Using the Gas LawsA Directed Learning Activity for Hartnell College Chemistry 1

Funded by the Title V – STEM Grant #P031S090007 through Hartnell College

For information contact lyee@hartnell.edu Start

Student Learning Objectives

This tutorial will help you to:1. Manipulate the ideal gas laws to

calculate pressure, volume, temperature and amount of gas present &

2. Use balanced equations and the ideal gas laws to predict the amounts of reagents and/or products for gaseous reactions

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Getting Started

This set of Power Point slides will lead you through a series of short lessons and quizzes on the topics covered by this Directed Learning Activity tutorial.

Move through the slideshow at your own pace. There are several hyperlinks you can click on to take you to additional information, take quizzes, get answers to quizzes, and to skip to other lessons.

You can end this slide show at any time by hitting the “ESC” key on your computer keyboard.

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Table of Topics

What You Should Already Know Boyle’s Law Charles Law Gay-Lussac’s Law Combined Gas Law Avogadro’s Law Ideal Gas Law Putting it All Together (Gas Stoichiometry) Dalton’s Law of Partial Pressures

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What You Should Already Know How to manipulate algebraic equations Conversions between different measurement

units The basics of the Kinetic Molecular Theory of

ideal gases Understand the “mole” Write balanced chemical equations for reactions

If you are uncertain about these skills, please refer to your lecture text for help.

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Boyle’s LawAt constant temperature (T), the volume (V) of a fixed mass of gas is inversely proportional to the Pressure (P).

If we have two sets of conditions (1 and 2) for the same gas, we can then write this equation, which is known as Boyle’s Law:

which is true when moles of gas and T are constant.

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Example 1 for Boyle’s Law1. A sample of an ideal gas occupies 2.00 L at 760 torr. What volume will this amount of gas occupy if the temperature remains constant but the pressure changes to 1.25 atm? Remember that 1 atm = 760 torr.

Solution: use Boyle’s law and substitute in the values for conditions 1 and 2.

Property 1 2

P 760 torr =1 atm

1.25 atm

V 2.00 L ?

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Example 1 for Boyle’s Law (cont’d)

Solve for the new volume

1.60 LNext

Example 2 for Boyle’s LawA 1.00 L sample of an ideal gas at 760 torr is compressed to 0.800 L at constant temperature. Calculate the final pressure of the gas.Solution: use Boyle’s law and substitute in the values for conditions 1 and 2.

Property 1 2

P 760 torr =1 atm

?

V 1.00 L 0.800 L

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Example 2 for Boyle’s Law (cont’d)

Solve for the new pressure

950 torrNext

Quiz Question 1

A mass of oxygen occupies 7.00 L under a pressure of 740 torr. Determine the volume of the same mass of gas at the standard pressure of 760 torr, the temperature remaining constant.

Check answerClick to review

Answer to Quiz Question 1Solution: 6.82 LExplanation:Solve for the new volume:

6.82 LNext questionClick to review

Quiz Question 2Ten (10.0) liters of hydrogen under 7.0 atm pressure is slowly compressed until it occupies only 4.0 L of volume. Assume that the temperature of the gas remains constant. What pressure is needed for the gas to remain compressed?

Check answerClick to review

Solution to Quiz Question 2Solution: 18 atmExplanation:

Solve for the new pressure

18 atmNext lessonClick to review

Charles’ LawAt constant pressure the volume (V) of a fixed mass of an ideal gas is directly proportional to the Kelvin temperature (T).

If we have two sets of conditions (1 and 2) for the same gas, we can then write this equation, which is known as Charles’ Law:

which is true when moles and P are constant.

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Example for Charles’ LawA given mass of chlorine gas occupies 25.0 L at 20 °C. What is the new volume at 45 °C, assuming that the pressure remains constant?

Solution: Use Charles’ Law and substitute the values for conditions 1 and 2. Remember temperature must be in Kelvin.

Property 1 2

V 25.0 L ?

T 20 + 273 K 45 + 273 K

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Example for Charles’ Law (cont’d)

Solve for V2 and substitute in values:

= 27.1 LNext

Quiz Question 3

A sample of gaseous argon is maintained at a constant pressure. The sample has an initial volume of 10.5 L at 25 °C. What will be volume be if the same sample is kept at the same pressure, but heated to 250 °C?

Check answerClick to review

Answer to Quiz Question 3Solution: V2 = 18.4 LExplanation: Use Charles’ Law. Use temperature in Kelvin.

Solve for V2 and substitute in values:

= 18.4 LNext questionClick to review

Quiz Question 4

A certain amount of gas occupies of volume of 100. mL at a temperature of 20 °C. What will the new volume be at 10 °C, if the pressure remains constant?

Check answerClick to review

Answer to Quiz Question 4Solution: V2 = 96.6 mLExplanation: Use Charles’ Law. Temperature in Kelvin.

Solve for V2 and substitute in values:

= 96.6 mLNext lessonClick to review

Gay-Lussac’s Law

The pressure (P)of a fixed mass of an ideal gas, at constant volume, is directly proportional to the Kelvin temperature.

If we have two sets of conditions (1 and 2) for the same gas, we can then write this equation, which is known as Gay-Lussac’s Law:

which is true when moles and V are constant.

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Example for Gay-Lussac’s Law

The air in a cylindrical tank has a pressure of 640 torr at 23 °C. When the tank was placed in the sun, the temperature rose to 48 °C. What was the final pressure in the tank if the mass and volume of the gas does not change?Solution : Use Gay-Lussac’s Law. Remember that temperature must be in Kelvin.

Property 1 2

P 640 torr ?

T 23 + 273 K 48 + 273 K

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Example for Gay-Lussac’s Law (cont’d)

Solving for = 694 torr

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Quiz Question 5A sealed glass bulb contains a sample of He gas at a pressure of 750 torr and 27 °C. The bulb was cooled down to -73 °C. What was the new gas pressure inside the bulb?

Check answerClick to review

Answer to Quiz Question 5Solution: P2 = 500 torrExplanation: Using Gay-Lussac’s Law and substituting in the values, solve for P2, Remember to convert the temperatures to Kelvin. = 500 torr

Next questionClick to review

Quiz Question 6

A steel tank contains carbon dioxide gas at 27 °C and at a pressure of 11.0 atm. Determine the internal pressure when the gas and its contents are heated to 100 °C. Assume that the amount of carbon dioxide and the volume of the tank are constant.

Check answerClick to review

Answer to Quiz Question 6

Solution: P2 = 13.7 atmExplanation: Using Gay-Lussac’s Law and substituting in the values, solve for P2. Remember to convert the temperatures to Kelvin. = 13.7 atm

Next lesson

Click to review

The Combined Gas Law

The Combined Gas Law is a combination of Boyle’s and Charles’ Laws. It may be used whenever the mass of an ideal gas remains constant and the Kelvin temperature (T) is used.

as long as the moles are constant. You can use this equation for two different conditions (1 and 2) and solve for any one of the six variables.

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Example for the Combined Gas Law

What would be the new pressure for a 2.00 L sample of gas at 1.00 atm and -20 °C that is compressed to a new volume of 0.500 L at 40 °C?Solution: Use the combined gas law. Temperatures must be converted to Kelvin.

1 2

P 1.00 atm ?

V 2.00 L -20 + 273 K

T 0.500 L 40 + 273 K

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Example for the Combined Gas Law (cont’d)

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Quiz Question 7

A 2.50 L sample of gas is at 0 °C and 1.00 atm pressure. What will the temperature of the gas be if it is placed in a 2.00 L container at 1.50 atm pressure?

Check answerClick to review

Answer to Quiz Question 7

Solution: T2 = 328 K

Explanation:Use the combined gas law and solve for T2. Remember to convert T to Kelvin.

Next lessonClick to review

Avogadro’s Gas Law

Under Standard Temperature and Pressure (STP) conditions, the volume of one mole of an ideal gas will occupy 22.414 Liters.

1 mole ideal gas = 22.414 L, at STP

STP conditions are 273K and 1 atmosphere (760 mm Hg) of pressure.

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The Ideal Gas Law

To adequately describe an ideal gas under a particular set of physical conditions, you need to know:the temperature, pressure and volume of the gas; andthe amount of gas.

This is summarized in the following equation:

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The Ideal Gas Law cont’d

where P is the pressure of the gasV is the volume of the gasn is the number of moles of the gas in the sampleT is the temperature in KelvinR is the Universal Gas Constant, which varies depending on the units of the other variables

R = 0.082058 or

R = 8.3145 Next

Example for the Ideal Gas LawWhat is the pressure in atmospheres of 3.4x10-3 moles of argon gas in a 75-mL glass bulb at 20 °C?Solution: The problem gives three out of the four properties of an ideal gas (moles, volume, and temperature) and asks for the fourth (pressure). Use the Ideal Gas Law.

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Example for Ideal Gas Law cont’d

Rearrange to solve for P. Convert the temperature to K. Convert the volume to L. Choose R = 0.082058 .

P = 1.1 atmNext

Quiz Question 8

An incandescent light bulb contains 0.0421 g of Ar in a 23.0-mL volume. The pressure inside the light bulb under these conditions is 952 torr. What is the temperature of the Ar gas under these conditions?

Check answerClick to review

Answer to Quiz Question 8Solution: T = 333 K.Explanation:We can use the Ideal Gas Law if we convert 0.0421grams of Ar to moles, convert 23.0 mL to Liters, and 952 torrs to atm.

= 333 KNext lessonClick to review

Putting it All Together – Gas StoichiometryIf we are given a chemical reaction where one or more of the reactants is a gas, we can use the balanced chemical equation to determine the volume of gas that is obtained if we know the amounts of the reagents. If we know the experimental conditions of temperature and pressure, we can use the Ideal Gas Law. Often problems like this are written to be solved under STP conditions, so the results of Avogadro’s Law can also be used. This kind of problem is sometimes called gas stoichiometry. Let’s look at an example.

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Example ProblemHow many liters of carbon dioxide at STP will be formed from the complete combustion of 82.60 g of ethanol, C2H5OH(l)? What would this volume be if we then changed the conditions of the gas to 23 °C and 0.95 atm to expand the gas after formation?

Solution:First we need to write the balanced equation for the reaction. C2H5OH(l) + 3 O2(g) → 2 CO2(g) + 2 H2O(l)

Next, we need to know how many moles of ethanol we have as starting material. This will allow us to use this procedure:g C2H5OH → mol C2H5OH → mol CO2 → L CO2 @ STP

For the last step, since the conditions are at STP, we know that each mole of CO2 = 22.414 L. If the conditions are different than STP, we have to use the Ideal Gas Law to determine the volume.

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Example Problem cont’d?= 80.37 L CO2 @ STPFor the second part of the problem, we can calculate for the new volume of CO2 under the new conditions: V2 = 91.7 L(Note that you could also solve by calculating for moles of CO2 at STP and substituting into the Ideal Gas Law.)

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Quiz Question 9

Calculate the volume of O2 that can be prepared at 60 °C and 760 torr by the decomposition of 20.0 g H2O2 to H2O and O2. The reaction is:

2 H2O2 → 2 H2O + O2.

Check answerClick to review

Answer to Quiz Question 9Solution: V = 8.03 LExplanation:Since the conditions are not at STP, you must use the Ideal Gas Law. This means that you must determine how many moles of O2 is produced from 20.0 g H2O2.

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Answer to Quiz Question 9 cont’d

V = 8.03 L

Next lessonClick to review

Dalton’s Law of Partial PressuresThe partial pressure of a gas in a mixture of gases is the portion of the total pressure that one gas contributes. Dalton’s Law of Partial Pressures is generally written as: or If you have a problem involving only gases and no chemical reaction involved, you may be able to use this formula to calculate either the total pressure or the pressure of one of the gases.

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Example Using Dalton’s Law3.00L oxygen gas is collected over water at 27 °C and when the barometric pressure is 787 torr. The vapor pressure of water at 27 C is 27 torr. What is the partial pressure of the dry oxygen gas under these conditions?

Solution:PO2 = Ptotal – PH2O = 787torr – 27torr = 760torrNext

Quiz Question 10

Exactly 100 mL of oxygen gas is collected over water at 23 °C and 800 torr. Calculate the standard volume of the dry oxygen if the vapor pressure of water at 23 °C is 21.1 torr.

Check answerClick to review

Answer to Quiz Question 10Solution: V2 = 94.5 mL

Explanation:We first use Dalton’s Law to find the partial pressure of oxygenPO2 = Ptotal – PH20 = 800torr – 21.1torr = 779torr

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Solution to Quiz Question 10 cont’d

1 2

P 779 torr 760 torr

V 100. mL ?

T 23 + 273 273

You must then use the combined gas law to determine the volume of the oxygen at STP. Here is what you know.

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Solution to Quiz Question 10 cont’d

V2 = 94.5 mL

NextClick to review

Congratulations!You have successfully completed this Directed Learning Activity tutorial. We hope that this has helped you to better understand this topic.

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© 2011 Hartnell College

Funded by the Title V – STEM Grant #P031S090007 through Hartnell College

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