Weather and Gas Laws Notes

WEATHER AND GAS LAWS

WEATHER AND THE GAS LAWS

• Physically Changing Matter
• Pressing Matter
• Concentrating Matter

PHYSICALLY CHANGING MATTER

• 9.1 Weather Science
• 9.2 Measuring Liquids
• 9.3 Density of Liquids and Solids
• 9.4 Thermometer
• 9.5 Kelvin Scale
• 9.6 Charle’s Law
• 9.7 Density, Temperature and Fronts

9.1 WEATHER SCIENCE

• Weather is:
  • The interaction of the Earth, water, and Sun.
  • The movement of matter around the planet.
  • Short term and limited in area.
• Climate:
  • Weather over a longer time and larger area.

What causes the weather?

• Weather is caused by the heating of the Earth by the Sun.

What do you need to know to determine/measure the "weather"?

• Atmosphere: All the gasses that surround us.
• Which gasses are in the atmosphere?
• How does the Jet Stream Work?
• Air Pressure
• Temperature highs in degrees Fahrenheit
• Air pressure highs and lows
• Precipitation: rain and snow
• Cloud cover
• Fronts
• Jet stream

9.2 MEASURING LIQUIDS

• How is rainfall usually measured? Describe the type of instrument you think is usually used.
• Which of these containers would make the best rain gauge? Explain your reasoning.
• How do meteorologists keep track of the amount of rainfall?
• Does the same amount of rain fall on each area? How could you measure the amount of rain that falls on the objects?

Proportional Relationships

• Proportionality constant
  • volume and height are related by a single number
    $volume = k \times height$

9.3 DENSITY OF LIQUIDS AND SOLIDS

Density of Water

Mass Versus Volume of Water

• Rain
• Ice
• Snow

Density of Ice

• Ice
  • Hydroper bond
• Liquid water
  • Hydrogen bond

Key points about density

• How much water is present in equal volumes of snow and rain?
• In density calculations, mass and volume are proportional to each other.
• The formula $D = \frac{m}{V}$ can also be written $m = DV$.
• When a substance changes phase (from solid to liquid to gas), its density changes. The mass stays the same, and the volume changes.
• Water is denser than snow. Ice is less dense than water.

9.4 THERMOMETER

• Gasses expand and contract
  • In hot water
  • In room-temperature water
  • In ice water

9.5 KELVIN SCALE

Kelvin Scale

• $273 K = 0 °C$
• Absolute Zero
  • Lowest possible temperature.
  • All motion stops.

9.6 CHARLE'S LAW

How can you predict the volume of a gas sample?

• $V₁ = 600 mL$; $T₁ = 300 K$; $V₂ = 400 mL$; $T₂ = 200 K$
• $V₁ = 800 mL$; $T₁ = 400 K$; $V₂ = 300 mL$; $T₂ = 200 K$
• $V₁ = 450 mL$; $T₁ = 300 K$; $V₂ = 600 mL$; $T₂ = 400 K$

Charles's Law Formula

• If pressure and the number of particles of a gas stay the same, then volume is proportional to the Kelvin temperature.
  $V = kT$ or $k = \frac{V}{T}$

9.7 DENSITY, TEMPERATURE AND FRONTS

• How does density affect weather fronts?
• What is happening to the density of the gas?
  • 200 K
  • 300 K
  • 400 K

Fronts

• Cold Front
  • Cold air
  • Warm
  • Fair
• Warm Front
  • Warm air
  • Cold
• Warm front
• Cold air mass
• Warm air mass
• Cold front

PRESSING MATTER

• 9.8 GAS DENSITY

What is Pressure?

• Pressure - Force of gas particles running into a surface
• As number of molecules increases, there are more molecules to collide with the wall
• Collisions between molecules and the wall increase Pressure increases
• If pressure is molecular collisions with the container…
• As # of molecules increases, pressure increases
• Pressure and Number of Molecules

Pressure and Volume

• As volume increases, molecules can travel farther before hitting the wall
• Collisions between molecules and the wall decrease Pressure decreases
• If pressure is molecular collisions with the container…
• As volume increases, pressure decreases

What is “Temperature”?

• Temperature – proportional to the average kinetic energy of the molecules
• Energy due to motion (Related to how fast the molecules are moving)
• As temperature increases
• Molecular motion increases
• Pressure increases

Pressure and Temperature

• As temperature increases, molecular motion increases
• Collisions between molecules and the wall increase
• If temperature is related to molecular motion…
• and pressure is molecular collisions with the container…
• As temperature increases, pressure increases

What is Atmospheric Pressure?

• Atmospheric Pressure – Pressure due to the layers of air in the atmosphere.
• Less layers of air Lower atmospheric pressure Climb in altitude
• As altitude increases, atmospheric pressure decreases.

Pressure In Versus Out

• Example: A bag of chips is bagged at sea level. What happens if the bag is then brought up to the top of a mountain.
• A flexible container will expand or contract until the pressure inside = atmospheric pressure outside
• The internal pressure is higher than the external pressure.
• The bag will expand in order to reduce the internal pressure.
• The internal pressure is from low altitude (high pressure)
• The external pressure is high altitude (low pressure).
• Higher pressure
• Lower pressure

Can Explodes! When Expansion Isn’t Possible

• Example: An aerosol can is left in a car trunk in the summer. What happens?
• Rigid containers cannot expand
• The internal pressure is higher than the external pressure.
• The can is rigid—it cannot expand, it explodes!
• Soft containers or “movable pistons” can expand and contract.
• Rigid containers cannot.
• The temperature inside the can begins to rise.
• As temperature increases, pressure increases.
• Higher pressure
• Lower pressure

KINETIC MOLECULAR THEORY

Definition

• Kinetic Molecular Theory (KMT) – An attempt to explain gas behavior based upon the motion of molecules

Assumptions of the KMT

1. All gases are made of atoms or molecules
2. Gas particles are in constant, rapid, random motion
3. The temperature of a gas is proportional to the average kinetic energy of the particles
4. Gas particles are not attracted nor repelled from one another
5. All gas particle collisions are perfectly elastic (no kinetic energy is lost to other forms)
6. The volume of gas particles is so small compared to the space between the particles, that the volume of the particle itself is insignificant

REAL GASES

• Real Gas – Last 3 of the assumptions of the Kinetic Molecular Theory are not valid
• Ideal Gas – All of the assumptions of the Kinetic Molecular Theory are valid

EFFUSION & DIFFUSION

Effusion

• Effusion -gas escapes from a tiny hole in the container
• Effusion is why balloons deflate over time!

Diffusion

• Diffusion - gas moves across a space
• Diffusion is the reason we can smell perfume across the room

Effusion, Diffusion & Particle Mass

• As particle size (mass) increases, the particles move slower it takes them more time to find the hole or to go across the room
• Rate of effusion and diffusion is lower
• How are particle size (mass) and these concepts related?
• As mass of the particles increases, rate of effusion and diffusion is lowered.
• Temperature = kinetic energy
  $KE = \frac{1}{2} m v^2$

Graham’s Law of Effusion

• A gas will effuse at a rate that is inversely proportional to the square root of its molar mass.

Comparing the rates of Effusion

• If the ratio is > 1 the molecule on top is moving faster than the bottom.
• If the ratio is < 1 the molecule on top is moving slower than the bottom.
• What if it = 1?

SECTION 3.7-GAS LAWS

Pressure Units

• Several units are used when describing pressure
  • Unit Symbol
    • atmospheres atm
    • Pascals, kiloPascals Pa, kPa
    • millimeters of mercury mm Hg
    • pounds per square inch psi
• $1 atm = 101300 Pa = 101.3 kPa = 760 mm Hg = 14.7 psi = 29.92 in Hg = 760 torr$

Definition

• Kelvin (K)– temperature scale with an absolute zero
• Temperatures cannot fall below an absolute zero
• A temperature scale with absolute zero is needed in Gas Law calculations because you can’t have negative pressures or volumes

Definition

• Standard Temperature and Pressure (STP) – 1 atm (or the equivalent in another unit – 760 mm of Hg 101.3 KPa) and 0°C (273 K)
• Problems often use “STP” to indicate quantities…don’t forget this “hidden” information when making your list!

GAS LAWS

• The Gas Laws are the experimental observations of the gas behavior that the Kinetic Molecular Theory explains.

WHAT IS A MOLE?

Definition

• Mole - SI unit for counting
• The only acceptable abbreviation for "mole", is "mol"…not "m"!!

What is a counting unit?

• You’re already familiar with one counting unit…a “dozen”
  • “Dozen” 12
    • A dozen doughnuts 12 doughnuts
    • A dozen books 12 books
    • A dozen cars 12 cars
    • A dozen people 12 people
• A dozen = 12

Why can’t we count atoms in “dozens”?

• Atoms and molecules are extremely small
• There are $6.02 \times 10^{23}$ water molecules in 18mL of water, how many molecules are there in 355ml?
• This means a 12 ounce bottle of water (355 mL) would have $1.2 \times 10^{25}$ molecules of water.
• That would be $1.0 \times 10^{23}$ “dozen” water molecules.
• These huge numbers are impractical!
• $355 mL \times \frac{6.02 \times 10^{23} molecules H2O}{18 mL} = 1.2 \times 10^{25} molecules H2O$
• $\frac{1.2 \times 10^{25} molecules}{\frac{1 dozen}{12}} = 1.0 \times 10^{23} dozen$

What does a “mole” count in?

• A mole = $6.02 \times 10^{23}$ (called Avogadro’s number)
  • “mole” $6.02 \times 10^{23}$
    • 1 mole of doughnuts $6.02 \times 10^{23}$ doughnuts
    • 1 mole of atoms $6.02 \times 10^{23}$ atoms
    • 1 mole of molecules $6.02 \times 10^{23}$ molecules
• $6.02 \times 10^{23} = 602,000,000,000,000,000,000,000$
• This means a 12 ounce bottle of water would have 19.7 “moles” of water…a much easier-to-work-with number!

Avogadro’s Law

• Avogadro’s Law relates # of particles (moles) and volume.
  • Where Temperature and Pressure are held constant
    • V = Volume
    • n = # of moles of gas
• Example: A sample with 0.15 moles of gas has a volume of 2.5 L. What is the volume if the sample is increased to 0.55 moles?
• The two volume units must match!
• $V2 = 9.2 L$

Boyles’ Law

• Boyles’ Law relates pressure and volume
  • Where temperature and # of molecules are held constant
    • P = pressure
    • V = volume
• The two pressure units must match and the two volume units must match!
• Example: A gas sample is 1.05 atm when 2.5 L. What volume is it if the pressure is changed to 0.980 atm?
• $P1 = 1.05 atm$; $V1 = 2.5 L$; $P2 = 0.980 atm$; $V2 = ? L$; $V2 = 2.7 L$

Mariotte’s Law or Boyle’s Law

• Discovered by Robert Boyle in 1662.
• On the continent of Europe, this law is attributed to Edme Mariotte, therefore those counties tend to call this law by his name.
• Mariotte, however, he did not publish his work until 1676.

Charles’ Law

• Charles’ Law relates temperature and volume
  • Where pressure and # of moles are held constant
    • V = Volume
    • T = Temperature
• The two volume units must match and temperature must be in Kelvin!
• Example: What is the final volume if a 10.5 L sample of gas is changed from 25°C to 50°C?
• $V1 = 10.5 L$; $T1 = 25°C$; $V2 = ? L$; $T2 = 50°C$
• Temperature needs to be in Kelvin!
• 25°C + 273 = 298 K
• 50°C + 273 = 323 K
• $V2 = 11.4 L$

Gay-Lussac’s Law

• Gay-Lussac’s Law relates temperature and pressure
  • Where volume and # of moles are held constant
    • P = Pressure
    • T = Temperature
• The two pressure units must match and temperature must be in Kelvin!
• Example: What is the final pressure if a sample of gas at 2 atm is changed from 25°C to 50°C?
• $P1 = 2 atm$; $T1 = 25°C$; $P2 = ? atm$; $T2 = 50°C$
• Temperature needs to be in Kelvin!
• 25°C + 273 = 298 K
• 50°C + 273 = 323 K

Combined Gas Law

• P = Pressure
• V = Volume
• n = # of moles
• T = Temperature
• Each “pair” of units must match and temperature must be in Kelvin!
• Example: What is the final volume if a 0.125 mole sample of gas at 1.7 atm, 1.5 L and 298 K is changed to STP and particles are added to 0.225 mole?
• $P1 = 1.7 atm$; $V1 = 1.5 L$; $n1 = 0.125 mole$; $T1 = 298 K$
• $P2 = 1.0 atm$; $V2 = ? L$; $n2 = 0.225 mole$; $T2 = 273 K$
• $V2 = 4.2 L$
• STP is standard temperature (273 K) and pressure (1 atm)

Why you really only need 1 of these

• The combined gas law can be used for all “before” and “after” gas law problems!
• For example, if volume is held constant, then and the combined gas law becomes:
• When two variables on opposites sides are the same, they cancel out and the rest of the equation can be used.

The Ideal Gas Law

• An ideal gas is one that follows all the gas laws under all conditions.
• The particles have no volume
• There is no attraction between particles (can’t be condensed or compressed)
• Real gases differ most at low temperature and high pressure

The Ideal Gas Law

• The Ideal Gas Law does not compare situations—it describes a gas in one situation.
  • P = Pressure
  • V = Volume
  • n = moles
  • R = Gas Law Constant
  • T = Temperature
• There are two possibilities for “R”:
  • Choose the one with units that match your pressure units!
  • Volume must be in Liters when using “R” to allow the unit to cancel!

Example

• The Ideal Gas Law does not compare situations—it describes a gas in one situation.
  • P = Pressure
  • V = Volume (in L)
  • n = moles
  • R = Gas Law Constant
  • T = Temperature
• Example: A sample with 0.55 moles of gas is at 105.7 kPa and 27°C. What volume does it occupy?

Example Solution

• $n = 0.55 moles$; $P = 105.7 kPa$; $T = 27°C + 273 = 300 K$; $V = ?$;$<br /> R = 8.31 \frac{L kPa}{mole K}$
• $V = 13 L$

Dalton’s Law of partial pressure

• Dalton’s law relates the total pressure of a mixture of gases to the partial pressure of the components making up the mixture.

Dalton’s Law of partial pressure

• Air contains oxygen, nitrogen, carbon dioxide and trace amounts of other gases.
• What is the partial pressure of oxygen at 101.3 kPa of total pressure if the partial pressure of nitrogen, carbon dioxide and the other gases are 79.0 kPa, 0.040 kPa and 0.94 kPa respectively?

Diffusion and Effusion

• Diffusion – tendency for molecules to move from an area of high concentration to an area of low concentration
• Effusion – gas escaping through a small hole

Graham’s Law of effusion

• Graham’s law states the rate of effusion is inversely proportional to the square root of the molar mass. (lower molar mass gases will diffuse and effuse faster)

Airbags

• States of Matter
• Use different Properties
• Changes
• Density
• Gas Laws
• Kinetic Molecular Theory
• With different Work because of changes
• One of which is Gas Properties explained by
• To produce Explanation for
• Which is a