# Gas Law Puzzle

## Student Activity Kit

### Materials Included In Kit

Color Poster Sheets, 15
Gas Law Puzzle Activity Sheets, 15

Board with writing instruments (optional)
Calculator (optional)
Periodic Table
Tape (optional)

### Safety Precautions

The materials in this kit are considered nonhazardous and are reusable. Follow all classroom or laboratory safety guidelines.

### Disposal

The gas law puzzle activity sheets and poster sheets may be stored for reuse.

### Lab Hints

• Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. Both parts of this laboratory activity can reasonably be completed in one 50-minute class period. The prelaboratory assignment may be completed before coming to lab or at the beginning of the class.
• After students have completed the gas law puzzle activity questions, they need to add up the total of all 12 squares to reach a sheet number. Once a proper sheet number has been matched a picture clue is given.

### Teacher Tips

• Before beginning the activity, copy the Gas Law Puzzle Activity Sheets so you will have extra copies.
• Cut out and laminate the color puzzle poster sheets.

### Science & Engineering Practices

Using mathematics and computational thinking

### Disciplinary Core Ideas

HS-PS1.A: Structure and Properties of Matter

### Crosscutting Concepts

Scale, proportion, and quantity
Energy and matter

### Performance Expectations

HS-PS1-3: Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles.
HS-LS1-5: Use a model to illustrate how photosynthesis transforms light energy into stored chemical energy.

1. Where may the value of the molar mass of an element be found?

Molar mass is found on the Periodic Table

2. If pressure increases, and temperature and number of moles remain constant, does volume increase, decrease or remain the same? Explain in terms of a gas law.

Using Boyle’s Gas Law, pressure and volume have an inversely proportional relationship where if one variable increase the other decreases. When pressure increases the volume decreases.

3. If the temperature decreases, and the pressure and number of moles remain constant, does the volume increase, decrease or remain the same? Explain in terms of a gas law.

Using Charles’s Gas Law, temperature and volume have a directly proportional relationship where if one variable increases or decreases the other variable will do the same. When temperature decreases the volume decreases.

4. Write the ideal gas law with density terms, mass/volume, for a gas.

PV=nRT, density = mass/volume,moles = mass (g)/MM, so PV = m/MM RT, m/V=P - MM/RT

Answers to Gas Law Puzzle Activity

### References

Special thanks to Fran Zakutansky, Pascack Valley High School, Hillsdale, NJ, for sharing this activity with Flinn Scientific.

# Gas Law Puzzle

### Introduction

Whether you are climbing a mountain or diving deep in the sea, the gas laws are always in force! Expand your understanding of the gas laws with this cooperative classroom activity. Answer gas law puzzles as a class and assemble the collage to create a gas laws poster—illustrating many everyday applications of the gas laws. A great activity to tie together all the principles and concepts relating to the properties of gases!

### Concepts

• Combined gas law (Boyle’s + Charles’s + Gay-Lussac’s)
• Molar mass
• Ideal gas law
• Density
• Molar volume

### Background

Many scientists have studied gases—from the invisible pressure of the atmosphere to the pressure exerted from a trapped gas. Sometimes scientific discoveries come in one fell swoop but many times scientific knowledge builds over time piece-by-piece with many different contributors as the gas laws have. The systematic study of gases began almost 350 years ago with Robert Boyle (1627–1691). Boyle built a simple apparatus to measure the relationship between the pressure and volume of air. The apparatus consisted of a J-shaped glass tube that was sealed at one end and open to the atmosphere at the other end. A sample of air was trapped in the sealed end by pouring mercury into the tube (see Figure 1). In the beginning of the experiment, the height of the mercury column was equal in the two sides of the tube. The pressure of the air trapped in the sealed end was equal to that of the surrounding air, equivalent to 29.9 inches (760 mm) of mercury.

{12039_Background_Figure_1}
When Boyle added more mercury to the open end of the tube, the air trapped in the sealed end was compressed into a smaller volume (see Figure 2). The difference in height of the two columns of mercury (Δh in Figure 2) was due to the additional pressure exerted by the compressed air compared to the surrounding air. Boyle found that when the volume of trapped air was reduced to one-half its original volume, the additional height of the column of mercury in the open end of the tube measured 29.9 inches. The pressure exerted by the compressed air was twice as great as atmospheric pressure. The mathematical relationship between the volume of the air and the pressure it exerts was confirmed through a series of measurements.
{12039_Background_Figure_2}
Based on these measurements of pressure changes when air is compressed and expanded, Boyle published his findings in 1662 which is known today as Boyle’s Law. According to Boyle’s Law the pressure of a gas is inversely proportional to its volume if the temperature and number of moles are held constant. This relationship may be expressed mathematically as P ∝ 1/V or by Equation 1 for the initial and final conditions designated as P1 and V1, and P2 and V2, respectively.
{12039_Background_Equation_1}
In studying the behavior of gases, Robert Boyle was also aware of the effect of heat on gases—namely that gases tend to expand when heated. Since no temperature scale existed at the time, Boyle lacked a numerical means of mathematically relating the temperature of a gas to its volume or pressure.

French physicist, Jacques Charles (1746–1823) was a scientist as well as a balloonist and his studies transferred over to his hobby. Through years of experiments, Charles explored the proportional relationship of the volume of gases to temperature. After the development of absolute temperature and the Kelvin scale (1848) it was found that the volume of a gas is directly proportional to its temperature in Kelvins. According to Charles’s Law the volume of a gas is directly proportional to temperature if the pressure and number of moles are held constant. This relationship may be expressed mathematically as VT or by Equation 2 for the initial and final conditions.
{12039_Background_Equation_2}
Joseph Louis Gay-Lussac (1778–1850) systemically and mathematically studied temperature and its effect on the pressure and temperature of gases. In 1802, Gay-Lussac’s published these relationships. Charles’s Law shown above was published by Gay-Lussac but named after Charles. Gay-Lussac also published the relationship between the pressure and temperature of a gas. Today this law, commonly referred to as Gay-Lussac’s Law, states that the pressure of a fixed mass and fixed volume of a gas is directly proportional to the temperature of the gas in Kelvins. This law can be expressed mathematically as PT or by Equation 3 for the initial and final conditions.
{12039_Background_Equation_3}
Gay-Lussac also studied combining values and how gases combine in simple numerical proportions by volume. Gay-Lussac, who was also a balloonist, made a solo assent and took air samples at seven thousand meters—a 50-year record for balloon height. Upon analysis of the collected samples their composition was found to be the same as the air at the Earth’s surface. This lead to continued studies of gases.

Amedeo Avogadro (1776–1856) developed a hypothesis that explained Gay-Lussac’s Law. Avogadro’s Hypothesis, 1811, is an important gas principle that states that equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules. In other words, if samples of different gases at the same conditions contain the same number of molecules, then the volume of the gases must be equal. If the volume is for one mole of a gas, then the term used is molar volume. Assuming that one mole of gas is at standard conditions of 1 atmosphere of pressure and 273.15 K (0 °C) temperature, then the gas would occupy a molar volume of 22.4 liters. At constant temperature and pressure, using n for moles, can be expressed mathematically as Vn or by Equation 4 for the initial and final conditions.
{12039_Background_Equation_4}
The relationship among the four gas variables—pressure (P), volume (V), temperature (T) and the number of moles (n)—is expressed in the ideal gas law (Equation 5), where R is a constant called the universal gas constant.
{12039_Background_Equation_5}
The universal gas constant has several values depending on the units. When pressure is in units of atmospheres, volume in liters, n in moles, and temperature is Kelvins, R = 0.08206 Latm/mol•K.

The ideal gas law reduces to Equation 6, the combined gas law, if the number of moles of gas is constant. The combined gas law can be used to calculate any one of the variables if the other five are known for the initial and final conditions.
{12039_Background_Equation_6}
In using Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, the ideal gas law or the combined gas law, remember that temperature must be always be expressed in units of kelvins (K) on the absolute temperature scale. Kelvin is the only unit of temperature in which pressure and volume are directly proportional.

### Experiment Overview

The purpose of this cooperative class activity is to answer questions on the gas laws, molar mass, molar volume, and density of a gas. There are 15 different puzzle sheets, sets 1–15, each with 12 different puzzle questions covering Boyle’s Law, Charles’s Law, Gay–Lussac’s Law, the combined gas law, the ideal gas law, molar volume of gases, etc. Work with a partner to answer the questions and then take the sum of all the numerical answers to identify your piece of a colorful gas laws puzzle poster. After collaborating with other teams and re-checking the puzzle clues if necessary, assemble the collage with the class to create a gas laws poster. The poster illustrates many everyday applications of the gas laws.

### Materials

Board with writing instruments (optional)
Calculator (optional)
Color Poster Sheet
Gas Law Puzzle Activity Sheet
Periodic Table
Scissors
Tape (optional)

### Prelab Questions

1. Where may the value of the molar mass of an element be found?
2. If pressure increases, and temperature and number of moles remain constant, does volume increase, decrease or remain the same? Explain in terms of a gas law.
3. If the temperature decreases, and the pressure and number of moles remain constant, does the volume increase, decrease or remain the same? Explain in terms of a gas law.
4. Write the ideal gas law with density terms, mass/volume, for a gas.

### Safety Precautions

This activity is considered nonhazardous. Please follow all classroom or laboratory safety guidelines.

### Procedure

1. Obtain one Gas Law Puzzle Activity Sheet.
2. Working within your group, answer all 12 puzzle questions. Note: The answers are all whole numbers.
3. Add the answers to all 12 puzzle clues and report this number to your teacher. If correct, your teacher will issue a color poster sheet. If your answer is incorrect, corrections will be needed until the correct sum is determined.
4. Once the color poster sheet is obtained, cut the picture using the line for guidance.
5. Meet with other groups that have their color puzzle sheets and together build the Gas Law Puzzle Poster.
6. (Optional) Tape the color poster sheets together to form the Gas Law Puzzle Poster.

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