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### Gases

### The Gas Laws

### Ideal Gas Law

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.

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.

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

What is the ratio of the rate of diffusion for ammonia and hydrogen chloride?

Calculate the ratio of effusion rates for nitrogen gas and neon

- 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

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

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

- 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

- 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

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

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