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Unit 10: Gases

Chapter 14Test: February 25, 2009

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The Mole

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Gas Stoichiometry

1 mole = 22.4 L of a gas at STP All stoichiometric calculations will be done at STP

2 22 . ..

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STP

Standard temperature and pressure (STP) has been designated as: Temperature at 273 K Pressure at 1 atm 1 mole = 22.4 L

Used to compare gases Creates ideal conditions for

describing behavior of gases

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Gas Stoichiometry

? L H2 = 25 mol H2 x 22.4 L H2 = 560 L H2

1 1 mol H2

Example #1Volume MolesThere are 25 moles of hydrogen gas in a zeppelin. How many liters of hydrogen gas does it contain at STP?

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Gas Stoichiometry

? L O2 = 1.5 L C3H8 x 1 mol C3H8 x 5 mol O2 x 22.4 L O2 = 7.5 L O2

1 22.4 L C3H8 1 mol C3H8 1 mol O2

Example #2Volume VolumeWhen you are grilling steaks, how many liters of oxygen are required to burn 1.5 liters of propane in the reaction:C3H8 + 5O2 3CO2 + 4H2O?

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Gas Stoichiometry

? g Fe2O3 = 8.8 L O2 x 1 mol O2 x 4 mol Fe x 55.847 g Fe = 29.25 g Fe2O3

1 22.4 L O2 3 mol O2 1 mol Fe

Example #3Volume MassHow many grams of rust would be created from iron reacting with 8.8 L of oxygen gas in the reaction:4Fe + 3O2 → 2Fe2O3?

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Gas Characteristics

Gases have no definite shape or volume Gases diffuse rapidly Gases have low density Gases are compressible/expandable Gases exert pressure on their containers

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Kinetic Molecular Theory Explains the behavior of all matter (solids,

liquids, and gases) at a particle level - kinetic means ‘motion’

As related to gases, there are several basic principles of kinetic molecular theory (KMT):

1. Gas particles are in constant, random motion

2. Gas particles do not attract or repel each other

3. Gas particles have elastic collisions, meaning they do not lose kinetic energy when they collide

4. Gas particles’ kinetic energy depends on their temperature

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Physical Properties: Temperature Temperature is a measure of the average

kinetic energy of particles in a system Different from heat - amount of energy in a system

Temperature is measured in units of: Fahrenheit (oF) Celsius (oC) Kelvin (K)

Temperature is measured by athermometer

How does temperature change? As a result of its change, what does it effect?

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Physical Properties: Temperature

When talking about gases, we never work with Celsius – only Kelvin!

Converting Celsius to Kelvin = ?oC + 273 Ex: Room temperature is about 22oC. In Kelvin,

this would be 296 K.

• Absolute Zero (0 Kelvin or -273oC) is the temperature at which all particle motion ceases

• Absolute zero can never be achieved artificially, though it is possible to reach temperatures close to it through the use of cryocoolers.

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Physical Properties: Volume Volume is the space matter occupies Gases always occupy the volume of their container Volume of gas is measured in units of liters (L) or

milliliters (mL) 1 L = 1000 mL Gas volume can be expanded or compressed due

to changes in…– Temperature– Pressure– Amount of particles(mass or moles)

Describe the similarities and differences between the balloons. What accounts for their differences?

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Physical Properties: Pressure Pressure is the force over a given area

If someone stepped on your foot, which shoe would you prefer they wore?

• Pressure is measured in units of:– Atmospheres (atm)– Pascals (Newtons/m2)

• Pressure is measured by 2 instruments:– Barometer– Manometer

– psi (pounds per square inch)– mmHg (mm of Mercury)

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Physical Properties: Pressure Gas pressure can be altered due to

changes in…– Volume– Temperature– Amount of particles (mass or moles)

Describe the similarities and differences between the two basketballs. What accounts for their differences?

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Gas Laws The following laws explain the

relationships between temperature, volume, and pressure: Dalton’s Law Boyle’s Law Charles’ Law Gay-Lussac’s Law Combined Gas Law Ideal Gas Law

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Dalton’s Law

I’m John Dalton

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Dalton’s Law

Ex: The pressure on a tank of air with…+ 20.9 atm oxygen 78.1 atm nitrogen 0.97 atm argon 1.28 atm water vapor 0.05 atm carbon dioxide= 101.3 atm

Ptotal = P1 + P2 + P3…

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Boyle’s Law Explains the effect pressure has on volume Temperature stays constant• Inverse relationship

– As pressure increases, volume decreases PV

– As pressure decreases, volume increases PV

I’m Robert Boyle

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Boyle’s Law

KMT connection: the less space particles have to move, the more forces they exert on each other

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Boyle’s Law

Math Practice: If the pressure is tripled, what happens

to the volume? If the pressure is halved, what happens

to the volume?

Example:Squeezing syringe

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Charles’ Law Explains the effect temperature has on volume Pressure stays constant• Direct relationship

– As temperature increases, volume increases TV

– As temperature decreases, volume decreases TV

I’m JacquesCharles

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Charles’ Law

KMT connection: the more avg. kinetic energy particles have, the greater the distance between particles (increasing volume)

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Charles’ Law

Math Practice: If the temperature is quadrupled, what

happens to the volume? If the temperature is decreased by 1/3, what

happens to the volume?

Example:Hot air balloon

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Gay-Lussac’s Law Explains the effect temperature has on pressure Volume stays constant

• Direct relationship– As temperature increases, pressure increases TP

– As temperature decreases, pressure decreases TP

P PI’m Joseph LouisGay-Lussac

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Gay-Lussac’s Law

KMT connection: the more avg. kinetic energy particles have, the more forces they exert on each other

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Gay-Lussac’s Law

Math Practice: If the temperature is doubled, what happens to

the pressure? If the temperature is decreased by 1/4, what

happens to the pressure?

Example:Pressure cooker

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The gas laws may be integrated into a single equation called the combined gas law

Where… P = pressure in atm V = volume in L T = temperature in K “1” means initial “2” means final

Steps to solving1. Assign variables2. Convert oC to K (if necessary)3. “Drop” constants (see example)4. Solve problem

Combined Gas Law

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Combined Gas Law

Example: In the fall, at a temperature of 32oC, you fill your tires to a pressure of 2.18 atm. A cold front blows through, with temperatures dropping to 5oC, and your tires become flat. Knowing that the volume of your tires has not changed, what is the new pressure of the tires?

P1 = 2.18 atmV1 = constantT1 = 32oC + 273 = 305 KP2 = ? atmV2 = constantT2 = 5oC + 273 = 278 K

P1V1 = P2V2 2.18 atm = ? atm T1 T2 305 K 278 K P2 = 1.987 atm

What law best illustrates what happened to the tires in this problem?

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Ideal Gas Law Ideals gases are theoretical models Real gases behave like ideal gases at STP The ideal gas law relates pressure, temperature,

volume, and number of moles Equation includes universal gas constant R, which

“corrects” conditions to STP Where…

P = pressure in atm V = volume in L n = number of particles in moles R = universal gas constant T = temperature in K 0.821 L · atm

mol · K

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Ideal Gas Law Example: Tyler is scuba diving along a coral reef.

Your 10 liter air tank contains 2 moles of oxygen gas at 20oC. What is the pressure of your oxygen tank?

P = ? atmV = 10 Ln = 2 molesR = 0.821 L · atm mol · KT = 20oC + 273 = 293 K

PV = nRT ? atm * 10 L = 2 mol * 0.821 L · atm * 293 K mol · K

P = 48.11 atm