honors chemistry pogil: the abcs of gases unit …...the container. an ideal gas can consist of...

POGIL: The ABCs of GasesHonors Chemistry Unit 06 - Gases & KMT Page of 1 5

Name: Group Members:

!

Learning Objectives: Investigate the relationship between the volume and the pressure of a given sample of a gas at a set temperature. Investigate the effect of a temperature change on the volume of a given sample of gas at a constant pressure. Investigate the relationship between the quantity of a gas and the given volume of the sample at set T and P. Apply gas laws to problems involving the temperature, volume, and pressure of a contained gas sample. State Avogadro’s hypothesis and use it to answer conceptual problems involving gases. Identify, define, and explain: Kelvin, absolute temperature scale, direct relationship, and inverse relationship.

Text Reference: Chang and Goldsby (Chemistry: The Essential Concepts, McGraw-Hill, 2014) pp. 142-147.

Text Vocabulary: Boyle's law (p142) The volume of a fixed amount of gas i inversely proportional to the gas pressure, at constant temperature. Absolute temperature scale (p145) a temperature scale on which absolute zero (0 K) is the lowest temperature, also called the Kelvin temperature scale Absolute zero (p145) theoretically the lowest possible temperature Kelvin temperature scale (p145) see absolute temperature scale Charles's and Gay-Lussac's law (p146) see Charles’ Law Charles's law (p146) The volume of a fixed amount of gas is directly proportional to the absolute temperature of the gas when the pressure is held constant. Avogadro's law (p147) At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present

Information: Ideal Gases An ideal gas is a hypothetical gas consisting of identical particles with zero volume and with no intermolecular forces. Addition-ally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container. An ideal gas can con-sist of molecules (e.g. carbon dioxide molecules, CO2) or atoms (e.g. neon atoms, Ne). Real gases do not exhibit these exact prop-erties, although many gases behave as ideal gases at high temperatures and low pressure. The four properties of an ideal gas are:

• point masses (the volume of a gas particle essentially zero—if infinitely compressed, all the molecules of an ideal gas would occupy a single point of insignificant volume.

• random motion (constant random motion of gas particles) • intermolecular forces (there are NO intermolecular forces) • elastic collisions (all collisions are totally elastic)

Model I: Charles’ Law Charles’ Law is the relationship between the volume and temperature of an ideal gas. Condition: Charles’ Law requires that the pressure and the number of moles of the gas are constant.

Give complete answers to all questions. Provide explanations and show work, where necessary.

Balloonfilledwithgasatroomtemperature.

Balloonfilledwiththesameamount

ofgasinarefrigerator.

Revised 2018-2019 LCA

Name ___________________________________Chem 161, Section: _______Group Number: ______

ALE 21. Ideal Gases and the Gas Laws of 6

ALE 21. Ideal Gases and the Gas Laws

(Reference: Chapter 5 in Silberberg 5th edition)

How are the volume, temperature, and pressure of a gas related?

The Model: Charles’ Law

Charles’ Law: The relationship between the volume and temperature of an ideal gas. Condition: the pressure and the number of moles of the gas are constants. An ideal gas is a hypothetical gas consisting of identical particles with zero volume, with no intermolecular forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of the container. An ideal gas can consist of molecules (e.g. carbon dioxide molecules, CO2) or atoms (e.g. neon atoms, Ne). Real gases do not exhibit these exact properties, although many gases behave as ideal gases at high temperatures and low pressure. A good way of remembering the four properties that constitute an ideal gas is the acronym 'PRIE', which stands for:

� Point masses (the volume of a gas particle essentially zero—if infinitely compressed, all the molecules of an ideal gas would occupy a single point of insignificant volume.

� Random motion (constant random motion of gas particles) � Intermolecular forces (there are NO intermolecular forces) � Elastic collisions (all collisions are totally elastic)

Key Questions

1. When the pressure and the number of moles of a gas are constants, is the relationship between volume and temperature a direct relationship or an inverse relationship?

Balloon filled with gas at room temperature.

Balloon filled with same amount of gas in a refrigerator.

Place balloon in refrigerator.


Key Questions 1. When the pressure and the number of moles of a gas are constant, is the relationship between volume and tem-

perature a direct relationship or an inverse relationship? Explain/justify.

2. The graph to the right depicts the volumes of three different ideally-behaving gases (A, B, and C) as a function of their temperatures. Use a straightedge to determine the tempera-ture at which each gas would have a volume of 0 L. Check this temperature with your teacher.

3. Gas A, gas B, and gas C all share a common point (a set of x,y coordinates) in the plot in question 2. What is this point and what is the significance of this point?

Model II: Absolute Temperature Whenever the temperature of a gas is needed, it ought to be expressed on the absolute temperature scale. The abso-lute temperature is defined so that the gas has a volume of zero when the absolute temperature is 0 K. (The unit of temperature in the absolute scale is called Kelvin, K.) You convert between the temperature in oC and K using the formula: TK = TC + 273 Really it is 273.15, but we will use 273 in our calculations with 3 significant figures.

4. A mathematical way to represent Charles’ Law is " where the subscript 1 identifies the initial volume and

temperature of the gas and the subscript 2 identifies the final volume and temperature of the gas. The tempera-ture needs to be reported in the absolute scale (Kelvin).

(a) On a mathematical basis, explain why the temperatures in the above equation must be expressed in Kelvin and not Celsius. (Hint - What temperatures would make the equation invalid and how do these temperatures differ in Celsius and Kelvin?)

(b) Under what conditions may the above equation be used? (Hint - what may change and what may not?)

5. Exercise: An ideally-behaving gas has a volume of 18.25 L at a temperature of 15.9oC. The temperature of the gas is raised to 40.7oC while the number of moles and the pressure of the gas are kept constant. What is the new volume of the gas (in L)? Show all work using units and sig figs.

V1T1

= V2T2



2. The volumes of three different ideally-behaving gases (“A”, “B”, and “C”) are monitored as a function of their temperatures. Use a straightedge to determine the temperature at which each gas would have a volume of 0 L. (Confirm this temperature with your instructor or your textbook.)

3. Gas A, gas B, and gas C all share a common point (ordered pair of T and V coordinates) in the plot in

Question 2. What is this point, and what is the relevance of that point?

The Model: Absolute Temperature

Whenever the temperature of a gas is needed, it ought to be expressed on the absolute temperature scale. The absolute temperature is defined so that the gas has a volume of zero when the absolute temperature is 0 K. (The unit of temperature in the absolute scale is called Kelvin, K.) You convert between the temperature in qC and K using the formula:

T (K) = t (qC) + 273.15

Key Questions

4. A mathematical way to represent Charles’ Law is

TV

TV

2

2

1

1

where the subscript “1” identifies the initial volume and temperature of the gas and the subscript “2” identifies the final volume and temperature of the gas.

a. On a mathematical basis, explain why the temperatures in the above equation must be expressed in Kelvin and not in Celsius. (Hint: What if the temperature was 0 oC or -22 oC?.)

b. Under what conditions may the above equation be used? (Hint: You may need to refer back to The Model: Charles’ Law—what two factors must not change?)

A

B

C


Model I I I : Boyle’s Law Recall that where P = pressure (in kPa, atm, torr, etc)

F = force (in N, Newton) A = area over which the force is applied (in m2).

Common units of pressure: 1 atm = 760. mmHg = 760. torr = 101.325 kPa = 14.70 lb/in2 (psi)

Boyle’s Law is the relationship between the volume and pressure of an ideal gas. Condition: Boyle’s Law requires that the temperature and the number of moles of the gas are constant.

6. Does Boyle’s Law describe a direct relationship or an inverse between the pressure and the volume of an ideal gas? Explain/justify.

7. A mathematical way to represent Boyle’s Law is P1V1 = P2V2 where the subscript 1 identifies the initial volume and pressure of the gas and the subscript 2 identifies the final volume and pressure of the gas. When would it be inappropriate to use the above equation to relate an ideal gas’s pressure to its volume? (Hint - what may change and what may not?)

8. Exercise: An ideal gas has a volume of 10.8L at a temperature of 25.0oC and a pressure of 1.60 atm. The pressure of the gas is reduced to 370.0 mmHg, but the temperature and number of moles of the gas are kept constant. What is the new volume of the gas, in L? Show all work using units and sig figs.

1.00molofanidealgasina c y l i nde r w i th onemovablewall (piston) at atemperature of 25.0oCunder a pressure of 1.00atmpossessesavolumeof24.446L.

1.00molofanidealgasinthe same cylinder at thesametemperaturepossessavolumeof12.233L.

�


Exercise

A. An ideally-behaving gas has a volume of 18.25 L at a temperature of 15.9 qC. The temperature of the gas is raised to 40.7 qC while the number of moles and the pressure of the gas are kept constant. What is the new volume of the gas (in L)? Show work using units and sig figs. Circle your answer!

The Model: Boyle’s Law Recall from ALE 20…

Where… P is pressure (in kPa, kilopascal) F is force (in N, Newton) A is the area to which the force is applied (in m2).

Common Units of Pressure: 1 atm = 760 mm Hg = 760 torr = 101.325 kPa = 14.70 lb/in2

Boyle’s Law: The relationship between the pressure and the volume of an ideal gas. Conditions: the temperature and the number of moles of the gas are constants.

1.00 mol of ideal gas in cylinder with one movable wall (piston) at a temperature of 25.0 qC under a pressure of 1 atm possesses a volume of 24.466 L.

1.00 mol of ideal gas in the same cylinder at the same temperature possesses a volume of 12.233 L.

100 kg

200 kg

AF

P

�

ALE 21. Ideal Gases and the Gas Laws Page 3 of 6

Exercise

A. An ideally-behaving gas has a volume of 18.25 L at a temperature of 15.9 qC. The temperature of the gas is raised to 40.7 qC while the number of moles and the pressure of the gas are kept constant. What is the new volume of the gas (in L)? Show work using units and sig figs. Circle your answer!

The Model: Boyle’s Law Recall from ALE 20…

Where… P is pressure (in kPa, kilopascal) F is force (in N, Newton) A is the area to which the force is applied (in m2).

Common Units of Pressure: 1 atm = 760 mm Hg = 760 torr = 101.325 kPa = 14.70 lb/in2

Boyle’s Law: The relationship between the pressure and the volume of an ideal gas. Conditions: the temperature and the number of moles of the gas are constants.

1.00 mol of ideal gas in cylinder with one movable wall (piston) at a temperature of 25.0 qC under a pressure of 1 atm possesses a volume of 24.466 L.

1.00 mol of ideal gas in the same cylinder at the same temperature possesses a volume of 12.233 L.

100 kg

200 kg

AF

P


P = FA


Model IV: Avogadro’s Hypothesis Avogadro’s Hypothesis is the relationship between the volume and quantity of an ideal gas. Condition: Avo-gadro’s Hypothesis requires that the pressure and the temperature of the gas are constant.

9. What variables are changing in the representation of Avogadro’s hypothesis and what variables remain constant

10. Does Avogadro’s Hypothesis describe a direct relationship or an inverse between the quantity and the volume of an ideal gas? Explain/justify.

A mathematical way to represent Avogadro’s law is " where the subscript 1 identifies the initial volume and

quantity (in moles) of the gas and the subscript 2 identifies the final volume and quantity (in moles) of the gas.

11. Exercise: A 4.00g sample of helium has a volume of 24.4L at a temperature of 25.0oC and a pressure of 1.00 atm. The volume of the helium is reduced to 10.4L, but the temperature and pressure of the gas are kept con-stant. What is the new quantity of the gas, in moles? Show all work using units and sig figs.

Model V: STP and the Combined Gas Law Standard Temperature and Pressure = STP STP conditions: 0oC (273.15K) & 1 atm

At STP, 1 mole of an ideal gas has a volume of 22.4L. (Remember this relationship from Unit 06: Chemical Quantities.)

Balloonfilledwith1moleofagasatatmospheric

pressureandatroom

temperature.Ithasavolumeof

24L.

Balloonfilledwith2molesofagasatatmosphericpressureandat

roomtemperature.Ithasavolumeof

48L.�

Name ___________________________________Chem 161, Section: _______Group Number: ______

ALE 22 - The Ideal Gas Law Page 1 of 4

ALE 22. The Ideal Gas Law

(Reference: Chapter 5 in Silberberg 5th edition)

How do we relate all of the variables of a gas together?

The Model: Avogadro’s Hypothesis

Avogadro’s Hypothesis: Relationship between the volume and the number of moles of an ideal gas. Condition: the pressure and the temperature of the gas are constants.

Key Question

1. Suppose you have n1 moles of a gas at STP and n2 moles of the gas also at STP. If you wanted to relate the volumes of the two gases, which of the following two equations would you use? (Circle your choice.)

V1 n1 = V2 n2 OR � = � Briefly explain your choice. (Is volume directly proportional or inversely proportional to the number of moles of gas?)

The Model: Three Two-Variable Gas Laws

The individual gas laws (The “a”, “b”, and “c” in the equations are constants.): V = a·n V = � V = c·T Avogadro’s Hypothesis Boyle’s Law Charles’ Law (constant P, T ) (constant n, T ) (constant n, P)

Balloon filled with 1 mole of a gas at atmospheric pressure and at room temperature. It has a volume of 24 L.

Put more gas in balloon.

Balloon filled with 2 moles of a gas at atmospheric pressure and at room temperature. It has a volume of 48 L.

V1

n1

V2

n2

b

P

V1n1

= V2n2



Boyle’s Law, Charles’ Law, and Avogadro’s Hypothesis are used when 2 variables are held constant. One of the remain-ing two variables is changed and the final variable responds. Frequently, a sample of a gas with a fixed mass has more than one variable that gets changed. In this case, it is appropriate to use the combined gas law.

"

12. Use choices (A) through (F) to describe the relationship between the variables in each law listed.

__________ Charles’ Law (A) direct relationship between V and P (B) direct relationship between V and T __________ Boyle’s Law (C) direct relationship between V and n (D) inverse relationship between V and P __________ Avogadro’s Hypothesis (E) inverse relationship between V and T (F) inverse relationship between V and n

13. At constant temperature, the volume of a gas expands from 4.25L to 8.75L. If the initial pressure was 120. kPa, what is the final pressure?

14. The volume of a gas was originally 2.50L; its pressure was 104kPa and its temperature was 270.K. The volume of the gas expanded to 5.30L and its pressure decreased to 95.0kPa. What is the temperature of the gas?

15. What is the effect of the following on the volume of 1.00 mole of an ideal gas? The pressure changes from 760. torr to 202 kPa and the temperature changes from 37.0oC to 155K, while the moles of gas remain constant. Does the volume of the gas change? If it does, by what factor does the volume of the gas increase or decrease?

P1V1T1

= P2V2T2


honors chemistry pogil: the abcs of gases unit …...the container. an ideal gas can consist of...

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