section 11–2: the gas laws coach kelsoe chemistry pages 369–375

Section 11–2:Section 11–2:The Gas LawsThe Gas Laws

Coach KelsoeCoach Kelsoe

ChemistryChemistry

Pages 369–375Pages 369–375

Section 11–2 ObjectivesSection 11–2 Objectives Use the kinetic-molecular theory to Use the kinetic-molecular theory to

explain the relationships between gas explain the relationships between gas volume, temperature, and pressure.volume, temperature, and pressure.

Use Boyle’s law to calculate volume-Use Boyle’s law to calculate volume-pressure changes at constant pressure changes at constant temperature.temperature.

Use Charles’s law to calculate volume-Use Charles’s law to calculate volume-temperature changes at constant temperature changes at constant pressure.pressure.

Section 11–2 ObjectivesSection 11–2 Objectives Use Gay-Lussac’s law to calculate Use Gay-Lussac’s law to calculate

pressure-temperature changes at pressure-temperature changes at constant volume.constant volume.

Use the combined gas law to calculate Use the combined gas law to calculate volume-temperature-pressure changes.volume-temperature-pressure changes.

Use Dalton’s law of partial pressures to Use Dalton’s law of partial pressures to calculate partial pressures and total calculate partial pressures and total pressures.pressures.

The Gas LawsThe Gas Laws

Scientists have been studying the physical Scientists have been studying the physical properties of gases for hundreds of years.properties of gases for hundreds of years.

In 1662, Robert Boyle discovered that gas In 1662, Robert Boyle discovered that gas pressure and volume are related pressure and volume are related mathematically. The observations of Boyle mathematically. The observations of Boyle and others led to the development of the gas and others led to the development of the gas laws.laws.

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

Boyle’s Law: Pressure-Volume Boyle’s Law: Pressure-Volume RelationshipRelationship

Robert Boyle discovered that doubling Robert Boyle discovered that doubling the pressure on a sample of gas at the pressure on a sample of gas at constant temperature reduces its constant temperature reduces its volume by one-half. Tripling the gas volume by one-half. Tripling the gas pressure reduces its volume to one-third pressure reduces its volume to one-third the original.the original.

As one variable increases, the other As one variable increases, the other reduces.reduces.


The general volume-pressure The general volume-pressure relationship is defined by Boyle’s law.relationship is defined by Boyle’s law.

Boyle’s lawBoyle’s law states that the volume of a states that the volume of a fixed mass of gas varies inversely with fixed mass of gas varies inversely with the pressure at constant temperature.the pressure at constant temperature.

Mathematically, Boyle’s law is Mathematically, Boyle’s law is expressed as follows:expressed as follows:

PV = kPV = k• The value of The value of kk is constant for a given gas. is constant for a given gas.


Boyle’s law can be used to compare Boyle’s law can be used to compare changing conditions for a gas.changing conditions for a gas.

Using PUsing P11 and V and V11 to stand for initial to stand for initial conditions and Pconditions and P22 and V and V22 to stand for to stand for new conditions, the formula can be new conditions, the formula can be represented as follows:represented as follows:

PP11VV11 = P = P22VV22

So if you are given three values, you So if you are given three values, you can solve for the unknown.can solve for the unknown.

Sample Problem 10-2Sample Problem 10-2

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?

PP11VV11 = P = P22VV22

(0.947 atm)(150. mL) = (0.987 atm)V(0.947 atm)(150. mL) = (0.987 atm)V22

VV2 2 = (0.947 atm)(150. mL)/0.987 atm= (0.947 atm)(150. mL)/0.987 atm VV2 2 = 144 mL O= 144 mL O22

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

The quantitative relationship between The quantitative relationship between volume and temperature was volume and temperature was discovered by the French scientist discovered by the French scientist Jacques Charles in 1787.Jacques Charles in 1787.

Charles discovered that there is a direct Charles discovered that there is a direct relationship between the volume of a relationship between the volume of a gas and its temperature. As one gas and its temperature. As one increases, the other increases.increases, the other increases.


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

Mathematically, Charles’s law can best Mathematically, Charles’s law can best be described as:be described as:

VV11TT22 = V = V22TT11

Temperature must be measured in Temperature must be measured in Kelvin by adding 273 to the Celsius Kelvin by adding 273 to the Celsius temperature.temperature.


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°C. That corresponding to -273°C. That temperature is the lowest one possible.temperature is the lowest one possible.

The temperature -273°C is referred to The temperature -273°C is referred to as as absolute zeroabsolute zero and is given a value and is given a value of zero in the Kelvin scale.of zero in the Kelvin scale.


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

VV11TT22 = V = V22TT11

(752 mL)(323 K) = V(752 mL)(323 K) = V22(298 K)(298 K) VV2 2 = (752 mL)(323 K)/298 K= (752 mL)(323 K)/298 K VV2 2 = 815 mL Ne= 815 mL Ne

Gay-Lussac’s Law: Pressure-Gay-Lussac’s Law: Pressure-Temperature RelationshipTemperature Relationship

For a fixed quantity of gas at constant For a fixed quantity of gas at constant volume, the pressure will be directly volume, the pressure will be directly proportional to the Kelvin temperature.proportional to the Kelvin temperature.

Joseph Gay-Lussac is given credit for Joseph Gay-Lussac is given credit for first identifying this relationship in 1802.first identifying this relationship in 1802.

According to According to Gay-Lussac’s lawGay-Lussac’s law, the , the pressure of a fixed mass of gas at pressure of a fixed mass of gas at constant volume varies directly with the constant volume varies directly with the Kelvin temperature.Kelvin temperature.

Gay-Lussac’s Law: Pressure-Gay-Lussac’s Law: Pressure-Temperature RelationshipTemperature Relationship

Mathematically, Gay-Lussac’s law is as Mathematically, Gay-Lussac’s law is as follows:follows:

PP11TT2 2 = P= P22TT11

When three of the four values are When three of the four values are known, we can solve for the one known, we can solve for the one unknown.unknown.


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

PP11TT2 2 = P= P22TT11

(3.00 atm)(325 K) = P(3.00 atm)(325 K) = P22(298 K)(298 K) PP2 2 = (3.00 atm)(325 K)/(298 K) = 3.27 atm= (3.00 atm)(325 K)/(298 K) = 3.27 atm

Combined Gas LawCombined Gas Law

A gas sample often undergoes changes A gas sample often undergoes changes in temperature, pressure, and volume in temperature, pressure, and volume all at the same time. When this occurs, all at the same time. When this occurs, three variables must be dealt with at three variables must be dealt with at once.once.

Boyle’s law, Charles’ law, and Gay-Boyle’s law, Charles’ law, and Gay-Lussac’s law can be combined into a Lussac’s law can be combined into a single expression that is useful in such single expression that is useful in such situations.situations.

Combined Gas LawCombined Gas Law

The The combined gas lawcombined gas law expresses the 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.

The combined gas law can be expressed The combined gas law can be expressed as follows:as follows:

PP11VV11TT2 2 = P= P22VV22TT11

The units for pressure and volume do The units for pressure and volume do not matter, but temperature MUST be not matter, but temperature MUST be measured in Kelvins!measured in Kelvins!


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

PP11VV11TT2 2 = P= P22VV22TT11

(1.08 atm)(50.0 L)(283 K)=(0.855 atm) (1.08 atm)(50.0 L)(283 K)=(0.855 atm) VV22(298 K)(298 K)

VV2 2 = (1.08 atm)(50.0 L)(283 K)/(0.855 = (1.08 atm)(50.0 L)(283 K)/(0.855 atm)(298 K) = 60.0 Latm)(298 K) = 60.0 L

NOTE THIS!!!NOTE THIS!!!

The formulas I gave you for Charles’s The formulas I gave you for Charles’s law, Gay-Lussac’s law, and the law, Gay-Lussac’s law, and the combined gas law are not written in the combined gas law are not written in the same manner. I use the formulas in this same manner. I use the formulas in this powerpoint because the math seems to powerpoint because the math seems to be less fuzzy in this format.be less fuzzy in this format.

The IMPORTANT thing to keep in mind The IMPORTANT thing to keep in mind are which values belong together! That are which values belong together! That will be the difference in what is correct will be the difference in what is correct and what is wrong!and what is wrong!

Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures

John Dalton, the English chemist who John Dalton, the English chemist who proposed the atomic theory, also proposed the atomic theory, also studied gas mixtures.studied gas mixtures.

He found that He found that in the absence of a in the absence of a chemical reactionchemical reaction, the pressure of a gas , the pressure of a gas mixture is the sum of the individual mixture is the sum of the individual pressures of each gas alone.pressures of each gas 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

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

The law is true no matter how many gases are The law is true no matter how many gases are present.present.

Dalton’s law may be expressed as such:Dalton’s law may be expressed as such:

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

• Where PWhere PTT is the total pressure and where P is the total pressure and where P11, P, P22, , and Pand P33 are the partial pressures of gases 1, 2, & 3. are the partial pressures of gases 1, 2, & 3.

Gases Collected by Water Gases Collected by Water DisplacementDisplacement

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

You can apply Dalton’s law of partial You can apply Dalton’s law of partial pressures in calculating the pressures of pressures in calculating the pressures of gases collected this way.gases collected this way.

A gas collected by water displacement is not A gas collected by water displacement is not pure but is always mixed with water vapor. pure but is always mixed with water vapor. That is because water molecules at the liquid That is because water molecules at the liquid surface evaporate and mix with the gas surface evaporate and mix with the gas molecules.molecules.

Water vapor, like other gases, exerts a Water vapor, like other gases, exerts a pressure, known as pressure, known as water-vapor pressurewater-vapor pressure..


Suppose you wanted to determine the total Suppose you wanted to determine the total pressure of the gas and water vapor inside a pressure of the gas and water vapor inside a collection bottle. You would raise the bottle collection bottle. You would raise the bottle until the water levels inside and outside were until the water levels inside and outside were the same so that the total pressure inside the the same so that the total pressure inside the bottle would be the same as the atmospheric bottle would be the same as the atmospheric pressure, Ppressure, Patmatm..

According to Dalton’s law of partial pressures, According to Dalton’s law of partial pressures, the following is true:the following is true:

PPatmatm = P = Pgasgas + P + PH2OH2O


So how do we know the pressure of So how do we know the pressure of water vapor? Someone has already water vapor? Someone has already done that work for us!done that work for us!

In Appendix A in the back of your In Appendix A in the back of your textbook there is a table that gives you textbook there is a table that gives you the water-vapor pressure for a given the water-vapor pressure for a given temperature.temperature.

For example, the water-vapor pressure For example, the water-vapor pressure at 22.0°C is 19.8 mm Hg (or 19.8 torr) at 22.0°C is 19.8 mm Hg (or 19.8 torr) or 2.64 kPa.or 2.64 kPa.


Oxygen gas from the decomposition of Oxygen gas from the decomposition of potassium chlorate, KClOpotassium chlorate, KClO33, was , was collected by water displacement. The collected by water displacement. The barometric pressure and the barometric pressure and the temperature during the experiment temperature during the experiment were 731.0 torr and 20.0°C, were 731.0 torr and 20.0°C, respectively. What was the partial respectively. What was the partial pressure of the oxygen collected?pressure of the oxygen collected?


Given: PGiven: Patmatm = 731.0 torr, P = 731.0 torr, PH2OH2O = 17.5 torr = 17.5 torr (from Appendix A-8), P(from Appendix A-8), Patmatm = P = PO2O2 + P + PH2OH2O

Unknown: PUnknown: PO2O2 in torr in torr PPatmatm = P = PO2O2 + P + PH2OH2O

PPO2O2 = P = Patmatm - P - PH2OH2O

PPO2O2 = 731.0 torr - 17.5 torr = 713.5 torr = 731.0 torr - 17.5 torr = 713.5 torr

VocabularyVocabulary

Absolute zeroAbsolute zero Boyle’s lawBoyle’s law Charles’s lawCharles’s law Combined gas lawCombined gas law Dalton’s law of partial pressuresDalton’s law of partial pressures Gas lawsGas laws Gay-Lussac’s lawGay-Lussac’s law Partial pressurePartial pressure

section 11–2: the gas laws coach kelsoe chemistry pages 369–375

Documents