Gas LawsGas LawsChapter 14Chapter 14

Properties of GasesProperties of Gases

Gases are easily Gases are easily compressedcompressed because because of the space between the particles in of the space between the particles in the gas.the gas.

Properties of GasesProperties of Gases

The The amountamount of gas, of gas, volumevolume, and , and temperaturetemperature affect the pressure of a affect the pressure of a gas.gas.

Properties of GasesProperties of Gases

Doubling the number of particles in the Doubling the number of particles in the container would double the pressure container would double the pressure on a contained gas at constant on a contained gas at constant temperature.temperature.

Boyle’s Law PBoyle’s Law P11VV11 = P = P22VV22

A) 50 kPa A) 50 kPa B) 33 kPa B) 33 kPa C) inverse proportion - as one C) inverse proportion - as one

increases the other decreasesincreases the other decreases

Reducing the Reducing the volumevolume of a contained of a contained gas to one third, while holding gas to one third, while holding temperature constant, causes pressure temperature constant, causes pressure to become to become tripled.tripled.

A gas occupies a volume of 2.50 L at a A gas occupies a volume of 2.50 L at a pressure of 350.0 kPa. If the temperature pressure of 350.0 kPa. If the temperature remains constant, what volume would the remains constant, what volume would the gas occupy at 1750 kPa?gas occupy at 1750 kPa?

V VV V22 = ? V = ? V11 = 2.50 L P = 2.50 L P11 = 350.0 kPa = 350.0 kPaPP22 = 1750 kPa = 1750 kPa

F PF P11VV11 = P = P22VV22

S (350.0 kPa)(2.50 L) = (1750 kPa)VS (350.0 kPa)(2.50 L) = (1750 kPa)V22

A VA V22 = 0.500 L = 0.500 L

..

If the volume of a container of gas is If the volume of a container of gas is reduced, the reduced, the pressurpressure inside the e inside the container will container will increaseincrease..

Boyles Law & Temperature 14BBoyles Law & Temperature 14B

The graph of several pressure-volume The graph of several pressure-volume readings on a contained gas at readings on a contained gas at constant temperature would be a constant temperature would be a curved linecurved line..

If a balloon is If a balloon is squeezedsqueezed, the pressure , the pressure of the gas inside the balloon increases.of the gas inside the balloon increases.

Temperature Temperature is directly proportional to is directly proportional to the average kinetic energy of the the average kinetic energy of the particles in a substance. particles in a substance.

As the temperature of the gas in a As the temperature of the gas in a balloon balloon decreasesdecreases, the average kinetic , the average kinetic energy of the gas decreases.energy of the gas decreases.

Absolute zero is the temperature at Absolute zero is the temperature at which the average kinetic energy of which the average kinetic energy of particles would theoretically be particles would theoretically be zerozero..

This is the This is the lowestlowest possible possible temperature. temperature. (-273.15°C)(-273.15°C)

To get kelvins add To get kelvins add 273273 to the °C. to the °C. To get °C To get °C subtractsubtract 273 from the kelvins. 273 from the kelvins.

A temperature of -25°C is equivalent to A temperature of -25°C is equivalent to 248 K. [ -25+273=248]248 K. [ -25+273=248]

A temperature of 295 K is equivalent to A temperature of 295 K is equivalent to 22 °C. [295-273=22C]22 °C. [295-273=22C]

When the Kelvin temperature of an When the Kelvin temperature of an enclosed gas doubles, the particles of enclosed gas doubles, the particles of the gas the gas move fastermove faster..

The Kelvin temperature must be used The Kelvin temperature must be used when working with when working with proportions.proportions.

Problem:Problem: A balloon contains 30.0 L of helium gas A balloon contains 30.0 L of helium gas

at 103 kPa. What is the volume of the at 103 kPa. What is the volume of the helium when the balloon rises to an helium when the balloon rises to an altitude where the temperature stays altitude where the temperature stays the same but the pressure is only 25.0 the same but the pressure is only 25.0 kPa?kPa?

V VV V22 = ? = ? •PP11 =103 kPa V =103 kPa V11 = 30.0 L = 30.0 L

•PP22 = 25.0 kPa = 25.0 kPa V V22 = ? = ?

F PF P11VV11 = P = P22VV22

S S (103 kPa)(30.0 L) = (25.0 kPa)V(103 kPa)(30.0 L) = (25.0 kPa)V22

A VA V22 = 124 L = 124 L

Charles’ Law Charles’ Law Notes 14C Notes 14C

when the temperature is when the temperature is expressed in expressed in kelvins.kelvins.

2

2

1

1

T

V

T

V

At constant pressure, the At constant pressure, the volumevolume of a of a fixed mass of gas and its Kelvin fixed mass of gas and its Kelvin temperature are said to be temperature are said to be directly directly related.related.

If a balloon is If a balloon is heatedheated, the , the volume of the air in the balloon volume of the air in the balloon increasesincreases if the pressure is if the pressure is constant.constant.

The temperature of 6.24 L of a gas is The temperature of 6.24 L of a gas is increased from 125 K to 250 k at increased from 125 K to 250 k at constant pressure. What is the new constant pressure. What is the new volume of the gas?volume of the gas?

V VV V22 =? V =? V11 = 6.24 L = 6.24 L

TT11 = 125 K T = 125 K T22 = 250. K = 250. K FF S S A VA V22 = 12.48 L = 12.48 L

2

2

1

1

T

V

T

V

K.250

V=

K125

L24.6 2

A) kelvins B) increases C) 0 LA) kelvins B) increases C) 0 L

Combined Gas Law Combined Gas Law Notes 14 D Notes 14 D

Gay-Lussac’s LawGay-Lussac’s Law

2

2

1

1

T

P

T

P

If the Kelvin temperature of a gas in a If the Kelvin temperature of a gas in a closed container closed container increasesincreases the the pressure of the gas pressure of the gas increases increases proportionally.proportionally.

As the temperature of a fixed volume of As the temperature of a fixed volume of a gasa gas increases increases, the pressure will , the pressure will increase.increase.

A sample of chlorine gas has a A sample of chlorine gas has a pressure of 9.99 kPa at 27°C. What will pressure of 9.99 kPa at 27°C. What will its pressure be at 627°C if its volume its pressure be at 627°C if its volume remains constant?remains constant?

V PV P2 2 = ? P= ? P11 = 9.99 kPa = 9.99 kPa

TT11 = 300. K T = 300. K T22 = 900. K = 900. K

F F S S A PA P22 = 29.97 kPa = 29.97 kPa

2

2

1

1

T

P

T

P

K900

P=

K.300

kPa99.9 2

The Combined Gas LawThe Combined Gas Law

2

22

1

11

T

VP

T

VP

The combined gas law relates temperature, pressure, and volume.

If a sample of oxygen occupies a If a sample of oxygen occupies a volume of 6.00 L at a pressure of 68.0 volume of 6.00 L at a pressure of 68.0 kPa and a temperature of 264 K, what kPa and a temperature of 264 K, what volume would this sample occupy at volume would this sample occupy at 204 kPa and 528 K?204 kPa and 528 K?

V VV V22 =? V =? V11 = 6.00 L = 6.00 L PP11 = 68.0 kPa T = 68.0 kPa T11 = 264 K = 264 K PP22 = 204 kPa T = 204 kPa T22 = 528 K = 528 K FF

S S

A VA V22 = 4.00 L = 4.00 L

2

22

1

11

T

VP

T

VP

( )( ) ( )K528

VkPa204=

K264

L00.6kPa0.68 2

Ideal Gas Law Ideal Gas Law Notes 14E Notes 14E

Ideal Gas Law Ideal Gas Law PV = nRTPV = nRT Where n = the number of molesWhere n = the number of moles

R is the Ideal Gas Constant R is the Ideal Gas Constant

The ideal gas law can be used to The ideal gas law can be used to calculate the calculate the number of molesnumber of moles of a of a contained gas.contained gas.

molK

kPaL31.8R

What is the volume (in L) that would be What is the volume (in L) that would be occupied by 1.00 mol of Ooccupied by 1.00 mol of O22 at STP? at STP?

V V = ? n = 1.00 mol T = 273K V V = ? n = 1.00 mol T = 273K P = 101.3P = 101.3 kPa kPa

F PV = nRTF PV = nRT S S (101.3 kPa)V = (1.00 mol) (101.3 kPa)V = (1.00 mol) (273 K)(273 K)

A Vol = 22.4 LA Vol = 22.4 L

molK

kPaL31.8R

molK

kPaL31.8R

How many moles of HHow many moles of H22 would be would be

contained in 83.1 L of the gas at contained in 83.1 L of the gas at 137 kPa and 1.0°C?137 kPa and 1.0°C?

V n = ? V = 83.1 L P = 137 kPa V n = ? V = 83.1 L P = 137 kPa T = 1.0°C = 274 K T = 1.0°C = 274 K

F PV = nRTF PV = nRT S (137 kPa)(83.1 L) = n (274. K)S (137 kPa)(83.1 L) = n (274. K) A n = 5.00 molA n = 5.00 mol

molK

kPaL31.8R

molK

kPaL31.8

Gas Mixtures Gas Mixtures 14 F 14 F

Dalton’s Law - In a mixture of gases, Dalton’s Law - In a mixture of gases, the the totaltotal pressure is the sum of the pressure is the sum of the partial pressurespartial pressures of the gases. of the gases.

PPTotalTotal = P = P11 + P + P22 + P + P33 + … + …

A sample of HA sample of H22 is collected over water is collected over water such that the combined hydrogen-such that the combined hydrogen-water vapor sample is held at a water vapor sample is held at a pressure of 1 standard atmosphere. pressure of 1 standard atmosphere. What is the partial pressure of the HWhat is the partial pressure of the H2 2 if if that of the water vapor is 2.5 kPa?that of the water vapor is 2.5 kPa?

1 atm = 1 atm = 101.3 kPa101.3 kPa

101.3 kPa – 101.3 kPa – 2.5 kPa2.5 kPa = = 98.898.8 kPa kPa

The tendency of molecules to move The tendency of molecules to move toward areas of toward areas of lower concentrationlower concentration is is called called diffusion.diffusion.

The gas propellant in an aerosol can The gas propellant in an aerosol can moves from a region of moves from a region of highhigh pressure pressure to a region of to a region of lowerlower pressure. pressure.

The process that occurs when a gas The process that occurs when a gas escapesescapes through a tiny hole in the through a tiny hole in the container is called container is called effusion.effusion.

The substance with the smallest The substance with the smallest molar mass would have the molar mass would have the fastest fastest rate of rate of effusion.effusion.

So CHSo CH44 effuses effuses fasterfaster than NO than NO22.. 16g/mol 46g/mol16g/mol 46g/mol