GAS LAWS

Gay-Lussac’s Law states that as the PRESSURE of a gas

increases (decreases) its TEMPERATURE also increases

(decreases) at constant volume and amount of matter (mole).

Application of Gay-Lussac’s gas law

• PRESSURE COOKER

The accumulated steam increases the pressure and the boiling point of water. The pressure cooker utilizes high pressure to cook the food in 1/3 the time required by conventional cooking methods.

Applying the Temperature-Pressure Relationship

PROBLEM:

A steel tank used for fuel delivery is fitted with a safety valve that opens when the internal pressure exceeds 1.00x103 torr. It is filled with methane at 230C and 0.991 atm and placed in boiling water at exactly 1000C. Will the safety valve open?

PLAN: SOLUTION:

P1(atm) T1 and T2(0C)

P1(torr) T1 and T2(K)

P1 = 0.991atm P2 = unknown

T1 = 230C T2 = 100

0C

P2(torr)

1atm=760torr

x T2/T1

K=0C+273.15

P1

T1

P2

T2=

0.991 atm

1.00 atm

760 torr= 753.2 torr

P2 = P1T2

T1= 753.2 torr

373.15K

296.15K= 949.0

torr

n and V are constant

THE IDEAL GAS LAW

PV = nRT

IDEAL GAS LAW PV = nRT

Boyle’s Law

V =constant

P

R = PV

nT=

1atm x 22.414L

1mol x 273.15K=

0.0821atm*L

mol*K

V = V =

Charles’s Law

constant x T

Avogadro’s Law

constant x n

fixed n and T fixed n and P fixed P and T

R is the universal gas constant

3 significant figures

Avogadro’s Law states that if the amount of gas in a

container is increased (decreased), the volume of a gas

also increases (decreases).

A molecular description of Avogadro’s Law.

A sample of gas with a volume of 9.20 L is known to

contain 1.225 moles. If the volume increased to

21.4 L, how much amount of gas (moles) was added

if pressure and temperature remain constant?

Initial condition Final condition

V1 = 9.20 L V2 = 21.4 L

n1 = 1.225 mol n2 = ?

Formula: V1 = V2 n2 = V2n1

n1 n2 n2

n2 = (21.4 L) (1.225 mol)

9.20L

= 2.84946 mol

n2 = 2.85 mol

Applying the Volume-Amount Relationship

PROBLEM:

A scale model of a blimp rises when it is filled with helium to a volume of 55 dm3. When 1.10 mol of He is added to the blimp, the volume is 26.2 dm3. How many more grams of He must be added to make it rise? Assume constant T and P.

PLAN:

SOLUTION:

We are given initial n1 and V1 as well as the final V2. We have to find n2and convert it from moles to grams.

n1(mol) of He

n2(mol) of He

mol to be added

g to be added

x V2/V1

x M

subtract n1

n1 = 1.10 mol n2 = unknownV1 = 26.2 dm

3V2 = 55.0 dm

3

P and T are constant

V1

n1

V2

n2=

n2 = n1V2

V1

n2 = 1.10 mol55.0 dm3

26.2 dm3= 2.31 mol

4.003 g He

mol He= 4.84 g He1.21 mol

Δn = 2.31 – 1.10 = 1.21 mol

Exercises for Gay-Lussac’s & Avogadro’s gas law

1) A fire extinguisher has a pressure of 150 psi at 35OC. What is the pressure in atmospheres if the fire extinguisher is used at a temperature of 80OC?

2) A gas occupies 250 mL at 680 torr and 30OC. When the pressure is changed to 460 torr, what temperature (OC) is needed to maintain the same volume?

3) At a certain temperature & pressure, a balloon with10.0 g of oxygen has a volume of 7.00 L. What will itsvolume be after 5.00 g of oxygen is added to theballoon?

4) A sample of 8.00 moles of Argon has a volume of 20.0 L. A small leak causes half of the molecules to escape. What is the new volume of the gas?

COMBINED GAS LAW contains six variables. It combines three gas laws: Boyle, Charles and Gay-Lussac.

CONSTANT: Amount of gas (n)

APPLICATION OF COMBINED GAS LAW

An Industrial Chemist regulating the pressure and gas flow with a series of valves.

A toy balloon has an internal pressure of 1.05 atm and a volume of 5.0 L. If the temperature where the balloon is released is 200

C, what will happen to the volume when the balloon rises to an altitude where the pressure is 0.65 atm and the temperature is–150 C?

Given: Find: Vf1.05 atm = P1 0.65 atm = P2200 C = T1 –15

0 C = T25.0 L = V1Formula: V1P1 = V2 P2 Vf2 = V1 P1 T2 = (5.0 L) (1.05 atm) (258.15K)

T1 T2 P2 T1 (0.65 atm) (293.15 K)

= 7.1125966

= 7.1 L

Exercises for Combined Gas Law

1) A gas measures 10.0 mL at 27OC and 760 mm Hg.

What will be the volume of the gas at 15OC and

750 mm Hg?

2) Sixty milliliters of gas is measured at 85OC and

2.0 atm. What is the volume at STP?

3) A sample of methane gas (CH4) has a volume of

125 mL at 0.600 atm pressure and 25OC. How many

milliliters will it occupy at a pressure of 1.50 atm

and 25OC?

Dalton’s Law of Partial Pressures

Ptotal = P1 + P2 + P3 + ...

Mixtures of Gases

•Gases mix homogeneously in any proportions.

•Each gas in a mixture behaves as if it were the only gas present.

A molecular description of Dalton’s law of partial pressures.

Henry’s Law

States that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas

above the surfacae of the solutions

Applies only to gases such as OXYGEN and HYDROGEN

Mixtures of Gases

•Gases mix homogeneously in any proportions.

•Each gas in a mixture behaves as if it were the only gas present.

Vapor Pressure of Water (P ) at Different TH2O

T(0C) P (torr) T (0C) P (torr)

05

10111213141516182022242628

3035404550556065707580859095

100

31.842.255.371.992.5

118.0149.4187.5233.7289.1355.1433.6525.8633.9760.0

4.66.59.29.8

10.511.212.012.813.615.517.519.822.425.228.3

The concept of partial pressure helps SCUBA DIVERS avoid a possibly fatal sickness.

Ordinary air in scuba tanks

=> high pressure exerted by

the water (150 ft) creates

high pressure on the

nitrogen component in the air

= high conc. of N2 in blood

(Decompression sickness

or “Bends”)

http://en.wikipedia.org/wiki/File:Aladin-pdc.jpghttp://en.wikipedia.org/wiki/File:Aladin-pdc.jpghttp://en.wikipedia.org/wiki/File:Nasa_decompression_chamber.jpghttp://en.wikipedia.org/wiki/File:Nasa_decompression_chamber.jpg

There are several major air pollutants in the environment that one should be aware of.

Sulfur Dioxide

Particulate Matter

Nitrogen Oxides

Carbon Monoxide

Ozone

Lead

Volatile Organic Compounds (VOCs)

Kinetic Molecular Theory of Gases

1) Gases are made up of tiny molecules.

2) Gas molecules are always in constant motion.

3) The forces of attraction between gas molecules are negligible.

4) Gas molecules undergo elastic collisions.

5) The average kinetic energy of gas molecules is proportional to the Kelvin temperature of the gas.