Chapter 11

Gas Laws

Objectives

• Describe the properties of gases

• Describe the Kinetic Molecular Theory, Ideal Gases

• Explain air pressure and barometers

• Convert pressure units

• Perform calculations using the ideal gas law

Why Study Gases?

• We deal with gases on a daily basis

– Filling your car tires

– Barometric Pressure (Weather)

– Breathing air

• Many reactants and products are gases

– We need to know how to work with gases

– In the lab gases are usually measured in volumes instead of masses

Assumptions of Gases

• We are going to make a few assumptions about gases to study them.

• These assumptions are bases on years of study.

• They work well at normal temperatures and pressures

– Especially well at high temps and low pressures. (In case you were wondering)

Properties of Gases

• Gases expand to fill their container• Gases can be compressed• Gases are fluids

– Meaning they flow• Gases have a low density

– Liq. N2 = .807g/mL at -196ºC– Gas N2 = .625 g/L at 0ºC– Or about 1000 times different!

• Gases effuse and diffuse (To be Cont.)

Kinetic Molecular Theory

• Particles of a gas are in constant motion

• Volume of the individual particles is zero

• Particles colliding with the side of the container cause pressure

• Particles exert no force on each other

– Means = No Intermolecular Forces

• Temperature of a gas is directly related to its Kinetic Energy

What’s Wrong?

• Gas particles do have volume

– However the ratio of the particle volume to container volume is almost zero

• Gas particles experience intermolecular forces

– However, the particles are relatively far apart and free to move so

– Forces are weak

Ideal Gas

• Gases that behave according to the kinetic molecular theory (KMT)

• No such gas exists

• Good approximation most of the time

• Simplifies are treatment of gases

• Corrections for real gases are fairly small

How do you know this is an ideal gas?

Gas Variables

• Pressure (P) in atm, mmHg, torr, kPa

• Volume (V) in mL, L

• Temperature (T) in K

• Moles (n) in mol

• These 4 variables can completely describe a gas

Pressure

• Measure of force per unit area

– Force/Area

– SI Unit is N/m2 or Pascal (Pa)

– 1 Newton is about 100 grams

– So, 1 Pa is about 100 grams on 1m2

• Or a very small pressure

• Atmospheric pressure is quite substantial

– 101,300 Pa or 101.3 kPa

Measuring Pressure

• Pressure is most commonly measured with a barometer

• Invented by Evangelista Torricelli in approximately 1644

• Filled a glass tube with liquid mercury and inverted the tube in a dish of mercury

• At sea level the column stood at 76 cm

• When the barometer was taken to higher elevation the level dropped

Torricelli’s Explanation

•Air pressed down on the dish of mercury

•Mercury was forced up the column

•Mercury rose until the weight of the mercury equaled the weight of the air

Figure 11.404a

Pressure Measurements

• Normal pressure at sea level in a barometer

– 760. millimeters mercury (mmHg)

– 1.00 atmospheres (atm)

– 101.3 kilopascals (kPa)

– 760. torr (in honor of Torricelli)

– 14.7 pounds per square inch (psi)

– 29.9 inches of mercury (inHg)

– We will use the first three the most

Example

• Convert 728 mmHg to A) atm B) kPa

Temperature

• Kelvin temperature is the ONLY scale used in gas calculations

• Used because 0 K is absolute zero• Note it is NOT ºK!• Converting from Celsius to Kelvin

– Temp. in K = Temp in C + 273• 0 ºC = 273 K• 100 ºC = 373 K• Room temp is about 22 ºC or 295 K

The Ideal Gas Law

• Mathematical equation that relates all variables for a gas

• PV=nRT– P,V,n,T have been discussed

– What is R?

– Universal Gas Constant

• Same for ALL gases

• But can change with pressure unit

Universal Gas Constant

• The units of R can change as the pressure units change

• R has two values

• R = 8.314 (L*kPa)/(mol*K)

• R = 0.08206 (L*atm)/(mol*K)

– Use the first if you are in kPa

– Use the second if you are in atm

– If you are in mmHg convert

Units in the Ideal Gas Law

• PV=nRT• P can be in atm or kPa

• V must be in Liters (L)

• n must be in moles (mol)

• T must be in Kelvins (K)

Changing the Law

• The ideal gas law can be manipulated to solve for an unknown variable

• Often used in stoichiometry problems

• You will always know R.

– It is never a variable

• Just use algebra to isolate the variable you desire

Solve for T

Solve for P

Solve for V

Example• A sample of gas at 25ºC and 3.40 L

contains 3.33 moles. What is the pressure (in kPa)?

Example• 5.69 grams of Oxygen gas at 250.ºC has a

pressure of 722mmHg. What is the volume?

Homework

• p.418 # 18,24,27 41,44,49,51,52,53

Changing Gas Conditions

• The conditions of a gas can change

• If two variables change the other two do not

– They are constant

• If three variables change the other one does not

• Rearrange the ideal gas law to solve

– Place variables that change on the same side of the equation

Changing Pressure and Volume

• PV=nRT

Pressure and Volume

• 2.0 L of a gas at 3.0 atm is compressed to 1.0 L what is the new pressure?

Pressure and Volume

• Pressure and Volume are inversely related

• As one increases the other decreases

• Sketch a graph of pressure vs. volume

– Pressure on the Y axis

– Volume on the X axis

Changing Volume and Temp

• PV=nRT

Volume and Temp.

• Volume and Temp. are directly related

• As one increases so does the other

• Sketch a graph of volume vs. temp.

– Volume on the Y axis

– Temp. on the X axis

Volume and Temperature

• 1.0 L of a gas at 10.ºC is heated to 30ºC. What is the new volume?

Changing Others

• PV=nRT

Changing Three Variables

• Pressure, Volume, Temperature

• Pressure, Volume, Moles

STP

• Standard Temperature and Pressure

– Short way to state a temp and pressure

• Temperature is 0ºC or 273K

• Pressure is 1.00atm or 760. mmHg

More Ideal Gas Law Fun!

• Ideal gas law can be used to find three more items.

• Density

– Mass/Volume

• Molar Mass

– Grams/Moles

• Molar Volume

Molar Mass

• Molar mass can be found two different ways

• 1) Solve for moles then divide grams/moles

• 2) Rearrange the ideal gas law

– Molar mass is hiding in the equation

Density

• Density can be found two ways

• 1) Divide Mass/Volume

• 2) Rearrange the ideal gas law

– Mass/Volume is hiding in the equation

Calculate This

• What volume does 1.00 mol of a gas at STP occupy?

Molar Volume

• Volume occupied by 1 mole of a gas • At STP 1 mole of a gas occupies 22.4L

Molar Volume

• What does this mean?

– One mole of any gas at the same temp and pressure occupies the same volume!

• Gas volume is independent of identity

1 mol N2

1 mol Cl2 1 mol CH4

1 mol Ne 1 mol CO2

1 mol He1 mol H2 1 mol O2

Homework

• P.418 #’s 58,60,62

Objectives

• Perform gas stoichiometry calculations

• Describe volume ratios

• Relate gas temperature to Kinetic Energy

• Perform calculations using Grahams Law of Effusion

• Describe the dependence of gas variables

Gas Stoichiometry

• We can perform stoichiometry with gases

• Must use the ideal gas law

– Use the ideal gas law to find moles

– Use at beginning or the end

– Perform normal stoichiometry

• Balanced equation

• Mole ratios

• Molar masses

Example• 4.55 grams of sodium carbonate is added to

excess hydrochloric acid. What volume of carbon dioxide can be produced at STP?

Example• 0.39 grams of MgO is produced when

magnesium is burned in air at 800.ºC and 729mmHg. What volume of oxygen gas is required for the complete combustion?

Dalton’s Law of Partial Pressure

• Each gas in a container contributes its own pressure to the total

• Ptot = PA + PB + PC + . . .

– Each gas is independent of the others

– Assumption of the ideal gas law

• Gases exert no force on each other

Gas Collection Over Water

• Bubbling of a gas into a container filled with water

• Convenient way of collecting gases

– Gas rises to the top of the container

• Less dense

– Allows us to measure the volume

Image from: http://www3.moe.edu.sg/edumall/tl/digital_resources/chemistry/images/img_CH_00004.jpg

Water Vapor Pressure

• The gas you are trying to collect is not the only gas above the water

• Water vapor is also present

– Liq. water is always evaporting

• Water vapor contributes to total pressure

• Need to subtract waters vapor pressure to get the real pressure of the gas

• Ptot = PA + PH2O

Image from: http://www3.moe.edu.sg/edumall/tl/digital_resources/chemistry/images/img_CH_00004.jpg

Water Vapor Pressure

• Vapor Pressure increases with temperature– Evaporation increases with temp

Temp ºC Vapor Pressure mmHg

Temp ºC Vapor Pressure mmHg

0 4.6 25 23.6

15 12.8 50 92.5

20 17.5 70 233.7

22 19.8 100 760.0

Volume Ratios

• The coefficients in balanced equations can be mole and volume ratios

• From the ideal gas law

– V=nRT/P

– Therefore Volume and Moles are directly related

Volume Ratios

• The equation

2H2(g) + O2(g) 2H2O(g)

– Means

• 2 mol H2 and 1 mol O2 2 mol H2O

• OR

• 2 L H2 and 1 L O2 2 L H2O

Kinetic Energy

• Energy of motion

• KE = 1/2mv2

– m = mass

– v = velocity

• Speed

Kinetic Energy & Temperature

• All gases at the same temperature have the same kinetic energy

– Assumption of Kinetic Molecular Theory

• Temp. directly related to Kinetic Energy

• All gases at the same temp. do not have the same velocity

– Gases have different masses

Kinetic Energy & Temperature

• According to the equation

– KE = 1/2mv2

– KE depends on mass on velocity

– If two gases have the same KE

m1v12 = m2v2

2

– The gas with the SMALLER mass has the LARGER velocity

1 mol N2

1 mol Cl2 1 mol CH4

1 mol Ne 1 mol CO2

1 mol He1 mol H2 1 mol O2

All gases are at 298K and 1.00 atm.

Which gas has

Greatest KE?

Highest Velocity?

Smallest Velocity?

Effusion

• The process of a gas entering a vacuum thru a small opening.

• The rate of effusion varies with molar mass

– Molar mass changes the velocity

Image from: http://itl.chem.ufl.edu/2045_s00/lectures/lec_d.html

Graham’s Law of Effusion

1

2

2

1

MM

MM

rate

rate

• 1 and 2 designate the gases• MM is molar mass• Usually the lighter gas is designated as 1• Rates can be relative or velocities

Example• Compare the rates of effusion for oxygen

and helium gas

Diffusion

• Random movement of gas particles among other particles

• Process is similar to effusion

• Larger gases diffuse slower smaller gases

– Due to velocity

Explain

• Why pressure and volume are inversely related. (Moles and Temp. constant)

• Why volume and temperature are directly related. (Pressure and Moles constant)

• Why pressure and moles are directly related. (Volume and Temp. constant)

• Why pressure and temperature are directly related. (Volume and Moles constant)

Homework

• Page 420 #’s 68-71