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Gases. Chapters 12.1 and 13. 12.1 Main Idea. Gases expand, diffuse, exert pressure, and can be compressed because they are in a low-density state consisting of tiny, constantly moving particles. Objectives. Predict the behavior of gases using the kinetic-molecular theory

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### Gases

Chapters 12.1 and 13

12.1 Main Idea

Gases expand, diffuse, exert pressure, and can be compressed because they are in a low-density state consisting of tiny, constantly moving particles

Objectives
• Predict the behavior of gases using the kinetic-molecular theory
• Explain how mass affects the rates of diffusion and effusion
• Calculate the partial pressure of a gas
• Measure gas pressure
Review Vocabulary
• Kinetic energy
• Molar mass
New Vocabulary
• Kinetic-molecular theory
• Elastic collision
• Temperature
• Diffusion
• Graham’s Law
• Pressure
• Barometer
• Manometer
• Pascal (Pa)
• Dalton's law of partial pressure
• Atmosphere (atm)
Kinetic-Molecular (KM) Theory
• Assumptions
• Particle size is very small
• Particles take up relatively no space
• Particles are far apart
• Very little interaction of particles
• Collisions are elastic
• No kinetic energy is lost in a collision
Particle Energy
• Determined by mass and velocity
• Temperature- the average kinetic energy of particles in matter
Behavior of Gases
• Pressure- gases will expand to fill the space they occupy
Behavior of Gases
• Compression and expansion- density of material can be changed by changing the available volume
Behavior of Gases
• Diffusion- movement of one material through another
• Concentration gradient
• Effusion- gas escaping from a confined space through tiny openings
• RH/RHe=0.849
Pressure
• Pressure (P) is defined as the force per unit area on a surface. (P=F/A)
• Gas pressure is caused by collisions of the gas molecules with each other and with surfaces with which they come into contact.
• The pressure exerted by a gas depends on volume, temperature, and the number of molecules present.
• The greater the number of collisions of gas molecules, the higher the pressure will be.
Gas Pressure

Barometer

Manometer

Manometers measure gas pressure in a closed system

• Barometers measure atmospheric pressure
• open system
Gas Pressure
• Units
• Pascal (1 Pa = 1 /m2)
• Atmosphere (1 atm = 101.3 kPa)
• mm Hg (1 atm = 760 mm Hg)
• Torr(1 torr = 1 mm Hg)
Dalton’s Law of Partial Pressures
• total pressure is the sum of the partial pressures
• Ptot=P1 + P2 + P3 + … Pn

A mixture of O2, CO2 and N2 has a total pressure of 0.97 atm. What is the partial pressure of O2 if the partial pressure of CO2 is 0.70 atm and the partial pressure of N2 is 0.12 atm?

• 0.97 atm = 0.70 atm + 0.12 atm + x
• X = 0.15 atm
Can you…
• Predict the behavior of gases using the kinetic-molecular theory
• Explain how mass affects the rates of diffusion and effusion
• Calculate the partial pressure of a gas
• Measure gas pressure

### The Gas Laws

Chapter 13.1

13.1 Main Idea

For a fixed amount of gas, a change in one variable- pressure, volume or temperature- affects the other two.

13.1 Objectives
• State the relationships among pressure, volume, temperature, and the amount of gas
• Apply gas laws to problems involving pressure, volume, temperature, and the amount of gas
• Create graphs of the relationships among pressure, volume, temperature, and the amount of gas
• Solve problems related to fixed amounts of gases
Review Vocabulary
• Scientific law
• Directly related
• Indirectly (inversely) related
• Kelvin
New Vocabulary
• Ideal gas
• Absolute zero
• Boyle’s law
• Charles’s law
• Gay-Lussac’s law
• Combined gas law
Ideal gas
• Non-existent, but assumes the following:
• Completely elastic collisions
• Particles occupy no volume
• Large number of particles
• No attractive or repellent forces between particles
• Molecules are in completely random motion
Boyle’s Law
• Constants: amount of gas (n) and temperature (T)
• Boyle's Law in Motion

A diver blows a 0.75 L air bubble 10 m under water. As it rises, the pressure goes from 2.25 atm to 1.03 atm. What is the volume of the bubble at the surface?

• P1V1=P2V2

2.25 atm

0.75 L

= 1.6 L

1.03 atm

Charles’s Law
• Constants: amount of gas (n) and pressure (P)
• Temperature is in Kelvin (K)
• K= C + 273.0
• Charles' Law in Motion

A helium balloon in a closed car occupies a volume or 2.32 L at 40°C.If the temperature rises to 75°C, what is the new volume of the balloon?

• V2=V1T2/T1

348.0 K

2.32 L

= 2.58 L

313.0 K

Gay-Lussac’s Law
• Constants: amount of gas (n) and volume (V)
• T must be in Kelvin
• Gay-Lussac in Motion

The pressure of oxygen gas inside a canister is 5.00 atm at 25°C. the canister is placed in a cold environment where the temperature is -10°C; what is the new pressure in the canister?

• P2=P1T2/T1

263.0 K

5.00 atm

= 4.41 atm

298.0 K

Predict
• The relationship between pressure and amount of gas at a fixed temperature and volume
• Pressure-Moles relationship
• The relationship between volume and the amount of gas at a fixed temperature and amount of gas
• Volume-Moles relationship
Combined Gas Law
• Combination of Boyle’s, Charles’, and Gay-Lussac’s laws

A gas at 110 kPa and 30.0°C fills a flexible container with an initial volume of 2.00L. If the temperature is raised to 80.0°C and the pressure increases to 440 kPa, what is the new volume?

• 0.58 L
Can you…
• State the relationships among pressure, volume, temperature, and the amount of gas
• Apply gas laws to problems involving pressure, volume, temperature, and the amount of gas
• Create graphs of the relationships among pressure, volume, temperature, and the amount of gas
• Solve problems related to fixed amounts of gases

### Ideal Gas Law

13.2

13.2 Main Idea

The ideal gas law relates the number of particles to pressure, temperature, and volume

13.2 Objectives
• Relate the number of particles and volume using Avogadro’s principle
• Relate the amount of gas present to its pressure, temperature, and volume using the ideal gas law
• Compareandcontrast the properties of real gases and ideal gases
• Solve problems using the ideal gas law
Review Vocabulary
• Mole
• Molar mass (M)
New Vocabulary
• STP
• Avogadro’s principle
• Molar volume
• Ideal gas constant (R)
• Ideal gas law
STP
• Standard temperature and pressure
• Standard temperature
• 0.00000°C = 273.15 K
• Standard pressure
• 1 atm = 760 torr = 101.325 kPa
Avogadro’s Principle
• Equal volumes of (ideal) gases, at the same temperature and pressure, contain equal numbers of particles
• 1 mol gas = 22.4 L at STP
How much volume do the following gases fill at STP

1 mol CH4

1 mol CO2

1 mol H2O

1 mol Ne

2 mol He

1 mol O2

Molar Volume
• The main component of natural gas used for home heating and cooking is methane (CH4). Calculate the volume that 2.00 kg of methane will occupy at STP.
• M = m/n
• M = molar mass
• m = mass
• n = number of moles

The main component of natural gas used for home heating and cooking is methane (CH4). Calculate the volume that 2.00 kg of methane will occupy at STP.

• Molar mass (M) = 16.05 g/mol (C + 4H)

The main component of natural gas used for home heating and cooking is methane (CH4). Calculate the volume that 2.00 kg of methane will occupy at STP.

• Molar mass (M) = 16.05 g/mol (C + 4H)
• Number of moles (n) = ??
• M = m/n
• n = m/M

2000 g CH4

1 mol

= 125 mol

16.05 g

The main component of natural gas used for home heating and cooking is methane (CH4). Calculate the volume that 2.00 kg of methane will occupy at STP.

• Molar mass (M) = 16.05 g/mol (C + 4H)
• Number of moles (n) = 125 mol

2000 g CH4

1 mol

= 125 mol

16.05 g

The main component of natural gas used for home heating and cooking is methane (CH4). Calculate the volume that 2.00 kg of methane will occupy at STP.

• Molar mass (M) = 16.05 g/mol (C + 4H)
• Number of moles (n) = 125 mol
• Molar volume = ??

125 mol

22.4 L

= 2800 L

1 mol

Ideal Gas Law
• PV=nRT
• P = pressure (atm)
• V = volume (L)
• n = number of moles of gas (mol)
• R = gas constant (L•atm)/(mol•K)
• T = temperature (K)
Calculate the number of moles of ammonia gas contained in a 3.0 L vessel at 300 K with a pressure of 1.50 atm.
• P = 1.50 atm; V = 3.0 L; n = ?; T = 300 K
• R = 0.0821 (L•atm)/(mol•K)
• N= PV/RT

1.50 atm (mol•K)

3.0 L

= 0.18 mol

0.0821 (L•atm)

300 K

Molar mass and density
• PV=nRT
• n=m/M
• PV=mRT/M
• M=mRT/PV
• D=m/V
• D=MV/RT
Ideal gas and Real gases

Ideal gas

Real gas

Particles occupy volume

KE is lost during collisions

Limited numbers of molecules

Inter-molecular forces exist

• Particles occupy no volume
• All collisions are perfectly elastic
• Infinitely large number of molecules
• No forces between molecules
Can you…
• Relate the number of particles and volume using Avogadro’s principle
• Relate the amount of gas present to its pressure, temperature, and volume using the ideal gas law
• Compareandcontrast the properties of real gases and ideal gases
• Solve problems using the ideal gas law

### Gas Stoichiometry

13.3

Main Idea

When gases react, the coefficients in the balanced chemical equation represent both molar amounts and the relative volumes.

13.3 Objectives
• Determine volume ratios for gaseous reactants and products by using coefficients from chemical equations
• Apply gas laws to calculate amounts of gaseous reactants and products in a chemical reaction
Review Vocabulary
• Stoichiometry
• Coefficient
• Chemical equation
Stoichiometry with Gases
• Only works with gases!
• 2H2 (g) + O2 (g) 2 H2O (g)
• 2 moles of hydrogen + 1 mole of oxygen react to form 2 moles of water
• 2 liters of hydrogen + 1 liter of oxygen react to form 2 liters of water

What volume of oxygen gas is needed for the complete combustion of 4.00 L of propane gas assuming that pressure and temperature are constant?

• C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g)

4.00 L C3H8

5 L O2

= 20.0 L O2

1 L C3H8

Can you…
• Determine volume ratios for gaseous reactants and products by using coefficients from chemical equations
• Apply gas laws to calculate amounts of gaseous reactants and products in a chemical reaction
Can you…
• Predict the behavior of gases using the kinetic-molecular theory
• Explain how mass affects the rates of diffusion and effusion
• Calculate the partial pressure of a gas
• Measure gas pressure
• State the relationships among pressure, volume, temperature, and the amount of gas
• Apply gas laws to problems involving pressure, volume, temperature, and the amount of gas
• Create graphs of the relationships among pressure, volume, temperature, and the amount of gas
• Solve problems related to fixed amounts of gases
• Relate the number of particles and volume using Avogadro’s principle
• Relate the amount of gas present to its pressure, temperature, and volume using the ideal gas law
• Compareandcontrast the properties of real gases and ideal gases
• Solve problems using the ideal gas law
• Determine volume ratios for gaseous reactants and products by using coefficients from chemical equations
• Apply gas laws to calculate amounts of gaseous reactants and products in a chemical reaction