1

Chemistry

Name:__________________

Period:____

Behavior of a Gas

Packet 3

Day In Class Work Homework

1 Kinetic Molecular Theory

2 Behavior of Gas Lab

3 Temperature vs Volume Lab Data table

4 Graphing T vs V pg 8-9

5 Pressure and Volume Lab pg 11-12

6 Combined Gas Laws pg 14-16

7 Bic Lab

8 Self Test/ Review Review for test

9 Packet Test

Outcomes Students will state the four variables of the gaseous state

Student will state and calculate Charle’s Law and Boyle’s Law

Students will define absolute zero, temperature, pressure, and volume

Students will change Celsius degree to Kelvin Degree

Students will problem solve using the Combined Gas Law and STP conditions.

2

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the forces between molecules and the energy that they

possess. This theory has 3 basic assumptions.

Matter is composed of small particles (molecules). The measure of space that the molecules

occupy (volume) is derived from the space inbetween the molecules and not the space the

molecules contain themselves.

The molucules are in constant motion. This motion is different for the 3 states of matter.

Solid - Molecules are held close to each other by their attractions of charge. They will

bend and/or vibrate, but will stay in close proximity.

Liquid - Molecules will flow or glide over one another, but stay toward the bottom of

the container. Motion is a bit more random than that of a solid.

Gas - Molecules are in continual straightline motion. The kinetic energy of the

molecule is greater than the attractive force between them, thus they are much farther

apart and move freely of each other.

When the molecules collide with each other, or with the walls of a container, there is no loss

of energy.

The Kinetic Molecular Theory of Gases begins with five postulates that describe the behavior of

molecules in a gas. These postulates are based upon some simple, basic scientific notions, but they

also involve some assumptions that simplify the calculations. In reading a postulate, do two things.

First, try to understand and appreciate the basic physical idea embodied in the postulate; this idea

will ultimately be important in understanding the macroscopic properties of the gas in terms of the

behavior the microscopic molecules making up the gas. Second, identify possible weakness or flaws

in the postulates. Inaccurate predictions by a theory derive from flawed postulates used in the

derivation of the theory.

Postulates

1. A gas consists of a collection of small particles traveling in straight-line motion and obeying

Newton's Laws.

2. The molecules in a gas occupy no volume (that is, they are points).

3. Collisions between molecules are perfectly elastic (that is, no energy is gained or lost during

the collision).

4. There are no attractive or repulsive forces between the molecules.

5. The average kinetic energy of a molecules depend on temperature

3

Variables of Gaseous States of Matter

1. Volume- amount of space occupied by the particles

2. Temperature- measure the average kinetic energy of the particles

3. Pressure- the measure of how often and with what force the particles strike the wall of the

container.

4. Number of particles- the number of atoms or molecules present in a sample

Volume Temperature Pressure # of Particles

Volume X

Temperature X

Pressure X

# of Particles X

Gas Variable Lab

Identify the volume of gas which is involved in the experimentation

Observe and record the changes

Determine and record which of the four factors are varying and which are constant

Determine the relation ship between the variables

Station # Observation Temperature Pressure Volume # of

Particles

Relationship

4

Lord Kelvin (William Thompson)

Temperature Scales (Lord Kelvin)

At the beginning of the 1800s, a relationship was discovered between the volume and the

temperature of a gas. This relationship suggests that the volume of a gas should become zero at a

temperature of -273.15oC. In 1848 the British physicist William Thompson, who later became Lord

Kelvin, suggested that this observation could be used as the basis for an absolute temperature scale.

On the Kelvin scale, absolute zero (0 K) is the temperature at which the volume of a gas becomes

zero. It is therefore the lowest possible temperature, or the absolute zero on any temperature scale.

Zero on the Kelvin scale is therefore -273.15oC.

0 K = -273.15oC

Each unit on this scale, or each kelvin, is equal to 1 degree on the Celsius scale. There is a subtle

difference between the units on these scales, however. Because the Celsius scale is based on two

arbitrary references points, the difference between the temperatures of these two points is divided

into degrees. The Kelvin scale, however, is an absolute scale. Zero is not arbitrarily defined; it is the

lowest possible temperature that can be achieved. Thus, temperatures on the Kelvin scale are not

divided into degrees. Temperatures on this scale are reported in units of "kelvin," not in "degrees

kelvin."

-273.15 oC 0

oC 100

oC

0 K 273.15 K 373.15 K

To determine Kelvin-

To determine oC-

Convert the following temperatures from one scale to the other

28 oC = __________K 10

oC __________K

296 K = _________

oC 200K __________

oC

422 oC = _________K 1768K _________

oC

50 K = _________

oC 35

oC __________K

5

Determination of Absolute Zero: Charles's Law Objective: Determine absolute zero from extrapolation of volume and temperature data using

Charles's Law

Materials and Procedures:

1. Prepare a cold water bath using a battery jar approximately 3/4 full.

2. Fit the dry 125 mL Erlenmeyer flask with a one-hole stopper.

3. Prepare a hot water bath using a Bunsen Burner and a 600 mL beaker.

4. Clamp the Erlenmeyer flask in the hot water bath such that most of it is under water.

5. Allow the water to boil 5 min to allow the zeroth law of thermodynamics to take effect.

6. Record the temperature of the boiling water to 0.5o C.

7. Place the solid glass rod into the one hole stopper, then remove the Erlenmeyer flask from the

beaker. Allow it to cool for 2-3 minutes until cool to the touch

8. Invert the Erlenmeyer flask and place it in the cold water bath. Remove the glass rod while

under water and still inverted, then totally submerge the inverted flask for 5 min.

9. Stir occasionally. Record the temperature of the ice bath to 0.5o C just prior to removing the

Erlenmeyer flask.

The next step should be done as quickly as possible to avoid warming of the flask. 10. Using your finger tips, raise the inverted flask until the water level inside and outside the flask

are equal. Now seal the inverted flask with the glass rod.

11. Determine the volume of water collected in the inverted flask, then the volume of the entire

flask. This will allow you to calculate the volume of the air at both temperatures.

Draw a visual of this lab

Data Temperature of boiling water _____ Volume of empty flask_____

Temperature of ice bath _____ Volume of water in ice bath flask_____

Volume of air in ice bath flask _____

Calculations

Charles Law - V1/ T1 = V2/ T2

volume of air in ice bath = volume of air in hot water bath

temperature ice bath (K) temperature of hot water bath (K)

What is the volume of air in the flask of the hot water bath?

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Analysis 1. Plot the volume (y-axis) of the air in the flask vs.

oC temperature. Allow room on your graph to

extrapolate back to zero volume on the y-axis such that the absolute zero temperature can be

determined. Turn the graph paper on its side. Place the x axis 5 squares from the bottom of the

paper. Place the y axis 33 squares from the left. Label the intersection of the two line as (0,0).

Divide the x-axis from -300 oC to 90

oC. Graph

2. In your analysis, respond to the following questions:

a) Why did the water flow into the flask when inverted in the cold water bath? Explain in terms of

kinetic theory.

b) From your graph, what is the predicted temperature for zero volume of a gas. Calculate a %

error.

c) Explain why the temperature cannot drop below absolute zero.

d) What happens to air before it gets close to absolute zero that would prevent an accurate

determination of absolute zero?

e) Theoretically, what happens to molecules at absolute zero

f) Explain Charles Law

h) How could this lab be designed to be more accurate?

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Charles’ Law Worksheet

Charles Law - V1/ T1 = V2/ T2 *** Remember temperature must be in Kelvin

1) The temperature inside my refrigerator is about 40 Celsius. If I place a balloon in my fridge

that initially has a temperature of 220

C and a volume of 0.5 liters, what will be the volume

of the balloon when it is fully cooled by my refrigerator?

2) A man heats a balloon in the oven. If the balloon initially has a volume of 0.4 liters and a

temperature of 20 0C, what will the volume of the balloon be after he heats it to a

temperature of 250 0C?

3) On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they

have not been opened. If I have a 250 mL bag at a temperature of 19 0C, and I leave it in my

car which has a temperature of 600

C, what will the new volume of the bag be?

4) A soda bottle is flexible enough that the volume of the bottle can change even without

opening it. If you have an empty soda bottle (volume of 2 L) at room temperature (25 0C),

what will the new volume be if you put it in your freezer (-4 0C)

5) Some students believe that teachers are full of hot air. If I inhale 2.2 liters of gas at a

temperature of 180

C and it heats to a temperature of 380

C in my lungs, what is the new

volume of the gas?

6) How hot will a 2.3 L balloon have to get to expand to a volume of 400 L? Assume that the

initial temperature of the balloon is 25 0C.

7) I have made a thermometer which measures temperature by the compressing and expanding

of gas in a piston. I have measured that at 1000

C the volume of the piston is 20 L. What is

the temperature outside if the piston has a volume of 15 L? What would be appropriate

clothing for the weather?

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Boyle's Law

In the 1700's a number of people investigated gas behavior in the laboratory. Robert Boyle

investigated the relationship between the volume of a dry ideal gas and its pressure. Since there are

four variables that can be altered in a gas sample, in order to investigate how one variable will affect

another, all other variables must be held constant or fixed. Boyle fixed the amount of gas and its

temperature during his investigation. He found that when he manipulated the pressure that the

volume responded in the opposite direction. For example, when Boyle increased the pressure on a

gas sample the volume would decrease. Mathematically, PV = constant value if the gas is behaving

as an Ideal Gas. A practical math expression of Boyle's findings is as follows:

P1V1 = P2V2

where the variables with the 1 subscript mean initial values before the manipulation and the

variables with the 2 subscript mean final values after the manipulation.

Boyles Law Lab

Lower the iron ring and wire gauze. Remove the rubber stopper, wood and hanger. Adjust the

plunger to read 20. Replace rubber stopper by twisting it into the end of the syringe. Move the

iron ring and wore gauze up to support the syringe. Add the block of wood, hanger, and 1000 gram

quantities of mass to the hanger into a maximum of 7000 grams is reached. Design a data table

and record the masses and corresponding volumes in the data table.

What is the independent variable in this experiment? ___________ What is the dependent variable

in this experiment? __________ State the relationship of this experiment. ___________________

Are the gas particles inside the syringe moving? _____ When the gas particles hit the walls of the

syringe and each other a force called ______________ is created. If the volume of the container is

decreased the particles will hit each other more often therefore the pressure will __________.

Create a visual picture of the relationship between pressure and volume by graphing the data in the

data table. Draw a smooth curve through the series of points.

9

Boyles’ Law

P1V1 = P2V2

1) 1.00 L of a gas at 2 atm is compressed to 473 mL. What is the new pressure of the gas?

2) In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches

4.0 x 106 atm. When the bomb casing is destroyed by the explosion, the gas is released into

the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after

the explosion?

3) Synthetic diamonds can be manufactured at pressures of 6.00E4 atm. If we took 2.00 liters

of gas at 1.00 atm and compressed it to a pressure of 6.00E4 atm, what would the volume of

that gas be?

4) The highest pressure ever produced in a laboratory setting was about 2.0E6 atm. If we have a

1.0E-5

liter sample of a gas at that pressure, then release the pressure until it is equal to 0.275

atm, what would the new volume of that gas be?

5) Atmospheric pressure on the peak of Mt. Everest can be as low as 150 mm Hg, which is

why climbers need to bring oxygen tanks for the last part of the climb. If the climbers carry

10.0 liter tanks with an internal gas pressure of 3.04E4 mm Hg, what will be the volume of

the gas when it is released from the tanks?

6) Submarines need to be extremely strong to withstand the extremely high pressure of water

pushing down on them. An experimental research submarine with a volume of 15,000 liters

has an internal pressure of 1.2 atm. If the pressure of the ocean breaks the submarine

forming a bubble with a pressure of 250 atm pushing on it, how big will that bubble be?

7) Divers get “the bends” if they come up too fast because gas in their blood expands, forming

bubbles in their blood. If a diver has 0.05 L of gas in his blood under a pressure of 250 atm,

then rises instantaneously to a depth where his blood has a pressure of 50.0 atm, what will

the volume of gas in his blood be? Do you think this will harm the diver?

10

Combined Law

The combined gas law is a combination of Boyle's Law and Charles's Law; hence its name the

combined gas law. In the combined gas law, the volume of gas is directly proportional to the

absolute temperature and inversely proportional to the pressure.

This can be written as PV / T = constant. Since for a given amount of gas there is a constant then we

can write P1V1 / T1 = P2V2 / T2.

P1 is the initial pressure

V1 is the initial volume

T1 is the initial temperature (in Kelvin)

P2 is the final pressure

V2 is the final volume

T2 is the final temperature (in Kelvin)

This equation is useful if you have the current volume, temperature, and pressure of a gas, and if

you have two of the three final values of the gas.

STP= standard temperature and pressure = 273.15K and 1atm or 760 mm of Hg

For example if you have 4.0 liters of gas at STP, and you want to know the volume of the gas at 2.0

atm of pressure and 30o C, the equation can be setup as follows:

(1.0)(4.0) / 273 = (2.0)(V2) / 303

(V2)(2)(273) = (1)(4)(303)

V2 = 2.2

Therefore the new volume is 2.2 liters.

1) A toy balloon has an internal pressure of 1.05 atm and a volume of 5.0 L. If the temperature

where the balloon is released is 200 C, what will happen to the volume when the balloon rises to an

altitude where the pressure is 0.65 atm and the temperature is –150 C?

2) A small research submarine with a volume of 1.2 x 105 L has an internal pressure of 1.0 atm and

an internal temperature of 150 C. If the submarine descends to a depth where the pressure is 150

atm and the temperature is 30 C, what will the volume of the gas inside be if the hull of the

submarine breaks?

11

Combined Gas Law Problems

Use the combined gas law to solve the following problems: identify all variables then solve

1) If I initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a temperature of

200 K, and then I raise the pressure to 14 atm and increase the temperature to 300 K, what is

the new volume of the gas?

V1 = V2 =

P1 = P2 =

T1 = T2 =

2) A gas takes up a volume of 17 liters, has a pressure of 2.3 atm, and a temperature of 299 K.

If I raise the temperature to 350 K and lower the pressure to 1.5 atm, what is the new volume

of the gas?

V1 = V2 =

P1 = P2 =

T1 = T2 =

3) A gas that has a volume of 28 liters, a temperature of 45 0C, and an unknown pressure has its

volume increased to 34 liters and its temperature decreased to 35 0C. If I measure the

pressure after the change to be 2.0 atm, what was the original pressure of the gas?

V1 = V2 =

P1 = P2 =

T1 = T2 =

4) A gas has a temperature of 14 0C, and a volume of 4.5 liters. If the temperature is raised to

29 0C and the pressure is not changed, what is the new volume of the gas?

V1 = V2 =

P1 = P2 =

T1 = T2 =

5) If I have 17 liters of gas at a temperature of 67 0C and a pressure of 88.89 atm, what will be

the pressure of the gas if I raise the temperature to 94 0C and decrease the volume to 12

liters?

V1 = V2 =

P1 = P2 =

T1 = T2 =

6) I have an unknown volume of gas at a pressure of 0.5 atm and a temperature of 325 K. If I

raise the pressure to 1.2 atm, decrease the temperature to 320 K, and measure the final

volume to be 48 liters, what was the initial volume of the gas?

V1 = V2 =

P1 = P2 =

T1 = T2 =

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Gas Laws

For each question state what law is being used, write out the correct initial and final volumes,

temperatures, and pressures and then label the answer correctly.

1) If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its

volume is 4.8 L, what will the new pressure inside the piston be?

2) I have added 15 L of air to a balloon at sea level (1.0 atm). If I take the balloon with me to

Denver, where the air pressure is 0.85 atm, what will the new volume of the balloon be?

3) I’ve got a car with an internal volume of 12,000 L. If I drive my car into the river and it

implodes, what will be the volume of the gas when the pressure goes from 1.0 atm to 1.4

atm?

4) If I have 45 liters of helium in a balloon at 250

C and increase the temperature of the balloon

to 550 C, what will the new volume of the balloon be?

5) Calcium carbonate decomposes at 12000 C to form carbon dioxide and calcium oxide. If 25

liters of carbon dioxide are collected at 12000 C, what will the volume of this gas be after it

cools to 250 C?

6) I have 130 liters of gas in a piston at a temperature of 2500 C. If I cool the gas until the

volume decreases to 85 liters, what will temperature of the gas be?

7) If I initially have 4.0 L of a gas at a pressure of 1.1 atm, what will the volume be if I increase

the pressure to 3.4 atm?

8) A toy balloon has an internal pressure of 1.05 atm and a volume of 5.0 L. If the temperature

where the balloon is released is 200 C, what will happen to the volume when the balloon

rises to an altitude where the pressure is 0.65 atm and the temperature is –150 C?

13

9) A small research submarine with a volume of 1.2 x 105 L has an internal pressure of 1.0 atm

and an internal temperature of 150 C. If the submarine descends to a depth where the

pressure is 150 atm and the temperature is 30 C, what will the volume of the gas inside be if

the hull of the submarine breaks?

10) People who are angry sometimes say that they feel as if they’ll explode. If a calm person

with a lung capacity of 3.5 liters and a body temperature of 360 C gets angry, what will the

volume of the person’s lungs be if their temperature rises to 390 C. Based on this, do you

think it’s likely they will explode?

Ideal Gas Law

The ideal gas law is a combination of all the gas laws.

The ideal gas law can be expressed as PV = nRT.

P is the pressure in atm

V is the volume in liters

n is the number of moles

R is a constant

T is the temperature in Kelvin

The constant R is calculated from a theroretical gas called the ideal gas. The most commonly used

form of R is .0821 L * atm / (K * mol). This R will allow the units to cancel so the equation will

work out.

To find the volume of 2.00 moles gas that is at 1.00 atm of pressure and 235 Kelvin, use the ideal

gas law equation.

(1.00 atm)(V) = (2.00 mol)(.0821 L * atm / (K * mol))(235 kelvin)

V = (38.587 L * atm) / (1.00 atm)

V = 38.6 L

14

Ideal Gas Law Problems

Use the ideal gas law to solve the following problems:

1) If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the

temperature?

P =

V=

n =

R=

T =

2) If I have an unknown quantity of gas at a pressure of 1.2 atm, a volume of 31 liters, and a

temperature of 87 0C, how many moles of gas do I have?

P =

V=

n =

R=

T =

3) If I contain 3 moles of gas in a container with a volume of 60 liters and at a temperature of

400 K, what is the pressure inside the container?

P =

V=

n =

R=

T =

4) If I have 7.7 moles of gas at a pressure of 0.09 atm and at a temperature of 56 0C, what is the

volume of the container that the gas is in?

P =

V=

n =

R=

T =

5) If I have 17 moles of gas at a temperature of 67 0C, and a volume of 88.89 liters, what is the

pressure of the gas?

P =

V=

n =

R=

T =

15

Can You Do It?

The kinetic molecular theory.

1.

2.

3.

4.

Gases

List the 4 characteristics of a gas ______________, ______________, ______________, &

______________.

Charles Law deals with what 2 variables? ___________ & ____________. What is their

relationship?__________

Write the mathematical equation and a graph for Charles Law:

Problem-

A volume of helium increased from 100ml to 250ml by increasing its temperature. If the initial temperature

of the gas was 15° C what is the final temperature of the gas?

If I have 45 liters of helium in a balloon at 250 C and increase the temperature of the balloon to 55

0 C, what

will the new volume of the balloon be?

Boyle’s Law deals with what 2 variables? ___________ & ____________. What is their

relationship?___________

Write the mathematical equation and a graph for Boyle’s Law:

Problem-

I have added 15 L of air to a balloon at sea level (1.0 atm). If I take the balloon with me to Denver, where

the air pressure is 0.85 atm, what will the new volume of the balloon be?

If I initially have 4.0 L of a gas at a pressure of 1.1 atm, what will the volume be if I increase the pressure to

3.4 atm?

Combined Gas Law deals with what three variables? ______________, ______________, &

______________.

Write the mathematical equation for the Combined Gas Law.

Problem-

A toy balloon has an internal pressure of 1.05 atm and a volume of 5.0 L. If the temperature where the

balloon is released is 200 C, what will happen to the volume when the balloon rises to an altitude where the

pressure is 0.65 atm and the temperature is –150 C

16

I have 130 liters of gas in a piston at a temperature of 2500 C. If I cool the gas until the volume decreases to

85 liters, what will temperature of the gas be?

Coke Cola Classic Inside one can of Coke Classic the volume of CO2 is 3.7L and the pressure is 3.75atm at

23.60 C.

Problem- For each problem state the law used and show all work.

When a can is opened the pressure decreases to 1atm. What is the new volume of CO2.

A can of Coke Classic is sitting in the sun and reaches a temperature of 36 0 C. Will this alter

that taste of the soda? Why? (hint warm liquids cannot dissolve as much gas as cold object)

If the volume of CO2 in a Coke Classic can increased to 4.2 L the pressure inside the can

must be?

While sitting at a Colorado Rockies game you decide to open Coke Classic. The

temperature at the game is 200 C and the atmospheric pressure is .87atm because of elevation.

Calculate the volume of CO2 released when the can is opened.

How will air crush a can?

1. Record the volume and temperature of an empty 12 oz soda in the, before heating section,

table below.

2. Fill a battery jar half full of ice water. Record the temperature of the water. ______0 C =

_____K

3. Add 10 ml of water to the can and heat it until the temperature inside the can is 80° C.

4. Invert the can into the ice bath.

5. What happened?____________________________________________________________

6. What variable change caused the can to crush? volume, pressure, temperature, or number of

particles

7. Repeat steps 1-4

Complete the table below using Charles and Boyle’s Law Trial 1

Inside the soda bottle Bottle at Room Temp. Can at 800 C Can in Ice Water

Pressure (atm) 1 atm

Volume (mL) 355 ml

Temperature (K) 296 K

17

WHAT IS THE MOLECULAR WEIGHT OF THE GAS IN A DISPOSABLE LIGHTER? A. INTRODUCTION: There are many brands of disposable lighters available on the market. When these were first introduced they were called butane lighters and were filled with butane gas under pressure. In this lab, you will try to determine the molecular weight of the gas inside a disposable lighters and determine if the gas in the lighter is, in fact, butane. You will be using the ideal gas law and the ideal gas law constant to calculate the molecular weight of the gas.

Pre-Lab Assignment Review the ideal gas law and how to correct for water vapor when a gas is collected over water. If you wish, bring your own disposable lighter to class to determine the molecular weight of the gas in it.

B E F O R E Y O U B E G I N

SAFETY AND WASTE DISPOSAL 1. Safety goggles are optional. 2. Do not light a match or any other open flame during this lab. 3. Your instructor may allow you to flare off the excess gas. Do so only with the permission of your instructor and under a fume hood.

EQUIPMENT A disposable lighter (Bic, Cricket, etc.), a large graduated cylinder, gas collecting trough, balance (.001 grams), thermometer, barometer.

B. Procedure 1. Set up the gas collecting equipment as described in the photo. 2. Weigh a clean, dry butane lighter to .001 grams. 3. Hold the nozzle of the lighter under the inverted graduated cylinder

filled with water. 4. Depress the lever on the lighter and bubble the gas into the cylinder

. Collect as large a volume of gas as you have time for. (Do not allow the level of the gas to go beyond the graduations.)

5. Record the volume of the gas (.1 mL), the temperature of the water

(.1o C), and the barometric pressure (.1 torr). 6. Dry the butane lighter and weigh it again.

18

DATA Initial Mass of the Lighter ___________________ Final Mass of the Lighter ___________________ Volume of the Gas ___________________ Temperature of the Water ___________________ Barometric Pressure ___________________

Calculations 1. Calculate the volume of the DRY gas at STP 2. Calculate the Density of gas at STP 3. Calculate the molecular weight of the gas.

QUESTIONS The formula for butane is (C4H10). Based on the results of your experiment, do you think the butane lighter you tested

contained pure butane? Explain.

19

The Gas Laws Review

P R E S S U R E U N I T S

1 atm = 760 mmHg = 760 torr = 101.3 kPa = 14.7 psi

Gas Laws Background:

Pressure is defined as Force / Area such as pounds per square inch (psi).

The weight of air pushing down per square inch is 14.7 pounds per square inch or 14.7 psi.

A barometer can be used to measure pressure. A column of mercury (Hg) that is 0.760 meter (760 mm) tall

has the same weight as a column of air from sea level to the edge of the stratosphere. The height of this

column is a good measure of air pressure… 760 mmHg.

Evangelista Torricelli did a lot of experiments with pressure and so 1 mmHg is also called 1 torr. So, air

pressure has a value of 760 torr. This amount of pressure is also called 1 atm (one atmosphere) because

it IS the atmosphere.

In metric units, pressure if Newtons (force) per square meter (area). One Newton is not very much

pressure… about the weight of a small apple (get it… apple… Newton)… and if that force is exerted

over a square meter, the amount of pressure is very small and called a pascal (Pa). It is more useful to

talk of kilopascals (kPa) which would be the weight of 1000 small apples exerted over a square meter.

Air pressure is equal to 101.3 kPa.

Since each of these values (see the top of the page) represent the same amount of pressure, any two of them

can be used as a conversion factor. You can convert one pressure unit into another.

Example:

What is 515 mmHg in kPa? 515 mmHg x mmHg

kPa

760

3.101 = 68.6440789 kPa = 68.4 kPa

Problems:

1. 745 mmHg into psi 5. 522 torr into kPa

2. 727 mmHg into kPa 6. 1.10 atm into psi

3. 52.5 kPa into atm 7. 800. mmHg into atm

20

The Gas Laws

B O Y L E ’ S L A W

Boyle’s Law states that the volume of a gas varies inversely with its pressure if temperature is held

constant.

(If one goes up, the other goes down.) We use the formula:

P1 V1 = P2 V2

Solve the following problems (assuming constant temperature). Assume all number are 3

significant figures.

1. A sample of oxygen gas occupies a volume of 250 mL at 740 torr pressure. What volume will

it occupy at 800 torr pressure?

2. A sample of carbon dioxide occupies a volume of 3.50 Liters at 125 kPa pressure. What

pressure would the gas exert if the volume was decreased to 2.00 liters?

3. A 2.00-Liter container of nitrogen had a pressure of 3.20 atm. What volume would be

necessary to decrease the pressure to 1.00 atm?

4. Ammonia gas occupies a volume of 450 mL as a pressure of 720 mmHg. What volume will it

occupy at standard pressure (760 mmHg)?

5. A 175 mL sample of neon had its pressure changed from 75.0 kPa to 150 kPa. What is its

new volume?

6. A sample of hydrogen at 1.50 atm had its pressure decreased to 0.50 atm producing a new

volume of 750 mL. What was the sample’s original volume?

7. Chlorine gas occupies a volume of 1.20 liters at 720 torr pressure. What volume will it

occupy at 1 atm pressure?

21

The Gas Laws

C H A R L E S ’ S L A W

Charles’ Law states the volume of a gas varies directly with the Kelvin temperature, assuming the

pressure is constant. We use the following formulas:

2

2

1

1

T

V

T

V or V1 T2 = V2 T1

K = C + 273

Solve the following problems assuming a constant pressure. Assume all numbers are 3

significant figures.

1. A sample of nitrogen occupies a volume of 250 mL at 25 C. What volume will it occupy at

95 C?

2. Oxygen gas is at a temperature of 40 C when it occupies a volume of 2.30 Liters. To what

temperature should it be raised to occupy a volume of 6.50 Liters?

3. Hydrogen gas was cooled from 150 C to 50 C. Its new volume is 75.0 mL. What was its

original volume?

4. Chlorine gas occupies a volume of 25.0 mL at 300 K. What volume will it occupy at 600 K?

5. A sample of neon gas at 50 C and a volume of 2.50 Liters is cooled to 25 C. What is the new

volume?

6. Fluorine gas at 300 K occupies a volume of 500 mL. To what temperature should it be

lowered to bring the volume to 300 mL?

7. Helium occupies a volume of 3.80 Liters at –45 C. What volume will it occupy at 45 C?

22

The Gas Laws

T H E C O M B I N E D G A S L A W

In practical terms, it is often difficult to hold any of the variables constant. When there is a change

in pressure, volume and temperature, the combined gas law is used.

2

22

1

11

T

VP

T

VP or P1 V1 T2 = P2 V2 T1

K = C + 273

Complete the following chart.

P1 V1 T1 P2 V2 T2

1

1.50 atm

3.00 L

20.0 C

2.50 atm

30.0 C

2

720. torr

256. mL 25.0 C 250. mL 50.0 C

3 600. mmHg 2.50 L 22.0 C 760. mmHg 1.80 L

4 750. mL 0.00 C 2.00 atm 500. mL 25.0 C

5 95.0 kPa 4.00 L 101. kPa 6.00 L 471. K or

198. C

6 650. torr 100. C 900. torr 225. mL 150. C

7 850. mmHg 1.50 L 15.0 C 2.50 L 30.0 C

8 125. kPa 125. mL 100. kPa 100 mL 75.0 C

23

The Gas Laws

T H E I D E A L G A S L A W

PV = nRT where

P = pressure in atmosphere

V = volume in liters

n = number of moles of gas

R = Universal Gas Constant = 0.0821 Latm/molK

T = Kelvin temperature

1. How many moles of oxygen will occupy a volume of 2.50 liters at 1.20 atm and 25 C?

___________________

2. What volume will 2.00 moles of nitrogen occupy at 720. torr and 20.C?

__________________

3. What pressure will be exerted by 25.0 g of CO2 at temperature of 25 C and a volume of 500.

mL? _________________

4. At what temperature will 5.00 g of Cl2 exert a pressure of 900. torr at a volume of 750. mL?

__________________

5. What is the density of NH3 at 800. torr and 25 C? ___________________

6. If the density of a gas is 1.2 g/L at 745 torr and 20.C, what is its molar mass?

__________________

7. How many moles of nitrogen gas will occupy a volume of 347 mL at 6680 torr and 27 C?

____________________

8. What volume will 454 grams (1 lb) of hydrogen occupy at 1.05 atm and 25 C?

___________________

9. Find the number of grams of CO2 that exert a pressure of 785 torr at a volume of 32.5 L and a

temperature of 32 C. _______________________

10. An elemental gas has a mass of 10.3 g. If the volume is 58.4 L and the pressure is 758 torr at a

temperature of 2.5 C, what is the gas? _____________________

24