Gas Laws: Pressure, Volume, and Hot Air NEXT Introduction This lesson will introduce three ways of...

Gas Laws: Pressure, Volume, and Hot Air

Introduction

This lesson will introduce three ways of predicting the behavior of gases: Boyle’s Law, Charles’ Law and Gay-Lussac’s Law. Never heard of them? Don’t worry– that’s the purpose of this lesson!

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Basic Terminology

Boyle’s Law

Charles’ Law

Ideal Gas Law

Review of all four lessonsReview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 1: Basic Terminology

This lesson reviews terms used to describe the properties and behavior of gases.

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Opening thoughts…

Have you ever:

Seen a hot air balloon?

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Opening thoughts…

Have you ever:

Seen a hot air balloon?

Had a soda bottle spray all over you?

Baked (or eaten) a nice, fluffy cake?

These are all examples of gases at work!

Major Components of the Earth’s Atmosphere

Nitrogen is the predominant gas in the atmosphere due to its geochemical inertness.

Oxygen is almost entirely biological.

Argon is the product that forms from the decay of the mantel and crust.

NitrogenNitrogen 78.08%78.08%

OxygenOxygen 20.95%20.95%

ArgonArgon 0.934%0.934%

Minor Components of the Earth’s Air

CO2 is most abundant of the minor gases.

He is a decay product of radioactive elements in the Earth.

Ne is probably primordial.

COCO22 0.036%0.036%

NeNe 0.0018180.001818%%

HeHe 0.0005240.000524%%

CHCH44 0.0002%0.0002%

KrKr 0.0001140.000114%%

Properties of GasesProperties of GasesGas properties can be modeled using math. Gas properties can be modeled using math.

Model depends on—Model depends on— V = volume of the gas (L)= V = volume of the gas (L)= vol. of containervol. of container

T = temperature (Kelvin) (K)T = temperature (Kelvin) (K) ALL temperatures in the entire chapter ALL temperatures in the entire chapter

MUST be in Kelvin!!! No Exceptions!MUST be in Kelvin!!! No Exceptions! n = amount (moles)n = amount (moles) P = pressure (atmospheres)P = pressure (atmospheres)

Properties of Gases

You can predict the behavior of gases based on the following properties:

Pressure

Volume

Amount (moles)

Temperature

Lets review each of these briefly…

PressureVolume

Amount (moles)

Temperature

Pressure

Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa.

• If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area).pressure explained

• Atmospheric pressure videoNEXTPREVIOUS

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PressurePressurePressure of air is measured Pressure of air is measured

with a BAROMETER with a BAROMETER Hg rises in tube until force of Hg Hg rises in tube until force of Hg

(down) balances the force of (down) balances the force of atmosphere (pushing up). (Just atmosphere (pushing up). (Just like a straw in a soft drink)like a straw in a soft drink)

P of Hg pushing down related to P of Hg pushing down related to Hg densityHg density column heightcolumn height

PressurePressureColumn height measures Column height measures

Pressure of atmospherePressure of atmosphere 1 standard atmosphere 1 standard atmosphere

(atm) (atm)

= 760 mm Hg = 760 mm Hg

= 760 torr= 760 torr

= 101.3 kPa (SI unit is = 101.3 kPa (SI unit is PASCAL) PASCAL)

= 101,300 Pascals= 101,300 Pascals

Pressure ConversionsA. What is 475 mm Hg expressed in atm?

760 mm Hg = 1 atm

475 mm Hg = x

x = 475/760 = 0.625 atm

B. The pressure of a tire is measured as 10 kPa. What is this pressure in mm Hg?

Pressure ConversionsA. What is 2 atm expressed in torr?

Scientists have agreed to use a set of standard conditions for reporting properties of gases and other substances, SATP.

Standard Ambient Temperature and Pressure (SATP) is 25° C and 100 kPa.

Previous conditions used were referred to as STP (standard temperature and pressure)

STP is 0°C and 101.325 kPa

SATP and STP

Pressure

VolumeAmount (moles)

Temperature

Volume

Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the Litre, L.

Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…)

Pressure

Volume

Amount (moles)Temperature

Amount (moles)

Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas.

By definition, one mole of a substance contains approximately 6.022 x 1023 particles of the substance. You can understand why we use mass and moles!

1 mol of any gas occupies 22.4L.

Pressure

Volume

Amount (moles)

Temperature

Temperature is the measurement with which you’re probably most familiar (and the most complex to describe completely). For these lessons, we will be using temperature measurements in Kelvin, K.

Temperature is the average kinetic energy of the particles in a substance.

The Kelvin scale starts at Absolute 0, which is -273.15°C. To convert Celsius to Kelvin, add 273.15.

Kelvin scale

Absolute zero

The Kelvin scale starts at Absolute 0, which is -273.15°C.

To convert Celsius to Kelvin, add 273.15.

To convert Kelvin to Celsius, subtract 273.15

How do they all relate?

Some relationships of gases may be easy to predict. Some are more subtle.Now that we understand the factors that affect the behavior of gases, we will study how those factors interact.

How do they all relate?

Some relationships of gases may be easy to predict. Some are more subtle.Now that we understand the factors that affect the behavior of gases, we will study how those factors interact.

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Let’s go!

Lesson 2: Boyle’s Law

This lesson introduces Boyle’s Law, which describes the relationship between pressure and volume of gases.

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Boyle’s Law

This law is named for Charles Boyle, who studied the relationship between pressure, p, and volume, V, in the mid-1600s.

Boyle determined that for the same amount of a gas at constant temperature,

p x V = constant This defines an inverse relationship:

when one goes up, the other comes down.

pressure

volume

What does Boyle’s Law mean?

p x V = constantSuppose you have a cylinder with a piston in the top so you can change the volume. The cylinder has a gauge to measure pressure, is contained so the amount of gas is constant, and can be maintained at a constant temperature.

A decrease in volume will result in increased pressure.

Hard to picture? Let’s fix that!

Boyle’s Law at Work…

Doubling the pressure reduces the volume by half. Conversely, when the volume doubles, the pressure decreases by half.

Application of Boyle’s Law

Boyle’s Law can be used to predict the interaction of pressure and volume.

If you know the initial pressure and volume, and have a target value for one of those variables, you can predict what the other will be for the same amount of gas under constant temperature.

Let’s try it!

p1 x V1 = p2 x V2

p1 = initial pressure

V1 = initial volume

p2 = final pressure

V2 = final volume

If you know three of the four, you can calculate the fourth.

p1 x V1 = p2 x V2

p1 = 1 KPa

V1 = 4 liters

p2 = 2 KPa

V2 = ?

Solving for V2, the final volume equals 2 liters.

So, to increase the pressure of 4 liters of gas from 1 KPa to 2 KPa, the volume must be reduced to 2 liters.

Boyle’s Law: Summary

Pressure * Volume = Constant p1 x V1 = p2 x V2

With constant temperature and amount of gas, you can use these relationships to predict changes in pressure and volume.

Charles’ Law

This lesson introduces Charles’ Law, which describes the relationship between volume and temperature of gases.

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Charles’ Law

This law is named for Jacques Charles, who studied the relationship volume, V, and temperature, T, around the turn of the 19th century.

He determined that for the same amount of a gas at constant pressure,

V / T = constant This defines a direct relationship:

an increase in one results in an increase in the other.

volume

temperature

What does Charles’ Law mean?

V / T = constantSuppose you have that same cylinder with a piston in the top allowing volume to change, and a heating/cooling element allowing for changing temperature. The force on the piston head is constant to maintain pressure, and the cylinder is contained so the amount of gas is constant.

An increase in temperature results in increased volume.

Hard to picture? Let’s fix it (again)!NEXTPREVIOUS

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Charles’ Law at Work…

As the temperature increases, the volume increases. Conversely, when the temperature decreases, volume decreases.

Application of Charles’ Law

Charles’ Law can be used to predict the interaction of temperature and volume.

If you know the initial temperature and volume, and have a target value for one of those variables, you can predict what the other will be for the same amount of gas under constant pressure.

Let’s try it!

V1 = initial volume

T1 = initial temperature

V2 = final volume

T2 = final temperature

If you know three of the four, you can calculate the fourth.

V1 = 2.5 litersT1 = 250 KV2 = 4.5 litersT2 = ?Solving for T2, the final temperature equals 450 K.So, increasing the volume of a gas at constant pressure from 2.5 to 4.5 liters results in a temperature increase of 200 K.

Charles’ Law: Summary

Volume / Temperature = Constant

With constant pressure and amount of gas, you can use these relationships to predict changes in temperature and volume.

Gay-Lussac’s LawGay-Lussac’s Law

He measured the temperature of air at different pressures, and observed a pattern of behavior which led to his mathematical law.Old man Lussac determined the relationship between temperature and pressure of a gas.During his experiments volume of the system and amount of gas were held constant.

Pressure Gauge

Car before a tripCar before a trip

Think of a tire...Think of a tire...

Let’s get onthe road

Car after a long tripCar after a long trip

Think of a tire...Think of a tire...

Pressure Gauge

How does Pressure and Temperature of gases relate

graphically?

How does Pressure and Temperature of gases relate

graphically?

P/T = k

Volume, # of particlesremain constant

Gay-Lussac’s Mathematical Law:Gay-Lussac’s Mathematical Law:

What if we had a change in conditions?What if we had a change in conditions?

since P/T = ksince P/T = k

T and P = Gay-Lussac’s LawT and P = Gay-Lussac’s Law

T1 = 127°C + 273 = 400K P1 = 3.0 atm T2 = 227°C + 273 = 500K P2 = ?

1) determine which variables you have:

2) determine which law is being represented:

Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C? Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C?

4) Plug in the variables:

(500K)(3.0atm) = P2 (400K)(500K)(3.0atm) = P2 (400K)

P2 = 3.8atmP2 = 3.8atm

3.0 atm P2

3.0 atm P2400K 500K400K 500K

=5) Cross multiply and

divide5) Cross multiply and

divide

Gas laws video Gas laws demos

LAWLAW RELAT-RELAT-IONSHIPIONSHIP LAWLAW CON-CON-

STANTSTANT

Boyle’sBoyle’s PP V V PP11VV1 1 = P= P22VV22 T, nT, n

CharlesCharles’’

VV T TVV11/T/T11 = = VV22/T/T22

P, nP, n

Gay-Gay-Lussac’Lussac’

ssPP T T

PP11/T/T11 = = PP22/T/T22

V, nV, n

Avogadro’s Hypothesis and Kinetic Molecular TheoryAvogadro’s Hypothesis and Kinetic Molecular Theory

P proportional to n

The gases in this experiment are all measured at the same T and V.

Avogadro’s Avogadro’s HypothesisHypothesis

Equal volumes of gases at the same T and P have the same number of molecules.

V and n are directly related.

twice as many molecules

A. Avogadro’s Principle Equal volumes of gases contain

equal numbers of moles at constant temp & pressure true for any gas

Combined Gas Law The good news is that you don’t

have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 P2 V2

= T1 T2

No, it’s not related to R2D2

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

= P1 V1

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law Problem

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?

Set up Data Table

P1 = 0.800 atm V1 = 180 mL T1 = 302 K

P2 = 3.20 atm V2= 90 mL T2 = ??

CalculationP1 = 0.800 atm V1 = 180 mL T1 = 302 KP2 = 3.20 atm V2= 90 mL T2 = ??

P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T2 = P2 V2 T1

T2 = 3.20 atm x 90.0 mL x 302 K

0.800 atm x 180.0 mL

T2 = 604 K - 273 = 331 °C = 604 K

Learning Check

A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

One More Practice Problem

A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

Try This One

A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

Pg 549 # 1,2 Pg 552 # 1,2 Pg 553 # 1-6 Pg 559 # 1-3 Pg 562 # 2-11

Lesson 3 Complete!

This concludes Lesson 3 on Charles’ Law!

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Click the Main Menu button below, then select Lesson 4 to put all the pieces together with the Ideal Gas Law.

Lesson 4: Ideal Gas Law

This lesson combines all the properties of gases into a single equation.

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Ideal GasesIdeal GasesAn “ideal” gas exhibits certain theoretical

properties. Specifically, an ideal gas … Obeys all of the gas laws under all conditions. Does not condense into a liquid when cooled. Shows perfectly straight lines when its V and T

& P and T relationships are plotted on a graph.In reality, there are no gases that fit this

definition perfectly. We assume that gases are ideal to simplify our calculations.

We have done calculations using several gas laws (Boyle’s Law, Charles’s Law, Combined Gas Law). There is one more to know…video

Ideal Gas Law

Combining Boyle’s and Charles’ laws allows for developing a single equation:

PV = nRTP = pressure

V = volume

n = number of moles

R = universal gas constant (we’ll get to that in a minute…)

T = temperature

Ideal Gas Law

PV = nRTThis is one of the few equations in chemistry that you should commit to memory!

By remembering this single equation, you can predict how any two variables will behave when the others are held constant.

A. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas LawA. Ideal Gas Law

UNIVERSAL GAS CONSTANT

R=0.0821 Latm/molKR=8.314 LkPa/molK

PV=nRT

You don’t need to memorize these values!

Gas Constant, R

The Ideal Gas Law as presented includes use of the Universal Gas Constant.

The value of the constant depends on the units used to define the other variables.

For the purposes of this lesson, we will use the equation only to predict gas behavior qualitatively. Specific calculations and units will be part of our classroom work.

Putting p*V=n*R*T to Work

After using Boyle’s and Charles’ law for predicting gas behavior, use of the Ideal Gas Law should be relatively straightforward.

Use NASA’s Animated Gas Lab to explore the interaction of these variables on gas behavior.

Follow the directions on the page for changing values for the variables.

When you’re finished, click the Back button on your browser to return to this lesson.

Link to site: Animated Gas Lab

Ideal Gas Law: Summary

PV = nRT Learn it! Use it!

This single equation can be used to predict how any two variables will behave when the others are held constant.

GIVEN:

P = ? atm

n = 0.412 mol

T = 16°C = 289 K

V = 3.25 LR = 8.314LkPa/molK

PV = nRT

P(3.25)=(0.412)(8.314)(289) L mol LkPa/molK K

C. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law Problems Calculate the pressure in atmospheres of

0.412 mol of He at 16°C & occupying 3.25 L.

GIVEN:

n = 85 g

T = 25°C = 298 K

P = 104.5 kPaR = 8.314 LkPa/molK

C. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law ProblemsC. Ideal Gas Law Problems

Find the volume of 85 g of O2 at 25°C and 104.5 kPa.

= 2.7 mol

85 g 1 mol = 2.7 mol

32.00 g

PV = nRT(104.5)V=(2.7) (8.314) (298) kPa mol LkPa/molK K

V = 64 L

Lesson 4 Complete!

This concludes Lesson 4 on the Ideal Gas Law!

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Click the Main Menu button below, then select Review to try some questions based on these lessons.

Review

This review contains multiple choice questions on the material covered by Lessons 1 – 4. Select an answer by clicking the corresponding letter.

If you choose an incorrect answer, you will be given feedback and a chance to try again. If you want to return to a lesson to review the material, click on the Main Menu button, then select the lesson. When you’re ready to complete the review again, go back to the Main Menu and click the Review button.

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Question 1

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.c. Not related

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Question 1 is Correct!

Decreasing volume increases pressure. Increasing volume decreases pressure.

pressure

volume

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Try Question 1 again…

You selected b. While pressure and volume are related, it is not a direct proportion. Try again!

TRYAGAIN

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You selected c. Pressure and volume are related. Is the relationship inverse or direct?

TRYAGAIN

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Question 2

Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are:

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You selected a. While volume and temperature are related, it is not an inverse proportion. Try again!

TRYAGAIN

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b. Directly proportional: if one goes up, the other goes up.

Increasing temperature increases volume. Decreasing temperature decreases volume.

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volume

temperature

You selected c. Pressure and volume are related. Is the relationship inverse or direct?

TRYAGAIN

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Question 3

Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire?

a. Increase the force pressing on the outside of the tire.b. Increase the temperature of the gas (air) in the tire.c. Increase the amount (number of moles) of gas in the tire.

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TRYAGAIN

While increasing the load in the car might increase the force on the tires, it would prove to be a difficult way to adjust tire pressure. Try again!

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TRYAGAIN

Increasing the temperature of the air in the tire would definitely increase pressure. That is why manufacturers recommend checking air pressures when the tires are cold (before driving). But how would you increase temperature without damaging the tire? Is there a more practical solution?

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When you inflate a tire with a pump, you are adding air, or increasing the amount of air in the tire. This will often result in a slight increase in temperature because a tire is not a controlled environment. Such deviations and quirks will be discussed in class!

Mission complete!

You have completed the lessons and review. Congratulations!

You should now have a better understanding of the properties of gases, how they interrelate, and how to use them to predict gas behavior.

Please click on the button below to reset the lesson for the next student. Thanks!

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Gas Laws: Pressure, Volume, and Hot Air NEXT Introduction This lesson will introduce three ways of...

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