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## Gases

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Presentation Transcript

manometers

pressure

Kinetic theory of gases

Units of pressure

Behavior of gases

Partial pressure

of a gas

Pressure vs.

volume

Pressure vs.

temperature

Temperature vs.

volume

Diffusion/effusion

Combined gas law

Ideal gas law

Properties of Gases

- Very low density
- Low freezing points
- Low boiling points
- Can diffuse (rapidly and spontaneously spread out and mix)
- Flow
- Expand to fill container
- Compressible

Kinetic Molecular Theory of Gases

- Particles move non-stop, in straight lines.
- Particles have negligible volume (treat as points)
- Particles have no attractions to each other (no repulsions, either).
- Collisions between particles are “elastic” (no gain or loss of energy)
- Particles exert pressure on the container by colliding with the container walls.

Kinetic Energy

- Energy due to motion
- KE = ½ mv2

Temperature

- Temperature is a measure of average kinetic energy.
- Temperature measures how quickly the particles are moving. (Heat IS NOT the same as temperature!)
- If temperature increases, kinetic energy increases.
- Which has greater kinetic energy: a 25 g sample of water at 25oC or a 25 g sample of water at -15oC?

Why use the Kelvin scale?

- In the Kelvin scale, there is an absolute correlation between temperature and kinetic energy.
- As temperature in Kelvin increases, kinetic energy increases.
- Absolute zero: All molecular motion ceases. There is no kinetic energy.
- 0 K

Kelvin-Celsius Conversions

- K = oC + 273.15
- oC = K – 273.15

Kelvin-Celsius conversions

- The temperature of liquid nitrogen is -196oC. What is this temperature in Kelvin?
- Convert 872 Kelvin to Celsius temperature.

Pressure

- Pressure = force/area
- Atmospheric pressure
- Because air molecules collide with objects
- More collisions greater pressure

Pressure Units

- Atmosphere
- Pounds per square inch (psi)
- mm Hg
- Torr
- Pascal (Pa) or kilopascal (kPa)

1 atm = 14.7 psi = 760 mm Hg = 760 torr = 101.3 kPa

Barometer

- Torricelli-1643
- Air molecules collide with liquid mercury in open dish
- This holds the column up!
- Column height is an indirect measure of atmospheric pressure

Manometer

- Two types: open and closed
- Use to measure the pressure exerted by a confined gas

Chapter 15 Wrapup (Honors)

- At the same temperature, smaller molecules (i.e., molecules with lower gfm) have faster average velocity.
- Energy flows from warmer objects to cooler objects.
- Plasma
- High energy state consisting of cations and electrons
- Found in sun, fluorescent lights

Boyle’s Law

- Pressure-volume relationships
- For a sample of a gas at constant temperature, pressure and volume are inversely related.
- Equation form:

P1V1 = P2V2

Charles’ Law

- Volume-temperature relationships
- For a sample of a gas at constant pressure, volume and temperature are directly related.
- Equation form:

Guy-Lussac’s Law

- Pressure temperature relationships
- For a sample of a confined gas at constant volume, temperature and pressure are directly related.

Combined Gas Law

- Sometimes, all three variables change simultaneously
- This single equation takes care of the other three gas laws!

Dalton’s Law of Partial Pressures

- For a mixture of (nonreacting) gases, the total pressure exerted by the mixture is equal to the sum of the pressures exerted by the individual gases.

Collecting a sample of gas “over water”

- Gas samples are sometimes collected by bubbling the gas through water

If a question asks about something relating to a “dry gas”, Dalton’s Law must be used to correct for the vapor pressure of water!

Table: Vapor Pressure of Water

Ideal Gas Law

- The number of moles of gas affects pressure and volume, also!
- n, number of moles
- n V
- n P
- P 1/V
- P T
- V T

Where R is the universal gas constant

R = 0.0821 L●atm/mol●K

Ideal vs. Real Gases

- Ideal gas: completely obeys all statements of kinetic molecular theory
- Real gas: when one or more statements of KMT don’t apply
- Real molecules do have volume, and there are attractions between molecules

When to expect ideal behavior?

- Gases are most likely to exhibit ideal behavior at…
- High temperatures
- Low pressures
- Gases are most likely to exhibit real (i.e., non-ideal) behavior at…
- Low temperatures
- High pressures

Diffusion and Effusion

- Diffusion
- The gradual mixing of 2 gases due to random spontaneous motion
- Effusion
- When molecules of a confined gas escape through a tiny opening in a container

Graham’s Law

- Thomas Graham (1805-1869)
- Do all gases diffuse at the same rate?
- Graham’s law discusses this quantitatively.
- Technically, this law only applies to gases effusing into a vacuum or into each other.

Graham’s Law

- Conceptual:
- At the same temperature, molecules with a smaller gfm travel at a faster speed than molecules with a larger gfm.
- As gfm , v
- Consider H2 vs. Cl2

Which would diffuse at the greater velocity?

Graham’s Law

- The relative rates of diffusion of two gases vary inversely with the square roots of the gram formula masses.
- Mathematically:

Graham’s Law Problem

- A helium atom travels an average 1000. m/s at 250oC. How fast would an atom of radon travel at the same temperature?
- Solution:
- Let rate1 = x rate2 = 1000. m/s
- Gfm1 = radon 222 g/mol
- Gfm2 = helium = 4.00 g/mol

Solution (cont.)

- Rearrange:
- Substitute and evaluate:

Applications of Graham’s Law

- Separation of uranium isotopes
- 235U
- Simple, inexpensive technique
- Used in Iraq in early 1990’s as part of nuclear weapons development program
- Identifying unknowns
- Use relative rates to find gfm

Problem 2

- An unknown gas effuses through an opening at a rate 3.16 times slower than that of helium gas. What is the gfm of this unknown gas?

Solution, cont.

- Substitute and evaluate:

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