It’s a Gas

GAS LAWS Mr. Trotts 2/14/2011

Lesson Objectives You will be able to: Name and describe 5 characteristics of gases Identify three differences between ideal gases and real gases. Define the term “STP” List 4 units for pressure measurement Explain and describe the relationship between temperature and pressure of gases, according to Charles’ Law. Explain and describe the relationship between volume and pressure of gases, according to Boyle’s Law. Explain how temperature, pressure, and volume of gases are all related according to the combined gas law. Solve mathematic problems about Charles’ Law, Boyle’s Law, and the combined gas law.

Vocabulary: Journal Pressure Volume Temperature Kelvin Boyle’s Law Charle’s Law Ideal Gas Law STP Combined Gas Law

Test questions: journal Describe the 5 characteristics of gases Compare the 3 real and ideal characteristics of gases

What are Characteristics of a GAS? E X P A N D A B L E Diffusible... Compressible Fluid Low Density

: Gas Laws Assumptions In the REAL WORLD: Gases are fat. (they have mass) Gases hog the sofa. (they have volume) Gases are pushy and have an attitude toward other gases. (they exert forces on each other) In an IDEAL WORLD: Gases are skinny. (they have no mass) Gases make themselves invisible. (they have no volume) Gases are not confrontational. (they do not interact… elastic collisions) Assumptions Image Source: mtv.com

IT’S A GAS… Daily grade: name those 5 characteristics given 2 slide ago. What were the 3 differences between a real gas (what is really happening) and an ideal gas (assumptions used to make gas laws work)

IT’S A GAS… List the physical characteristics of gases Describe the kinetic molecular theory (KMT) List the 3 assumption of the KMT

The Nature of Gases Gases have some interesting characteristics that have fascinated scientists for 300 years. The first gas to be studied was air & it was a long time before it was discovered that air was actually a mixture of particles rather than a single gas.

The Nature of Gases But this realization did not make the study of gas behavior more difficult. Although air is a mixture of several different gases, it behaves much the same as any single gas. Regardless of their chemical identity, gases tend to exhibit similar physical behaviors

The Nature of Gases Gas particles can be monatomic (Ne), diatomic (N2), or polyatomic (CH4) – but they all have these characteristics in common: 1) Gases have mass. 2) Gases are compressible. 3) Gases fill their containers. 4) Gases diffuse 5) Gases exert pressure. 6) Pressure is dependent on Temp.

Kinetic Molecular Theory There is a theory that modern day chemist’s use to explain the behaviors and characteristics of gases - the Kinetic Molecular Theory of Matter. The word kinetic refers to motion. The word molecular refers to molecules

Kinetic Molecular Theory The theory states that the tiny particles in all forms of matter in all forms of matter are in constant motion. This theory is used to explain the behaviors common among gases There are 3 basic assumptions of the KMT as it applies to gases.

KMT Assumption #1 A gas is composed of small hard particles. The particles have an insignificant volume and are relatively far apart from one another. There is empty space between particles. No attractive or repulsive forces between particles.

KMT Assumption #2 The particles in a gas move in constant random motion. Particles move in straight paths and are completely independent of each of other Particles path is only changed by colliding with another particle or the sides of its container.

KMT Assumption #3 All collisions a gas particle undergoes are perfectly elastic. No energy is lost from one particle to another, and the total kinetic energy remains constant.

Compare the density of several gases at STP Describe why gases are compressible Describe the expansion of gases

Gases have mass. Gases seem to be weightless, but they are classified as matter, which means they have mass. The density of a gas – the mass per unit of volume – is much less than the density of a liquid or solid, however.

Gases have mass. It’s this very low density that allows us to be able to walk through the room without concerning ourselves with air resistance. Since it is so easy to “swim” across the room we don’t put much thought into the mass of a gas. Really it is only noticeable if we have a large collection of gas in a container.

The Kinetic-Molecular theory explanation of it is that we assume that gases are composed of a collection of particles. You can’t see these particles directly, so they are very tiny, and to notice any mass you must weigh a collection of the particles. It is usually necessary to have a mole or more of gas particles to have significant a significant change in mass.

2nd– Gases “R” squeezable If you squeeze a gas, its volume can be reduced considerably A gases low density allows for there to a lot of empty space between gas molecules.

Gas particles have a high velocity, relative to their masses. This gives them a lot of energy and movement. The movement causes the gases to spread out, which leaves a lot of space between molecules. That empty space can be compressed by pressure allowing gas particles less room to move around thus decreasing the volume.

This empty space can be compressed simply by adding pressure. We can use this ability of a gas to do work for us. Think of a shocks on a car. You really are riding on a pillow of air. A bump in the road compresses the gas in the shocks until the bump’s energy is absorbed.

3rd – Gases fill their containers Gases expand until they take up as much room as they possibly can. Gases spread out to fill containers until the concentration of gases is uniform throughout the entire space. This is why that nowhere around you is there an absence of air.

The Kinetic-Molecular theory alludes to this by the fact that these particles are in constant random motion. Gases move in a straight line until it they collide with other particles or the sides of the container, which causes them to change directions until they collide with something else. This bouncing off of everything around them spread the particles out until they are uniform throughout the entire container.

There are really two properties going on here: If I opened up a bag of popcorn in front of the class you would soon be able to smell it in the back. The popcorn smell is a high energy molecule or group of molecules that is in the gas state. There are really two properties going on here: - This property of gases spreading out until they have filled the room - And the property of diffusion

Explain why when adding air to a balloon it will stop at a certain volume, and then when adding more air gets bigger and stops at a new volume

What is meant by gases diffuse? Explain how gases exert pressure

4th – Gases diffuse Gases can move through each other rapidly. The movement of one substance through another is called diffusion. Because of all of the empty space between gas molecules, another gas molecule can pass between them until each gas is spread out over the entire container.

The same logic from the observation that gases spread out applies here. If the gases are in constant random motion the fact that they are moving and colliding with everything around them then they will mix with other gases uniformly. This doesn’t happen at the same speeds for all gases though. Some gases diffuse more rapidly then other gases based on their size and their energy.

Diffusion explains why gases are able to spread out to fill their containers. It’s why we can all breath oxygen anywhere in the room. It also helps us avoid potential odoriferous problems.

5th – Gases exert pressure Gas particles exert pressure by colliding with objects in their path. The sum of all of the collisions makes up the pressure the gas exerts.

The Kinetic-Molecular theory alludes to this by the fact that these particles are colliding with anything in their path. Imagine a gas in a container as a room of hard rubber balls. The collisions of the balls bouncing around exert a force on the object that with which they collide. The definition of a pressure is a force per unit area – so the total of all of the tiny collisions makes up the pressure exerted by the gas.

The gases push against the walls of their containers with a force. The pressure of gases is what keeps our tires inflated, makes our basketballs bounce, makes hairspray come out of the can, etc.

Desribe what happens to the gases in a fixed volume container as the temperature is increased Give examples

6th – Pressure depends on Temp The higher the temperature of a gas -the higher the pressure that the gas exerts The reverse of that is true as well, a the temperature of a gas decreases – the pressure decreases. Think about the pressure of a set of tires on a car

Today’s temp: 35°F Pressure Gauge

Today’s temp: 85°F Pressure Gauge

6th – Pressure depends on Temp The reverse of that is true as well, a the temperature of a gas decreases – the pressure decreases. Think about the pressure of a set of tires on a car

Do you recall the definition of temperature? the average kinetic energy of the particles that make up an object The higher the temperature the more the energy The more the energy the more impacts the gases administer The more the impacts or collisions the more the pressure exerted.

The pressure increases when temperature increases because the molecules are moving with greater speed and colliding against the sides of their containers more often. Therefore, the pressure inside that container is greater, because there are more collisions.

13. What variables effect the characteristics of gases? Describe these variables What is STP?

Measuring Gases The conditions under which a gas is studied is very important to its behavior. Experimental work in chemistry requires the measurement of such quantities as volume, temperature, pressure, and the amount of sample. These quantities are called variables and if they are not accounted for then the results of the experiment might be jeopardized.

Gas variables In order to describe a gas sample completely and then make predictions about its behavior under changed conditions, it is important to deal with the values of: 1) amount of gas 2) volume 3) temperature 4) pressure

Amount (n) The quantity of gas in a given sample expressed in terms of moles of gas. This of course is in terms of 6.02 x 1023 molecules of the gas. Don’t forget to convert mass to moles you just divide by the molar mass of the gas.

Volume (V) The volume of the gas is simply the volume of the container it is contained in. The metric unit of volume is the liter (L) There might also be problems that use cubic meters as the unit for volume. - 1 L = 1 dm3

Kelvin = C° + 273 Temperature (T) The temperature of a gas is generally measured with a thermometer in Celsius. All calculations involving gases should be made after converting the Celsius to Kelvin temperature. Kelvin = C° + 273

Pressure (P) The pressure of a gas is the force exerted on the wall of the container a gas is trapped in. There are several units for pressure depending on the instrument used to measure it including: 1) atmospheres (atm) 2) Millimeters of Mercury (mmHg) 3) Kilopascal (kPa)

S T P The behavior of a gas depends very strongly on the temperature and the pressure at which the gas is held. To make it easier to discuss the behavior of a gas, it is convenient to designate standard conditions, called STP. - Temperature = 0°C or 273K - Pressure = 1atm or 760mmHg or 101.3kPa

What causes atmospheric pressure to vary? 1 atmosphere of pressure = how many mmHg, pascals, torres?

Atmospheric Pressure The gases in the air are exerting a pressure called atmospheric pressure Atmospheric pressure is a result of the fact that air has mass is and is attracted by gravity producing a force. Knowing this atmospheric pressure and predicting changes in the atmospheric pressure is how forecasters predict the weather.

Atmospheric Pressure Atmospheric pressure varies with altitude - the lower the altitude, the longer and heavier is the column of air above an area of the earth. Look on the back of a box of cake mix for the difference in baking times based on the atmospheric pressure in your region.

1 atm = 760mmHg = 760 torr = 101.3kPa

Atmospheric Pressure Low pressure or dropping pressure indicates a change of weather from fair to rain. High pressure is an indication of clear skies and sun. It all has to do with the amount of air pressing down on us.

Boyle’s Law Boyle’s Law: 18. Variables = ? 19. Constant = ? 20. Formula = ? 21. Examples of system

Gas Laws Studies of the behavior of gases played a major role in the development of physical sciences in the 7th and 8th centuries. The Kinetic Molecular theory marked a significant achievement in understanding the behavior of gases. Observations have become mathematical laws which we can use to predict quantitative outcomes.

Boyle’s Law Robert Boyle was among the first to note the relationship between pressure and volume of a gas. He measured the volume of air at different pressures, and observed a pattern of behavior which led to his mathematical law. During his experiments Temperature and amount of gas weren’t allowed to change

As the pressure increases Volume decreases

22. How does Pressure and Volume of gases relate graphically? PV = k Temperature, # of particles remain constant Pressure

Eg: A gas has a volume of 3.0 L at 2 atm. What is its volume at 4 atm? Boyle’s Mathematical Law: What if we had a change in conditions? since PV = k P1V1 = P2V2 Eg: A gas has a volume of 3.0 L at 2 atm. What is its volume at 4 atm?

determine which variables you have: P1 = 2 atm V1 = 3.0 L P2 = 4 atm V2 = ? determine which law is being represented: P and V = Boyle’s Law

V2 = 1.5L 3) Rearrange the equation for the variable you don’t know P1V1 = V2 P2 4) Plug in the variables and chug it on a calculator: (2.0 atm)(3.0L) = V2 (4atm) V2 = 1.5L

Complete practice sheet on Boyle’s Law

Charle’s Law Charle’s Law 23. Variable’s = ? 24. Constant = ? 25. Formula = ? 26. Example of system

Charles’s Law Jacques Charles determined the relationship between temperature and volume of a gas. He measured the volume of air at different temperatures, and observed a pattern of behavior which led to his mathematical law. During his experiments pressure of the system and amount of gas were held constant.

Volume of balloon at room temperature Volume of balloon at 5°C

27. How does Temperature and Volume of gases relate graphically? V/T = k Pressure, # of particles remain constant Temp

V1 V2 = T1 T2 Charles’s Mathematical Law: What if we had a change in conditions? since V/T = k V1 V2 T1 T2 = Eg: A gas has a volume of 3.0 L at 127°C. What is its volume at 227 °C?

determine which variables you have: T1 = 127°C + 273 = 400K V1 = 3.0 L T2 = 227°C + 273 = 5ooK V2 = ? determine which law is being represented: T and V = Charles’s Law

4) Plug in the variables: 3.0L V2 400K 500K = 5) Cross multiply and chug (500K)(3.0L) = V2 (400K) V2 = 3.8L

Complete practice sheet on Charle’s Law

Gay-Lussac’s Law Gay –Lussac’s Law: 28. Variables = ? 29. Constant = ? 30. Formula = ? 31. Example of system

Gay Lussac’s Law Old man Lussac determined the relationship between temperature and pressure of a gas. He measured the temperature of air at different pressures, and observed a pattern of behavior which led to his mathematical law. During his experiments volume of the system and amount of gas were held constant.

Think of a tire... Car before a trip Pressure Gauge Let’s get on the road Dude!

Think of a tire... Car after a long trip Pressure Gauge WHEW!

32. How does Pressure and Temperature of gases relate graphically? P/T = k Volume, # of particles remain constant Temp

P1 P2 = T1 T2 Lussac’s Mathematical Law: What if we had a change in conditions? since P/T = k P1 P2 T1 T2 = Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C?

determine which variables you have: T1 = 127°C + 273 = 400K P1 = 3.0 atm T2 = 227°C + 273 = 500K P2 = ? determine which law is being represented: T and P = Gay-Lussac’s Law

3.0atm P2 = 400K 500K P2 = 3.8atm (500K)(3.0atm) = P2 (400K) 4) Plug in the variables: 3.0atm P2 400K 500K = 5) Cross multiply and chug (500K)(3.0atm) = P2 (400K) P2 = 3.8atm

Complete practice sheet on Gay-Lussac’s Law

Boyle’s P V T, n Charles’ V T P, n Gay-Lussac’s P T V, n Summary LAW RELAT-IONSHIP CON-STANT Boyle’s P V P1V1 = P2V2 T, n Charles’ V T V1/T1 = V2/T2 P, n Gay-Lussac’s P T P1/T1 = P2/T2 V, n

Combined Gas Law Combined Gas Law: Variables Constant Formula

…THEREFORE: Temperature, Volume, and Pressure are all related! = V2 T2 Combined Gas Law

Practice 1. 100.0 cm3 oxygen at 10.50 kPa changes to 9.91 kPa. What is the new volume of the gas? V1 T1 P1 V2 T2 P2 = V1 P1 = V2 P2 Boyle’s Law! (10.50 kPa) x (100.0 cm3 O2) = (9.91 kPa) x (V2) V2 = (10.50 kPa) x (100.0 cm3 O2) = 106 cm3 O2 (9.91 kPa)

Practice 2. 150.0 mL sulfur dioxide at 748 mmHg changes to a new volume of 140.6 mL. What is the new pressure of the gas? V1 T1 V2 T2 = P1 P2 V1 V2 = P1 P2 x (748 mmHg) (150.0 mL SO2) = (P2) x (140.6 mL SO2) (150.0 mL SO2) (748 mmHg) (140.6 mL SO2) P2 = 798 mmHg

Complete practice sheet on Combined Gas Law

The Ideal Gas Law & Co. Mr. Trotts Feb 2011

A Reminder… assume ideal We that we live in an world where: Gas particles have no mass Gas particles have no volume Gas particles have elastic collisions These assumptions are used when trying to calculate the AMOUNT of a gas we have! 92

Why are these assumptions important? PV = nRT Image source: thefreedictionary.com

PV = nRT P V n R T The Ideal Gas Law RESSURE OLUME MOLES OF GAS GAS CONSTANT EMPERATURE Image source: popartuk.com

The MysteRious R 62.4 mmHg · L mol · K 8.31 kPa · L mol · K R is a constant (doesn’t change). Number value of R depends on other units. Units of R are a combination of many units. 62.4 mmHg · L mol · K 8.31 kPa · L mol · K 0.0821 atm · L mol · K Image source: toysrusemail.com

Ummm… What? PV = nRT P V R = n T (atm) (L)atm) (kPa) (mm Hg) L) R = Solve for R: P V R = n T Plug in units: (atm) (L)atm) (kPa) (mm Hg) L) R = (mol) (K)

! Charles' Law Boyle's Law Combined Gas Law Ideal Gas Law V1 T1 = V2 P1 x V1 = P2 x V2 P1 V1 P2 V2 = T1 T2 Combined Gas Law Ideal Gas Law P V = n RT Used with only ONE SET OF CONDITIONS

When to Use PV = nRT Calculating amount of gas in moles Calculating P, V, or T if moles of gas are known. IMPORTANT! We must have 3 out of 4 pieces of information: P V n T

Practice with the Ideal Gas Law A gas sample occupies 2.62 L at 285ºC and 3.42 atm. How many moles are present in this sample? PV = nRT P V n = R T (3.42 atm) (2.62 L) n = = 0.196 mol 0.0821 L · atm mol · K (558 K)

But Let’s Be Practical… We don’t usually measure in moles! We usually measure quantities in GRAMS! PV = nRT PVM = gRT

PVM = gRT P V M g R T RESSURE OLUME OLAR MASS OF GAS (g/mol) RAMS OF GAS GAS CONSTANT EMPERATURE Image source: popartuk.com

Practice with the Ideal Gas Law A balloon is filled with 0.2494 g of helium to a pressure of 1.26 atm. If the desired volume of the balloon is 1.250 L, what must the temperature be in ºC? P V M PVM = gRT T = g R 4.00 g mol (1.26 atm) (1.250 L) T = 308 K = - 273 0.0821 L · atm mol · K (0.2494 g) 35 ºC

PV=nRT vs. PVM=gRT Use PV=nRT when: Use PVM=gRT when: You are given moles in the problem. You are searching for moles as an answer. Use PVM=gRT when: You are given grams in the problem. You are searching for grams as an answer.

What Else Happens Under Unchanging Conditions? At constant V and T, pressure is easy to calculate! “The sum of the individual pressures is equal to the total pressure.” Total Pressure = Pressure of gas 1 + Pressure of gas 2 + Pressure of gas 3 + Pressure of gas 4 … Ptotal = P1 + P2 + P3 + … Dalton's Law of Partial Pressures

Partial Pressures Practice A sample of hydrogen gas is collected over water at 25ºC. The vapor pressure of water at 25ºC is 23.8 mmHg. If the total pressure is 523.8 mmHg, what is the partial pressure of the hydrogen? Ptotal = PH2 + PH2O = 523.8 mm Hg PH2 + 23.8 mm Hg = PH2 500.0 mm Hg Source: 2003 EOC Chemistry Exam

What do Changing Conditions Affect? We have learned that we can change 3 variables: Temperature, Volume, and Pressure. If MASS remains constant… …But VOLUME changes… Then DENSITY CHANGES! D = M V

Two Types of Density Problems: At STP: Not at STP: molar volume of any gas at STP = Determine new volume (V2 ) using Combined Gas Law 22.4 Liters P1 V1 P2 V2 = T1 T2 STP Values non-STP Density at STP = Density at non-STP = molar mass molar mass molar volume 22.4LLiters V2

Practice with Density Problems: Determine the density of ethane (C2H6) at STP: Determine the density of C2H6 at 3.0 atm and 41ºC. P1 V1 P2 V2 = T1 T2 V2 == 8.6 L 8.6 L molar mass D (at STP) = molar volume D = molar mass V2 V2 = P1 V1 T2 molar mass = 30.08 g T1 P2 P1 = 1.0 atm V1 = 22.4 L T1 = 273 K P2 = 3.0 atm V2 = ? T2 = 314 K molar volume = 22.4 L V2 = (1.0 atm) (22.4 L) (314 K) D = 30.08 gg 8.6 L = 3.5 g/L (273 K) (3.0 atm) 30.08 g D = = 1.34 g/L 22.4 L V2 = 8.6 L