PROPERTIES OF GASES &THE GAS LAWS

Chapter 14 Section 1 & 2

MEASURABLE PROPERTIES OF GASES

Pressure (P) Temperature (T)

Volume (V) Moles (n)

Units atm, Pa (SI unit), mmHg, torr

K (SI unit), ºC L, mL, cm3, m3

moles, mol

Instrument barometer, manometer

thermometer graduated cylinder

NA

Meaning force exerted over area by colliding gas particles

amount of average kinetic energy of particles

space occupied by particles, not the volume of particles

1 mol = 6.02×1023 particles

PROPERTIES OF GASES

Compressible Have mass Gas particles always in motion Gas particles exert pressure when they run into a wall Take up any shape and size of container – diffuse (=

to spread out) Are described with four variables: the amount of gas

(n), volume (V), pressure (P), and temperature (T)** variable = something you can change and

represented by a letter

PRESSURE VS. VOLUME(BOYLE’S LAW)

Describe the picture.

BOYLE’S LAW EQUATIONS

P1∙V1 = P2∙V2

“1” and “2” refer to two different sets of condition

Match the unit for each variable The volume is inversely proportional

to the pressure The volume increases (decreases) as the

pressure decreases (increases) The temperature and amount of gas

must remain unchanged for this law to work

BOLYE’S LAW(PRESSURE-VOLUME RELATIONSHIP)

hyperbola

EXAMPLE

A given sample of gas occupies 523 mL at 760 torr. The pressure is increased to 1.97 atm, while the temperature remains the same. What is the new volume of the gas?

PRACTICES ON BOYLE’S LAW1) A flask containing 155 cm3 of hydrogen gas

was collected under a pressure of 22.5 kPa. What pressure would have been required for the volume of the gas to have been 90.0 cm3?

2) A sample of oxygen gas has a volume of 150. mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains the constant?

3) A gas has a pressure of 1.26 atm and occupies a volume of 7.40 L. If the gas is compressed to a volume 2.93 L, what will its pressure be, assuming constant temperature?

PRESSURE-VOLUME DATA (BOYLE’S LAW)

Pressure(kPa) Volume (L) PV(kPa×L)

150 0.334 50.1

200 0.250 50.0

250 0.200 50.0

300 0.167 50.1

CHARLES’S LAW(TEMPERATURE – VOLUME

RELATIONSHIP)

Volume (mL) Temperature (K)

V/T (mL/K)

748 373 2.01

567 283 2.00

402 200 2.01

199 100 1.99

CHARLES’S LAW(TEMPERATURE-VOLUME

RELATIONSHIP)

CHARLES’S LAW

1)

2) The volume and temperature are directly proportional

3) The volume of gas increases (decreases) as the temperature increases (decreases)

4) The temperature MUST be in kelvin (K = C + 273)

5) Must keep the pressure and the amount of gas unchanged for this law to work

1 2

1 2

V V

T T

GRAPH OF CHARLES’S LAW(TEMPERATURE-VOLUME

RELATIONSHIP)

ExampleA balloon is inflated to 665 mL volume at 27°C. It is immersed in a dry-ice bath. What, at −78.5°C, is its volume, assuming the pressure remains constant?

PRACTICES1) A sample of neon gas occupies a volume of

752 mL at 25 ºC. What volume will the gas occupy at 50 ºC if the pressure remains constant?

2) A helium-filled balloon has a volume of 2.75 L at 20 ºC. The volume of the balloon decreases to 2.46 L after it is placed outside on a cold day. What is the outside temperature?

3) A gas at 65 ºC occupies 4.22 L. At what Celsius temperature will the volume be 3.87 L, assuming the same pressure?

COMBINED GAS LAW(VOLUME, TEMPERATURE & PRESSURE)

Combine Boyle’s law and Charles’s law:

For this law to work, the amount of gas must remain unchanged

With this law, 2 variables out of 3 can change

1 1 2 2

1 2

1 2

P V P V

V V

T T

1 1 2 2

1 2

P V P V

T T

EXAMPLE

520 mL of hydrogen gas at 750 mmHg and 25 °C is placed in a 1000. mL container and heated to 50 °C. What is the pressure of the gas in the container?

FROM COMBINED GAS LAW TO…. Boyle’s law: at constant temperature Charles’ law: at constant pressure

Gay-Lussac’s law: at constant volume

1 1 2 2

1 2

P V P V

T T

1 1 2 2

1 2

P V P V

T T

1 1 2 2

1 2

P V P V

T T

GAY-LUSSAC’S LAW

GRAPH OF GAY-LUSSAC’S LAW

GAY-LUSSAC’S LAW(TEMPERATURE-PRESSURE

RELATIONSHIP) Temperature and pressure are directly

proportional:

Temperature MUST be in kelvins Works only if the volume and the amount of

gas are kept constant

2

2

1

1

T

P

T

P

EXAMPLE

An aerosol can containing gas at 101 kPa and 22 ºC is heated to 55 ºC. Calculate the pressure in the heated can.

Answer: P2=112kPa

AVOGADRO’S LAW The volume (V) of gas is directly proportional to

the number of moles (n) of gas:

The type of gas doesn’t affect the volume; only the # of moles of gas does 1 mol of ANY gas at 1 atm and 0˚C takes up 22.4 L volume.

For this law to work, pressure and temperature must remain unchanged

1 2

1 2

V V

n n

COMBINE BOYLE, CHARLES, & AVOGADRO’S LAW

P1∙V1 = P2∙V2

1 2

1 2

V V

n n

1 2

1 2

V V

T T

IDEAL GAS LAW

1 mol of ANY gas at 1 atm and 0˚C takes up 22.4 L volume

Combine the two above information and get…

22

22

11

11

nT

VP

nT

VP

EXAMPLE

Determine the Celsius temperature of 2.49 moles of gas contained in a 1.00-L vessel at a pressure of 143 kPa.

SUMMARY OF GAS LAWS

Combine V, P, n, and T into one law.

From the combined gas law, get(1) Boyle’s law(2) Charles’ law(3) Gay-Lussac’s law(4) Avogadro’s law(5) Ideal gas law

KINETIC MOLECULAR THEORY

1) Gas particles are in constant, rapid, and random motion

2) The distance between gas particles are much larger than the size of atoms*The size of gas particle is almost nothing.

3) Gas particles colliding with surface creates pressure

4) Perfect elastic collisions between gas particles – no loss of energy during collisions but all transferred

5) Average kinetic energy of gas particles is proportional to kelvin temperature

6) Gas particles at the same temperature don’t have the same amount of kinetic energy (See the graph on the next slide)

NON-IDEAL GAS BEHAVIOR

Gas particles attract or repel each other

Gas particles do have a volume Imperfect collision – energy lost Non-ideal behavior becomes more ideal

at high temperature and low pressure

SUMMARY OF GAS LAWS

Boyle’s Charles’s Combined Gay-Lussac’s

Avogadro’s

SUMMARY OF GAS LAWS

Boyle’s Charles’s Combined Gay-Lussac’s

Avogadro’s

volume-pressure

volume-temperature

volume-pressure-temperature

pressure-temperature

volume-mole

V and P inversely proportional

V and T directly proportional

V and P inversely and V and T directly proportional

P and T directly proportional

V and n directly proportional

P1∙V1 = P2∙V2

T and n constant

P and n constant

n constant n and V constant

P and T constant

1 2

1 2

V V

T T 1 1 2 2

1 2

P V P V

T T

1 2

1 2

P P

T T 1 2

1 2

V V

n n