Chapter 12Gas Laws

and Behavior of

Gases

CA Standards

4c. Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.3’ video overview of three of the gas laws from Ted Ed (optional):http://ed.ted.com/lessons/1207-1-a-bennet-brianh264

Ideal GasesIdeal gases are imaginary gases that perfectly

fit all of the assumptions of the kinetic molecular theory.1. Gases consist of tiny particles that are far apart relative to their size. Therefore, gases are compressible.

2. There are no forces of attraction or repulsion between gas particles, so gas can expand and take the shape and volume of the container.

3. Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion. Collisions between gas particles and between particles and the walls of the container are elastic collisions. No kinetic energy is lost in elastic collisions. The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

Real Gases Do Not Behave Ideally

Real gases DO experience inter-molecular attractionsReal gases DO have volumeReal gases DO NOT have elastic collisions

Likely to behave nearly ideally

Gases at high temperature and

low pressure

Small non-polar gas molecules

Likely not to behave ideally

Gases at low temperature and

high pressure

Large, polar gas molecules

Compressibility

• Compressibility is a measure of how much the volume of a gas decreases under pressure.

• The molecules of a gas are far apart so that is why it can be compressed.

• The energy of a gas increases when it is compressed because the molecules absorb the energy (work) that is put into doing the compression.

• Example: air bags in cars absorb energy when the driver hits the bag and compresses it. So the gas increases in energy and the human has that much less energy due to the collision (less injury).

Variables that Describe a Gas

• Gas variables• P Pressure in kPa kilopascals• V Volume in liters• T Temperature in Kelvin• n Number of moles of gas

• Ideal Gas Law: PV = nRT

Section 12.2 Factors Affecting Gas Pressure

• Let’s say you are pumping up your bicycle tire because it is flat.

• Do you agree that by pumping you are adding more air molecules to the tire?

• As you pump, the air pressure in the tire increases because you are putting more air molecules into a fixed volume (of the tire).

• When you increase the number of molecules, that increases the number of collisions, which explains why the pressure increases, because P=F/A (pressure = force/area) and there is a small force every time a molecule collides with the wall of the tire.

• If the temperature stays the same (e.g. you pump slowly), then 2X the # particles = 2X the pressure.

Behavior of Gases

• When a sealed container of gas under pressure is opened, gas always moves from an area of high pressure to an area of low pressure (just as heat always moves from high T to low T).

• An aerosol can works because there is higher pressure inside the can. When the button is pushed, the higher pressure gas escapes to the lower pressure region outside the can.

Volume• How could you

increase pressure in a closed container without adding more gas?

• You could decrease the volume, keeping the same amount of gas inside.• An example is a piston, like in your car.

• If you cut the volume in half, that will double the pressure (as long as temperature stays constant).

• Or, if you double the volume, that will cut the pressure in half.

Temperature

• What is the effect of temperature on gas pressure for a sealed container?

• The speed, and therefore the kinetic energy (KE = ½mv2) of the gas particles increases when the particles absorb thermal energy.

• The faster particles now impact the walls of the container with more energy, creating more force per unit area (that’s pressure).

• If the average KE of the gas doubles due to heat being added, then the average Kelvin temperature doubles and the pressure of the gas also doubles. Note that when working with gas laws we always use Kelvin temperature and not Celsius.

12.3 The Gas Laws• Boyle’s Law – Pressure/Volume relationship• Consider a gas with P1 in volume V1. If we

change the pressure to P2, but keep the temperature constant, what happens to volume V2?

• Boyle’s Law: P1V1 = P2V2 (the product is constant)

𝑷𝟏

𝑷𝟐=𝑽𝟐

𝑽𝟏

Boyle’s Law

Pressure is inversely proportional to volume when temperature is held constant.

rearranges to

Can you see why it’s inversely proportional?

A Graph of Boyle’s Law

• Anything that is inversely proportional has a graph shaped like this.

• Inversely proportional means that when the x-axis variable increases, the y-axis variable decreases.

• Note that at any point on the P-V curve to the right, the product of P·V is constant.

Sample Problem 12-1 (Boyle’s Law)

• A high altitude balloon contains 30.0 L of helium gas at 103 kPa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume the temperature remains constant.)

• P1 = 103 kPa, V1 = 30.0 L, P2 = 25.0 kPa, find V2

• Rearrange Boyle’s Law

Boyle’s Law - now you try one:

• The pressure on 2.50 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if the temperature remains constant?

PhET Simulator – University of Colorado, Boulder

• Gas Laws Simulation from PhET.jar

Charles’s Law: Temperature – Volume Relationship

• 1787 – Jacques Charles investigated the effect of temperature on the volume of a gas (pressure stayed constant at 1 atm).

• The limitation of his experiments, of course, is that all substances must remain in the gas phase.

• When temperature then volume (at const. P)

• When temperature then volume (at const. P)

Charles’s Law

• From his experiments Charles determined that a Temperature vs. Volume plot would be linear.

• Each gas’s line was different, but he noticed they all extrapolated to volume = 0 at T = -273oC = 0 KNote that this graph expresses temperature in Celsius.

Charles’s Law Animation

Charles’s Law

• At a pressure of 100 kPa:

• At this pressure, the relationship is

Charles’s Law

• The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.

• Temperature must be in KELVIN• Pressure = constant

If you rearrange it you get this direct relationship

Sample problem 12-2 (Charles’s Law)

• A balloon inflated in a room at 24oC has a volume of 4.00 L. The balloon is then heated to a temperature of 58oC. What is the new volume if the pressure remains constant?

• V1=4.00 L, T1=24oC T2=58oC, V2= ?• Convert temperatures to Kelvin• T1 = 24 + 273 = 297 K

• T2 = 58 + 273 = 331 K

Charles Law: Your turn

• 5.00 L of air at -50.0oC is warmed to 100oC. What is the new volume if the pressure remains constant? (Don’t forget to convert to Kelvin)

PhET Simulator

• Gas Laws Simulation from PhET.jar

Gay Lussac’s Law – The Temperature-Pressure

relationship

• The pressure and temperature of a gas aredirectly related, provided that the volumeremains constant.

• If the V is constant, then when T increases, P will also increases proportionally.

Temperature must be in KELVIN!

Gay-Lussac’s LawVolume is constant

Gay-Lussac Law – try a problem:

• The pressure in an automobile tire is 198 kPa at 27oC. At the end of the trip the pressure has risen to 225 kPa. What is the temperature of the air in the tire? (assumes volume is constant)

The Combined Gas Law

• Overwhelmed yet? Well, the good news is that you don’t need to remember those individual relationships (Boyle’s, Charles’s, Gay-Lussac’s) to solve problems.

• The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

• Whichever variable is held constant just ends up cancelling out of the equation because it’s the same on both sides of the equation. How convenient.

Sample Prob. 12-4: Combined Gas Law

• The volume of a gas-filled balloon is 30.0 L at 40o C and 153 kPa pressure. What volume will the balloon have at standard temperature and pressure? (STP- recall STP is 00C and 1 atm)

• V1=30.0 L, T1=40oC = 313K, T2 = 273K (std.temp)

P1=153kPa, P2=101.3kPa (std. pressure) V2=??

solve for

𝑷𝟏𝑽 𝟏

𝑻𝟏=𝑷𝟐𝑽𝟐

𝑻𝟐

Section 12-4: Ideal Gas Law

• So far we have worked with P,V, and T. • The fourth variable is number of moles of

gas in the system, n.• The number of moles of gas is directly

proportional to the number of particles, and therefore also directly proportional to volume as well.

• Therefore the combined gas law can be modified by dividing both sides by n, to result in:

• Each side is a constant, and we can

calculate what that constant is for STP.

Ideal Gas Law – Ideal Gas Constant, R

• To calculate the value at STP, use • Volume = 22.4 L (the volume of 1 mole of

gas)• Pressure = 101.3 kPa or 1 atm• Temperature = 273 K (note it is in Kelvin)

• Or if you are working with pressure in atm:

Finally, the Ideal Gas Law

• Ideal Gas Law:• PV = nRT where R = 8.31 • Note this is not a before/after

type equation like the other four!

• Note that temperatures must be in Kelvin, volume in liters, and pressure in kPa, since those are the units used for R (the ideal gas constant).

Sample problem 12-5: Ideal Gas Law

• You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas (N2) to a final pressure of 2.00 x 104 kPa at 28oC (301 K). How many moles of N2 does the cylinder contain?

• PV = nRT so

Sample problem 12-6: Ideal Gas Law

• A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) at a pressure of 1.5 x 103 kPa and a temperature of 42oC (315 K). How many kilograms of CH4 does this natural gas deposit contain?

• mol CH4

• Now convert the number of moles to kilograms:

• Molar mass is 16.0 g/mole (12 for the C, 4 for H’s)

•

Ideal gas law – you try one:

• A child has a lung capacity of 2.20 L. How many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37oC (310 K)? (Assume the molar mass of air is 29 g/mol).

• First use ideal gas law to find moles• Then convert moles to grams of air

using molar mass

What is held constant? Graph for Boyle’s Law

Equation for Boyle’s Law Inverse or direct?

Temperature must be in Kelvin(Hint: good slide to put on study buddy)

Boyle’s Law

Temperature

𝑷 𝟏𝑽 𝟏=𝑷𝟐𝑽 𝟐 Inverse

What is held constant? Graph for Charles’s Law

Equation for Charles’ Law Inverse or direct?

Temperature must be in Kelvin(Hint: good slide to put on study buddy)

Charles’ Law

pressure

𝑽𝟏

𝑻 𝟏=𝑽 𝟐

𝑻 𝟐

Direct

What is held constant? Graph for Gay-Lussac’s Law

Equation for Gay Lussac’s Law Inverse or direct?

Temperature must be in Kelvin(Hint: good slide to put on study buddy)

Gay Lussac’s Law

volume

𝑷𝟏

𝑻 𝟏=𝑷𝟐

𝑻 𝟐Direct

1 1 2 2PV PV

1 2

1 2

V V

T T

1 2

1 2

P P

T T

1 1 2 2

1 2

PV PV

T T

Temperature must be in Kelvin.Remember STP = 1 atm and 0oC

Ideal Gas LawPV = nRT

Hmmm, good for Study buddy