Week 2

Ideal GasesLiceo Alfano

Reminder

Last week: Heat propagation

•Conduction

•Convection

•Radiation

This week: Ideal gases

Concept Question

The molecules in a gas are

1)Close together

2)Far apart

Concept Question

The molecules in a gas are

1)Close together

2)Far apart

Concept Question

As you add heat to a gas, the molecules move

1)Faster

2)Slower

Concept Question

As you add heat to a gas, the molecules move

1)Faster

2)Slower

What is an Ideal Gas?

• The movements of each molecule in a gas are so random that it’s impossible to model them exactly

• An ideal gas is a “perfect gas”– a gas where we simplify the movements so we can make calculations

• In an ideal gas, we pretend the molecules are very small and that they don’t interact with each other

• This is true of most situations, so it is a valid assumption

What is Pressure?

• Pressure is a measure of how much individual atoms are “pushing” on the sides of a container in a gas

• More collisions = higher pressure

• If you pump air into a container that can’t get any bigger, would the pressure increase or decrease?

What is Pressure?

• Pressure = Force/Area

• We control the pressure of a gas with a piston

• Measured in atmospheres (atm) or Pascales (Pa)

Concept Question

If I decrease the volume of an ideal gas container (at constant temperature), the pressure will

1)Increase

2)Decrease

Concept Question

If I decrease the volume of an ideal gas container (at constant temperature), the pressure will

1)Increase

2)Decrease

Video

As pressure decreases, volume does what?

Scuba Diving• Think of a scuba diver

coming up from the bottom of the ocean

• As he gets closer to the surface, what happens to the pressure?

• As the pressure decreases, what happens to the volume of the air in his lungs?

• If he comes up too quickly, his lungs might explode!

Concept Question

Now let’s look at pressure and temperature. If I increase the temperature of an ideal gas (at constant volume), the pressure will

1.Increase

2.Decrease

Concept Question

Now let’s look at pressure and temperature. If I increase the temperature of an ideal gas (at constant volume), the pressure will

1.Increase

2.Decrease

Video

When the temperature goes down after the fire stops, what happens to the pressure in the bottle?

Car Tires

• Think about the tires on a car

• If they get very hot, what will happen to the pressure of the air inside?

• The tires can’t get too hot, or they’ll explode!

Concept Question

Now let’s look at volume and temperature. If I increase the temperature of an ideal gas (at constant pressure), the volume will

1.Increase

2.Decrease

Concept Question

Now let’s look at volume and temperature. If I increase the temperature of an ideal gas (at constant pressure), the volume will

1.Increase

2.Decrease

Video

As the temperature drops, what happens to the volume of the air in the balloons?

Hot Air Balloon

• Think about when they are inflating a hot air balloon. What are they doing?

• They make the air inside the balloon hot, making it get bigger!

Football

• If you inflate a football inside then go play outside on a cold day, what happens to the volume of the football?

• The football actually gets a bit smaller!

Combined Gas Law

THE EQUATION: P1V1/T1 = P2V2/T2

•This is for ONE GAS in TWO STATES

•Does this agree with the conditions we just established?

•Let’s keep temperature constant

•Now let’s keep volume constant

•Now let’s keep pressure constant

Ideal Gas Law

Taking the combined gas law and plugging in STP (standard temperature and pressure) conditions, we get a new equation

THE EQUATION: PV = nRT

•P = pressure (atm)

•V = volume (L)

•n = number of moles of the gas

•R = ideal gas constant (0.0821 L*atm/mol*K or 8.31m3*Pa/K*mol)

•T = temperature (K)

Experiments

• Collapsing can (collasso della lattina)

• Dancing cap (Il tappo ballerino)

• Boiling syringe (La siringa ad ebollizione)

• “Pee-pee” boy

Practice Problems

Remember, PV = nRT (R=0.0821 L*atm/mol*K) and P1V1/T1 = P2V2/T2

If I have 21 mol of nitrogen gas at a pressure of 78 atm and a temperature of 900K, what is the volume of the gas?

A container filled with 0.25 mol of oxygen gas has a volume of 2.35L at a temperature of 45C. What is the pressure of the gas?

Practice Problems

Remember, PV = nRT (R=0.0821 L*atm/mol*K) and P1V1/T1 = P2V2/T2

An air bubble at the bottom of a lake, at a pressure of 120kPa, has a volume of 1cm3. If the temperature at the bottom of the lake is 5.5C and the temperature at the top is 21C, what is the volume of the bubble just before it reaches the surface?

•1 atm = 101kPa

•1L = 1000cm3

Practice Problems

Remember, PV = nRT (R=0.0821 L*atm/mol*K) and P1V1/T1 = P2V2/T2

I have 21.6kg of neon at a pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by 21.6kg of carbon gas? (volume and temperature don’t change)

•Molecular mass of neon= 0.020 kg/mole

•Molecular mass of carbon= 0.012 kg/mole