Unit 10: Unit 10: Gases Gases Chapter 14 Chemistry 1L Cypress Creek High School
Jan 29, 2016
Unit 10: GasesUnit 10: Gases
Chapter 14
Chemistry 1L
Cypress Creek High School
Table of ContentsTable of Contents• Chapter 14: Gases
– 14.4: Gas Stoichiometry– 14.1: KMT– 14.2: The Combined Gas Laws– 14.3: The Ideal Gas Law
The MoleThe Mole
14.414.4 Gas StoichiometryGas Stoichiometry
Avogadro’s Principle Avogadro’s Principle • Don’t forget that Mole Ratios indicate the molar
relationship between two chemicals in an equation
• In the early 1900s, Avogadro proposed that equal volumes of gases at the same conditions contain the same number of particles. – Avogadro’s principle states that one
mole (6.02 x 1023 particles) of any gas at STP occupies a volume of 22.4 L.
– Avogadro’s principle allows you to interrelate mass, moles, pressure, volume, and temperature for any sample of gas.
14.414.4 Gas StoichiometryGas Stoichiometry
Gas StoichiometryGas Stoichiometry
• 1 mole = 22.4 L of a gas at STP– All stoichiometric calculations will be done at STP
2 22 . ..
14.414.4 Gas StoichiometryGas Stoichiometry
STPSTP• 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.
14.414.4 Gas StoichiometryGas Stoichiometry
Stoichiometric CalculationsStoichiometric Calculations• There are three basic gas stoichiometric
calculations:– mole-to-volume conversions– volume-to-volume conversions– mass-to-volume conversions.
• All stoichiometric calculations begin with a balanced equation and mole ratios.
14.414.4 Gas StoichiometryGas Stoichiometry
Mole-to-Volume ConversionsMole-to-Volume Conversions• A zeppelin combusts H2 and O2 to form water. There are
25 moles of hydrogen gas in a zeppelin. How many liters of water vapor does it produce at STP?
• Given: 25 moles X L
H2 (g) + O2 (g) H2O (g)• Equation: 1 mol 1*(22.4L)
X L H2O = 25 mol H2
1*22.4 L H2O 1 mol H2
= 25 L H2O
14.414.4 Gas StoichiometryGas Stoichiometry
Volume-to-Volume ConversionsVolume-to-Volume Conversions• When 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?
• Given: 1.5 L x L
C3H8 + 5O2 3CO2 + 4H2O• Eq.: 1*(22.4L) 5*(22.4L)
X L O2 = 1.5 L C3H8
5* 22.4L O2 1*22.4L C3H8
= 7.5 L O2
14.414.4 Gas StoichiometryGas Stoichiometry
• The following reaction shows the production of ammonia. How many L of nitrogen are required to produce 85 grams of ammonia?
• Given: X L 85 g
• Equation: 1*(22.4L) 2*(17g)
X L N2 = 85g NH3
1*22.4L N2 2*(17 g NH3)
= 56 L NH3
Mass-to-Volume ConversionsMass-to-Volume Conversions
14.414.4 Gas StoichiometryGas Stoichiometry
14.414.4 Gas StoichiometryGas Stoichiometry
Gas Stoichiometry PracticeGas Stoichiometry Practice• Ammonium sulfate can be prepared by a
reaction between ammonia gas and sulfuric acid as follows.
• What volume of NH3 gas, measured at 78°C and a pressure of 1.66 atm, will be needed to produce 5.00 x 103 g of (NH4)2SO4?
Gas CharacteristicsGas 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
14.414.4 Gas StoichiometryGas Stoichiometry
Kinetic Molecular TheoryKinetic Molecular Theory• KMT 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
14.114.1 KMTKMT
Physical Properties: TemperaturePhysical 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 a thermometer
14.114.1 KMTKMT
How does temperature change? As a result of its change, what does it effect?
Physical Properties: TemperaturePhysical Properties: Temperature• When working with gases, we never use Celsius
– only Kelvin!• Converting Celsius to Kelvin
– K = 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.
14.114.1 KMTKMT
Physical Properties: VolumePhysical 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?
14.114.1 KMTKMT
Physical Properties: PressurePhysical 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)– psi (pounds per square inch)– mmHg (mm of Mercury)
• Pressure is measured by:– Barometer– Manometer
14.114.1 KMTKMT
Physical Properties: PressurePhysical Properties: Pressure• Gas pressure can be
altered due to changes in…– Volume– Temperature
– Amount of particles (mass or moles)
• The more often gas particles collide with the walls of their container, the greater the pressure.
Describe the similarities and differences between the two basketballs. What accounts for their differences?
14.114.1 KMTKMT
Click box to view movie clip.
Dalton’s LawDalton’s Law• The total pressure of a gas mixture is the
sum of the partial pressures of each individual gas
• Air is a mixture!
I’m John Dalton
14.114.1 KMTKMT
Dalton’s LawDalton’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…
14.114.1 KMTKMT
Gas LawsGas Laws• The gas laws apply to ideal gases,
which are described by the kinetictheory in the following five statements. – Gas particles do not attract or repel each other. – Gas particles are much smaller than the spaces
between them. – Gas particles are in constant, random motion. – No kinetic energy is lost when gas particles collide with
each other or with the walls of their container. – All gases have the same kinetic energy at a given
temperature.
• The following laws explain the relationships between temperature, volume, and pressure:
14.214.2 The Gas LawsThe Gas Laws
Boyle’s LawBoyle’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
14.214.2 The Gas LawsThe Gas Laws
V
P
Boyle’s LawBoyle’s Law
• KMT connection: the less space particles have to move, the more forces they exert on each other
14.214.2 The Gas LawsThe Gas Laws
Boyle’s LawBoyle’s Law
• Practice:– If the pressure is
tripled, what happens to the volume?
– If the pressure is halved, what happens to the volume?
• Example:– Squeezing syringe
14.214.2 The Gas LawsThe Gas Laws
Click box to view movie clip.
Charles’ LawCharles’ 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
14.214.2 The Gas LawsThe Gas Laws
V
T
Charles’ LawCharles’ Law
• KMT connection: the more avg. kinetic energy particles have, the greater the distance between particles
14.214.2 The Gas LawsThe Gas Laws
Charles’ LawCharles’ Law• 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
14.214.2 The Gas LawsThe Gas Laws
Click box to view movie clip.
Gay-Lussac’s LawGay-Lussac’s Law• Explains the effect temperature has on pressure• Volume stays constant• Direct relationship
– As temperature increases, pressure increases TP
• At higher temperatures, the particles in a gas have greater kinetic energy.
– As temperature decreases, pressure decreases TP
P PI’m Joseph LouisGay-Lussac
14.214.2 The Gas LawsThe Gas Laws
Gay-Lussac’s LawGay-Lussac’s Law
• KMT connection: the more avg. kinetic energy particles have, the more forces they exert on each other
14.214.2 The Gas LawsThe Gas Laws
Gay-Lussac’s LawGay-Lussac’s Law• 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
14.214.2 The Gas LawsThe Gas Laws
Combined Gas LawCombined Gas Law• 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 solving– Assign variables– Convert oC to K (if necessary)– “Drop” constants (see example)– Solve problem
14.214.2 The Gas LawsThe Gas Laws
Combined Gas LawCombined 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 atm– V1 = constant– T1 = 32oC + 273 = 305 K– P2 = ? atm– V2 = constant– T2 = 5oC + 273 = 278 K
P1V1 = P2V2 substitute 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?
14.214.2 The Gas LawsThe Gas Laws
• A sample of nitrogen monoxide has a volume of 72.6 mL at a temperature of 16°C and a pressure of 104.1 kPa. – What volume will the sample occupy at 24°C and 99.3
kPa?
Applying the Combined Gas LawApplying the Combined Gas Law
14.214.2 The Gas LawsThe Gas Laws
Ideal Gas LawIdeal Gas Law• Ideal gases are theoretical
– Real gases behave like ideal gases at STP
• The ideal gas law relates pressure, temperature, volume, and number of moles
• The 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 0.0821 L · atm
mol · K
14.314.3 The Ideal Gas LawThe Ideal Gas Law
Ideal Gas LawIdeal Gas Law• Example: Tyler is scuba diving along
a coral reef. His 10 liter air tankcontains 2 moles of oxygen gas at20oC. What is the pressure of hisoxygen tank?– P = ? atm– V = 10 L– n = 2 moles– R = 0.0821 L · atm
mol · K– T = 20oC + 273 = 293 K
• PV = nRT? atm * 10 L = 2 mol * 0.0821 L · atm * 293 K
mol · KP = 4.811 atm
14.314.3 The Ideal Gas LawThe Ideal Gas Law
• What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a 12.00-L tank at a temperature of 45°C?
• Determine the molar mass of an unknown gas if a sample has a mass of 0.290 g and occupies a volume of 148 mL at 13°C and a pressure of 107.0 atm.
14.314.3 The Ideal Gas LawThe Ideal Gas Law
Applying the Ideal Gas LawApplying the Ideal Gas Law
End of Unit 10End of Unit 10
Be Prepared for Unit 10 Test on Feb 25th.