Using the Gas Laws A Directed Learning Activity for Hartnell College Chemistry 1 Funded by a Title V STEM Grant from Hartnell College For information contact
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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. Next
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 Next
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. Next
Boyle’s Law At constant temperature (T), the volume (V) of a fixed mass of gas is inversely proportional to the Pressure (P). 1 𝑃 ∝ 𝑉 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: 𝑃1𝑉1 = 𝑃2𝑉2
which is true when moles of gas and T are constant. Next
Example 1 for Boyle’s Law 1. 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)
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Example 2 for Boyle’s Law A 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 Next
Example 2 for Boyle’s Law (cont’d)
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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.
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Answer to Quiz Question 1
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Quiz Question 2 Ten (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?
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Solution to Quiz Question 2
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Charles’ Law At constant pressure the volume (V) of a fixed mass of an ideal gas is directly proportional to the Kelvin temperature (T). 𝑉 ∝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: 𝑉1 𝑉2 = 𝑇1 𝑇2
which is true when moles and P are constant. Next
Example for Charles’ Law A 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? Remember that T must be in Kelvin. 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 °C + 273 K
45 °C + 273 K Next
Example for Charles’ Law (cont’d)
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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?
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Answer to Quiz Question 3
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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?
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Answer to Quiz Question 4
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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. 𝑃 ∝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 Gay-Lussac’s Law: 𝑃1 𝑃2 = 𝑇1 𝑇2
which is true when moles and V are constant. Next
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 °C + 273 K
48 °C + 273 K Next
Example for Gay-Lussac’s Law (cont’d)
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Quiz Question 5 A 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?
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Answer to Quiz Question 5
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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.
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Answer to Quiz Question 6
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The Combined Gas Law
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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 °C + 273 K
T
0.500 L
40 °C + 273 K Next
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?
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Answer to Quiz Question 7
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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. Next lesson
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; and the amount of gas. This is summarized in the following equation: Next
The Ideal Gas Law cont’d
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Example for the Ideal Gas Law What 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
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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?
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Answer to Quiz Question 8
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Putting it All Together – Gas Stoichiometry If 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. Next
Example Problem How 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
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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 H 2 O2 → 2 H 2 O + O2 .
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Answer to Quiz Question 9
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Answer to Quiz Question 9 cont’d
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Dalton’s Law of Partial Pressures
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Example Using Dalton’s Law
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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.
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Answer to Quiz Question 10
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Solution to Quiz Question 10 cont’d You must then use the combined gas law to determine the volume of the oxygen at STP. Here is what you know. 1
2
P
779 torr
760 torr
V
100. mL
?
T
23 + 273
273 Next
Solution to Quiz Question 10 cont’d
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