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### Chapter 11

Gases

10. 1 Kinetic Molecular Theory

State the kinetic-molecular theory of matter, and describe how it explains certain properties of matter.

List the five assumptions of the kinetic-molecular theory of gases.

Define the terms ideal gas and real gas.

Describe each of the following characteristic properties of gases: expansion, density, fluidity, compressibility, diffusion, and effusion.

Describe the conditions under which a real gas deviates from “ideal” behavior.

What is the Kinetic Molecular Theory?

- Break it down:
- Kinetic: movement
- Molecular: particles
- Theory: tested ideas

Tested ideas about the

movement of particles!

This theory is used to explain the energy and forces that cause the properties of solids, liquids, and gases.

KMT of Gases

- Ideal gas: hypothetical gas that satisfies all 5 ideas of KMT
- pressure is not too high
- temperature is not too low
- Gases consist of large numbers of tiny particles that are far apart relative to their size.
- Most of the volume is empty space
- Collisions between gas particles and between particles and container walls are elastic collisions.
- elastic collisionwhen there is no net loss of total kinetic energy

KMT cont.

- Gas particles are in continuous, rapid, random motion.
- There are no forces of attraction between gas particles.
- The temperature of a gas depends on the average kinetic energy of the particles of the gas.
- The kinetic energy of any moving object is given by the following equation:

Effusion

- Because gases have motion, they can travel.
- Effusion: process by which gas particles pass through a tiny opening

What determines have fast a gas effuses? Mass

- Gases at the same temperature have the same KE so…
- Heavier gases travel slower
- Lighter gases travel faster

11.1 Gases and Pressures

- Definepressure, give units of pressure, and describe how pressure is measured.
- State the standard conditions of temperature and pressure and convert units of pressure.
- Use Dalton’s law of partial pressures to calculate partial pressures and total pressures.

4 Variables of Gases

- Pressure (P) Volume (V)
- Temperature (T) Mols (n)
- What causes pressure?
- collisions of the gas molecules with each other and with surfaces with which they come into contact.
- depends on volume (mL or L), temperature (oF, oC, K), and the number of molecules present (mol, mmol).

Equation for Pressure

Pressure (P): the force per unit area on a surface.

Pressure = Force

Area

More force on a given area, the greater the pressure.

smaller the area is on which a given force acts, the greater the pressure.

- barometer: device used to measure atmospheric pressure

- Pressure of atmosphere supports a column of Hg about 760 mm above surface of mercury in dish
- Can change depending on weather & elevation

Units for Measuring Pressure

- mm Hg : millimeters of mercury
- A pressure of 1 mm Hg is also called 1 torr in honor of Torricelli for his invention of the barometer.
- atm : atmosphere of pressure
- kPa : kiloPascal
- Others…
- psi : pounds per square inch
- Bar
- torr

1 atm = 101.3 kPa = 760 mmHg = 760 torr

Pressure Conversions

The average atmospheric pressure in Denver, Colorado is 0.830 atm. Express this pressure in:

a. millimeters of mercury (mm Hg) and

b. kilopascals (kPa)

Given:atmospheric pressure = 0.830 atm

Unknown: a. pressure in mm Hg

b. pressure in kPa

STP

- STP : Standard Temperature & Pressure
- 1.0 atm (or any of units of equal value)
- 0 oC
- Used by scientists to compare volumes of gases

Dalton’s Law of Partial Pressures

- The pressure of each gas in a mixture is called the partial pressure.
- John Dalton discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present.
- Dalton’s law of partial pressures: the total pressure of a gas mixture is the sum of the partial pressures of each gas.

Dalton’s Law of Partial Pressures

- Dalton derived the following equation:

PT = P1 + P2 + P3 + …

Total Pressure = sum of pressures of each individual gas

Gases Collected by Water Displacement

- Water molecules at the liquid surface evaporate and mix with the gas molecules. Water vapor, like other gases, exerts a pressure known as vapor pressure.
- Gases produced in the laboratory are often collected over water. The gas produced by the reaction displaces the water in the reaction bottle.

Gases Collected by Water Displacement (ctd)

- Step 1: Raise bottle until water level inside matches the water level outside. (Ptot = Patm)
- Step 2: Dalton’s Law of Partial Pressures states:

Patm = Pgas + PH2O

To get Patm, record atmospheric pressure.

- Step 3: look up the value of PH2Oat the temperature of the experiment in a table, you can then calculate Pgas.

Dalton’s Law of Partial Pressures Sample Problem

KClO3decomposes and the oxygen gas was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0°C. respectively. What was the partial pressure of the oxygen collected?

Given:

PT = Patm= 731.0 torr

PH2O = 17.5 torr(vapor pressure of water at 20.0°C, from table A-8 in your book)

Patm = PO2+ PH2O

Unknown:PO2in torr

Dalton’s Law Sample Problem Solution

- Solution:

Patm = PO2+ PH2O

PO2 = Patm- PH2O

- substitute the given values of Patm and into the equation: PO2 =731.0 torr – 17.5 torr = 713.5 torr

Mole Fractions (X)

Mole fraction of a gas(XA) =

mole fraction: ratio of the number of moles of one component of a mixture to the total number of moles

Moles of gas A (nA)

Total number of moles of a gas

(ntot)

Calculating Partial Pressure

Partial pressures can be determined from mole fractions using the following equation:

PA= XAPT

11.2 The Gas Laws

- Use the kinetic-molecular theory to explain the relationships between gas volume, temperature and pressure.
- Use Boyle’s law to calculate volume-pressure changes at constant temperature.
- Use Charles’s law to calculate volume-temperature changes at constant pressure.
- Use Gay-Lussac’s law to calculate pressure-temperature changes at constant volume.
- Use the combined gas law to calculate volume-temperature-pressure changes.

Boyle’s Law

- If you increase the pressure on a gas in a flexible container, what happens to the volume?
- If you decrease the pressure, what happens the volume?
- Pressure and volume are ________ related.

P1V1 = P2V2

Variables: pressure & volume

Constant: temperature, amount of gas

Boyle’s Law Problem

A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant?

P1 = 0.947 atm P2 = 0.987 atm

V1 = 150.0 mL V2 = ?

Charles’ Law

- If you increase the temperature of gas, what will happen to the volume?
- If you decrease the temperature of a gas, what will happen to the volume?
- Volume and temperature are ______ related.
- Variables: volume & temperature
- Constant: pressure & amount of gas

Temperature in Charles Law

- To Convert to Kelvin

K = 273 + °C.

- absolute zero: when all motion stops

O K = -273 oC

Charles’ Law Problem

A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant?

Temperature must be in KELVIN!!!

V1 = 752 mL V2 = ?

T1 = 25°C T2 = 50°C

Gay-Lussac’s Law

- If you increase the temperature of a gas what will happen to the pressure?
- If you decrease the temperature of gas what will happen to the pressure?
- Pressure and temperature are _____ related.
- Variables: pressure & temperature
- Constant: volume & amount of gas

Gay-Lussac’s Law Problem

The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C?

Temperature must also be in KELVIN!!!

P1 = 3.00 atm P2 = ?

T1 = 25°C T2 = 52°C

The Combined Gas Law

Constant: amount of gas

- combined gas law: used when pressure, temperature, and volume change within a system

NOTE: P & V are directly related to T, while P is inversely related to V

Combined Gas Law Problem

A helium-filled balloon has a volume of 50.0 L at 25.0°C and 1.08 atm. What volume will it have at 0.855 atm and 10.0°C?

Temperature must be in KELVIN!!

P1 = 1.08 atm P2 = 0.855 atm

V1 = 50.0 L V2 = ?

T1 = 25.0°C T2 = 10.0°C

11.3 Gas Volumes and the Ideal Gas Law

- State Avogadro’s law and explain its significance.
- Definestandard molar volume of a gas and use it to calculate gas masses and volumes.
- State the ideal gas law.
- Using the ideal gas law, calculate pressure, volume, temperature, or amount of gas when the other three quantities are known.

Avogadro’s Law

- If you increase the amount of moles, what happens to the volume?
- If you decrease the amount of moles what happens to the volume?
- Amount of moles & volume are ____ related.
- Variables: volume , moles
- Constants: pressure, temperature

V1= V2

n1 n2

Because of Avogadro’s law equal volumes of gases at constant temperature and pressure contain equal numbers of molecules.

- Avogadro determined one mole of any gas (regardless of mass differences) will expand to the same volume every time
- standard molar volume of a gas:

22.41410 L (rounded to 22.4 L)

Deriving the Ideal Gas Law

Review: Write down the combined gas law; where do you think “n” fits in?

If both sides must equal each other, we can set one side equal to a constant. We’ll call this constant “R.”

The Ideal Gas Law Equation

PV =nRT

- ideal gas law: relates all variables – pressure, volume, moles, temperature

Deriving the Ideal Gas Law Constant

- R: ideal gas constant
- Its value depends on the units chosen for pressure, volume, and temperature in the rest of the equation.

What are the standard conditions for an ideal gas?

P = n =

V = T =

Plug in values into the equation and calculate. What is the constant that you get?

Usually rounded to 0.0821 (Latm/molK)

Numerical Values of The Gas Constant “R”

ALWAYS MATCH UP YOUR UNITS!!!!

Gas Stoichiometry

- Avogadro’s law can be applied in calculating the stoichiometry of reactions involving gases.
- The coefficients in chemical equations of gas reactions reflect not only mole ratios, but also volume ratios (assuming conditions remain the same).
- Discovered by Dalton, while exploring why water was a ratio of 2H to 1O
- example

2H2(g) + O2(g) → 2H2O(g)

2 molecules 1 molecule 2 molecules

2 mole 1 mole 2 mol

2 volumes 1 volume 2 volumes

Gas Stoichiometry Problem

Number 1 on Practice Sheet

- What volume of nitrogen at STP would be required to react with 0.100 mol of hydrogen to produce ammonia?

N2 + 3 H2 2 NH3

Gas Stoichiometry Problem Solution

0.100 mol H2 x 1 mol N2 x 22.4 L N2

3 mol H2 1 mol N2

= 0.747 L N2

Ideal Gas Law Sample Problem

- A sample of carbon dioxide with a mass of 0.250 g was placed in a 350. mL container at 400 K. What is the pressure exerted by the gas?

P= ?

V = 350. mL = 0.350 L

n = 0.250 g = ? mol

T = 400 K

Gas Stoich and Ideal Gas Law

Number 2 on Practice Sheet

- What volume of nitrogen at 215OC and 715 mmHg would be required to react with 0.100 mol of hydrogen to produce ammonia?

N2 + 3 H2 2 NH3

Note: This system is NOT at STP!!

Gas Stoichiometry Problem Solution

0.100 mol H2 x 1 mol N2= 0.0333 mol N2

3 mol H2

P = 715 mmHg

V = ?

n = 0.0333 mol N2

R = 62.4 LmmHg/molK

T = 25OC + 273 = 488 K

11.4 Diffusion and Effusion

- Describe the process of diffusion.
- State Graham’s law of effusion.
- State the relationship between the average molecular velocities of two gases and their molar masses.

Diffusion and Effusion

REMEMBER:

- EFFUSION:process when the molecules of a gas confined in a container randomly pass through a tiny opening in the container
- DIFFUSION: the gradual mixing of two or more gases due to their spontaneous, random motion

Graham’s Law Of Effusion

Graham’s law of effusion:

the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.

Sample Problem

- What is the rate of effusion of hydrogen if oxygen has a velocity of 175 m/s at the same temperature and pressure.

Graham’s Law of Effusion, continued

- Substitute the given values into the equation:
- Hydrogen rate of effusion is …

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