the partial pressure of he What was the partial pressure of he oxygen collected? The vapor pressure of oxygen collected? The vapor pressure of water at 20C, from table A-8, is 17.5 torrwater at 20C, from table A-8, is 17.5 torr

Volume- Mass Volume- Mass Relationship of GasesRelationship of Gases

Gay-Lussac’s law of combing volumes of Gay-Lussac’s law of combing volumes of gases – at constant temperature and pressure, gases – at constant temperature and pressure, the volume of gaseous reactants and products the volume of gaseous reactants and products can be expressed as ratios of small whole can be expressed as ratios of small whole numbers. numbers.

Hydrogen gas + chlorine gas Hydrogen gas + chlorine gas Hydrogen chloride Hydrogen chloride 1L 1L 1L 1L 2L2L

1 volume1 volume 1 volume 1 volume 2 volume 2 volume 1 molecule1 molecule 1 molecule1 molecule 2 molecules 2 molecules 1 mole 1 mole 1 mole1 mole 2 mole 2 mole

Avagardro’s law states that equal volumes of gases at the same Avagardro’s law states that equal volumes of gases at the same temperature and pressure contains equal numbers of molecules. temperature and pressure contains equal numbers of molecules.

Molar Volume of GasesMolar Volume of Gases

Standard molar Volume of a gas is the Standard molar Volume of a gas is the volume occupied by one mole of a gas at volume occupied by one mole of a gas at STP. STP.

1 mol/22.4L1 mol/22.4L

Practice:Practice:

A chemical reaction produces 0.0680 mol A chemical reaction produces 0.0680 mol of oxygen gas. What volume in liters is of oxygen gas. What volume in liters is occupied by this gas sample at STP?occupied by this gas sample at STP?

Use molar volume: 22.4L/molUse molar volume: 22.4L/mol

More Practice:More Practice:

A chemical reaction produced 98.0 mL of A chemical reaction produced 98.0 mL of sulfur dioxide gas, SOsulfur dioxide gas, SO22, at STP. What , at STP. What

was the mass of the gas produced?was the mass of the gas produced?