the gas laws chapter 9. kinetic molecular theory 1. a gas is composed of small particles (molecules)...

The Gas Laws

Chapter 9

Kinetic Molecular Theory

1. A gas is composed of small particles (molecules) that are spaced widely apart.

Compressible Low density - about a 1000 times less dense

than a liquid

2. The molecules of a gas are in rapid, constant motion

Pressure – the force of the molecules hitting the side of a container

Fill a container (like a balloon) evenly.

Kinetic Molecular Theory

3. All collisions are elastic Molecules don’t lose any energy when they

collide.

4. Gas molecules have little/no attractive force on one another.

Too far apart Mix thoroughly – unlike oil and water (too far

apart for polar/non-polar forces to matter)

Kinetic Molecular Theory

5. The temperature of a gas is a measure of average kinetic energy

Kinetic energy – energy in motion KE = ½ mv2

Graham’s Law of Diffusion – the higher the molar mass, the slower it moves

v1 = m2

v2 m1

Graham’s Law Example

At the same temperature, how much faster does an He atom move than an N2 molecule?

(Ans: 2.65 times faster)

Graham’s Law Example

Which is faster (and by how much): Cl2 or O2?

(Ans: O2 is about 1.5 times faster)

Which is faster and by how much: HCl or NH3?

Our Atmosphere

99% N2 and O2

78% N2

21% O2

1% CO2 and the Noble Gases

0

10

20

30

40

50

60

70

80

Gas

Nitrogen

Oxygen

CarbondioxideandNobleGases

Pressure

Pressure = Force

Area (Needles, High Heels, Snow shoes) Caused by the collisions of gases against a

container We live at about 1 atmosphere of pressure

Barometer

Torricelli (1643) Height of column stayed

about 760 mm (760 torr) The higher the

elevation, the lower the mercury

Weather Rising pressure – calm

weather Dropping pressure –

storm (fast moving air)

Units of Pressure

All of the following are equal:760 mm Hg (760 torr)29.9 inches Hg (weather reporting)1 atmosphere (chemistry)101.3 kPa (kiloPascals, physics)

760 mm = 29.9 in = 1 atmosphere = 101.3 kPa

Converting Pressures

Examples:

1. Express 485 torr in atmospheres.

2. Convert 2.4 atmospheres to mm Hg

3. Convert 95.0 kPa to atmospheres and mm Hg.

4. Convert 31.4 inches of mm to atmospheres.

The Ideal Gas Law

Combination of earlier work on gases. Works very well in situations close to Earth’s

pressures and temperatures Does not work for “extreme” situations

(Jupiter’s atmosphere is too cold and too dense)

The Ideal Gas Law

PV = nRT

P = pressure in atmosphereV = volume in Litersn = number of molesT = Temperature in KelvinR = gas constant

• R = 0.0821 L-atm / mol-K

The Ideal Gas Law

Examples:

1. What is the pressure of a 1.45 mol sample of a gas in a 20.0 L container at 25oC?

2. What volume will 5.00 grams of H2 occupy at 10.0oC and 1 atmosphere of pressure?

3. How many grams of O2 are needed to occupy a 500.0 mL aerosol can at 20.0oC and 0.900 atmospheres?

STP

Standard Temperature & PressureStandard Temperature = 0oC (273 K)Standard Pressure = 1 atm1 mole of a gas occupies 22.4 L at STP

1 mole or 22.4 L

22.4 L 1 mole

STP

Examples:

1. What volume will 0.180 moles of nitrogen gas occupy at STP?

2. How many grams of chlorine (Cl2) gas are present in 50.0 L at STP?

Comparing Two Situations

Sometimes we want to know what happens when a gas is under different conditions

Example: What happens to a basketball if you pump it indoors, then take it out on a cold day?

Comparing Two Situations

P1V1 = n1RT1 P2V2 = n2RT2

Solve both equations for R

R = P1V1 R = P2V2

n1T1 n2T2

P1V1 = P2V2

n1T1 n2T2

Comparing Two Situations

See what you can cross out (what you are not told)

Remember to convert to Kelvin and moles if needed.

Boyle’s Law

Boyle’s Law Apparatus Demo Boyle’s Law – The pressure and volume of a

gas are inversely related Bicycle pump example

Piston down – low volume, high pressurePiston up – high volume, low pressure

Boyle’s Law

Example:

1. The volume of a car’s cylinder is 475 mL at 1.05 atm. What is the volume when the cylinder is compressed and the pressure is 5.65 atm?

P1V1 = P2V2

n1T1 n2T2

Boyle’s Law

Collapses to:

P1V1 = P2V2

(Answer: 88.3 mL)

Boyle’s Law

Example:

2. A weather balloon has a volume of 40.0 liters on the surface of the earth at 1.00 atm. What will be the volume at 0.400 atm as it rises?

P1V1 = P2V2

n1T1 n2T2

Charles Law

Charles Law – The temperature and volume of a gas are directly related“HOTTER = BIGGER”A gas increases in volume 1/273rd per degree

celsiusCan be used to find absolute zeroTemperature must be in Kelvin

Charles Law

1. A basketball has a volume of 12.0 L when blown up at 25.00 oC. What will be the volume if it is taken outside on a day when it is only 5.00 oC?

P1V1 = P2V2

n1T1 n2T2

Charles Law

Collapses to:

V1 = V2

T1 T2

Charles Law

2. If a tire contains 30.0 L of air at 10.0 oC, what volume will it occupy when it is driven and warms up to 50.0 oC?

Guy-Lussac’s Law

Gay-Lussac’s Law = The temperature and pressure of a gas are directly related.

Temperature must be in Kelvin

1. Gas in a spray can has a pressure of 5.00 atm at 25.0 oC. What will be the pressure at 400.0 oC?

P1V1 = P2V2

n1T1 n2T2

Avagadro’s Law

Avagadro’s Law = The volume of a gas is directly proportional to the moles present

“MORE = BIGGER”

1. A balloon has a volume of 1.00 L when 50.0 grams of N2 are in the balloon. What is the volume if an additional 25.0 grams of N2 are added?

Putting it all together

Often you change more than one thing at a time.

Ex: In a car, volume, temperature, and pressure may change.

1. The volume of 0.0400 mol of a gas is 500.0 mL at 1.00 atm and 20.0 oC. What is the volume at 2.00 atm and 30.0oC?

Gases and Reaction Stoichiometry

1. What mass of Al is needed to produce 50.0 L of H2 at STP?

2Al(s) + 6HCl(aq) 2AlCl3(aq) + 3H2(g)

(ANS: 40.2 g Al)

Gases and Reaction Stoichiometry

2. What volume of NO gas measured at 0.724 atm and 25oC will be produced from the reaction of 19.5 g of O2?

4NH3(g) + 5O2(g) 4NO(g) + 6H2O(l)

(Ans: 16.4 L)

Gases and Reaction Stoichiometry

3. Car safety bags are inflated through the decomposition of NaN3. How many grams of NaN3 are needed to produce 36.0 L of N2 at 1.15 atm and 26.0oC?

2NaN3(s) 2Na(s) + 3N2(g)

(Ans: 72 g)

Gases and Reaction Stoichiometry

4. How many liters of H2 and N2 at 1.00 atm and 15.0oC are needed to produce 150.0 grams of NH3?

N2(g) + 3H2(g) 2NH3(g)

Dalton’s Law of Partial Pressures

John Dalton – Dalton’s Atomic Theory Dalton’s Law – the total pressure of a gas is

equal to the sum of the partial pressures Ptot = PA + PB + PC + PD +…..

Patm = PN2 + PO2 + Prest

1 atm = 0.78atm + 0.21atm + 0.01atm

Dalton’s Law of Partial Pressures

1. Three gases are mixed in a 5.00 L container. In the container, there are 255 torr of Ar, 228 torr of N2, and 752 torr of H2. What is the total pressure?

Dalton’s Law of Partial Pressures

2. On a humid day, the partial pressure of water in the atmosphere is 18 torr.

a) If the total pressure is 766 torr, what are the pressures of all of the other gases?

b) If the atmosphere is 78% N2 and 21% O2, what are their pressures on this humid day?

Dalton’s Law of Partial Pressures

3. What is the total pressure (in atm) exerted by a mixture of 12.0 g of N2 and 12.0 g of O2 in a 2.50 L container at 25.0oC?

8. CH4 (16.0) Fastest

Ne (20)

CO (28.0)

Ar (39.9)

Cl2 (71.0)

ClO2 (87.0) Slowest