CHAPTER 5

Three States of Matter

Pressure

Force exerted per unit area of surface by molecules in motion.

P = Force/unit area

Units for Pressure

1 atm = 14.7 psi1 atm = 760 mmHg1 atm = 29.92 inHg1 atm = 101,325 Pa1 Pa = 1 kg/m.s2

Properties of GasesKinetic Molecular Theory Volume of particles is negligibleParticles are in constant motionNo inherent attractive or

repulsive forcesThe average kinetic energy of a

collection of particles is proportional to the temperature

Compressibility – a gas at a certain volume can be compressed by adding pressure

Properties of Gases

Diffusibility - gases diffuse very quickly due to large empty spaces among molecules

Properties of Gases

Expansibility - when pressure is released the gas expands

↑ T, ↑ V - the particles gain more energy, move faster and move away from each other

Properties of Gases

Low density - gases have large intermolecular spaces, they have very large volumes when compared to their mass

density = mass volume

Properties of Gases

No definite shape or volume - the forces of attraction between gas molecules is too weak for them to maintain any kind of definitive shape/ volume

Properties of Gases

THE GAS LAWS

Boyle’s Law (Robert Boyle, English chemist)

“The volume of a sample of gas at a given temperature varies inversely with the applied pressure. ”

V α 1/P (constant moles and T)

Note:f – final conditionsi – initial conditions

Pi Vi = Pf Vf

A Problem to Consider

A sample of chlorine gas has a volume of 1.8 L at 1.0 atm. If the pressure increases to 4.0 atm (at constant temperature), what would be the new volume?

iiff VPVP using

)atm 0.4()L 8.1()atm 0.1(

PVP

Vf

iif

L 45.0Vf

Examples:Change of Pressure in a SyringeThe popping of a BalloonIncrease in size of bubbles as

they rise to the surfaceDeath of deep sea creatures due

to change in pressure.Popping of ears at high altitude

Charles’ Law (Jacques Alexandre Charles, French physicist)

“The volume occupied by any sample of gas at constant pressure is directly proportional to its absolute temperature.”

V α Tabs (constant moles and P)

i

i

f

f

TV

TV

A Problem to Consider

A sample of methane gas that has a volume of 3.8 L at 5.0°C is heated to 86.0°C at constant pressure. Calculate its new volume.

)K278()K359)(L8.3(

TTV

fi

fiV

L 9.4Vf

i

i

f

f

TV

TV

using

Gay-Lussac’s Law(Joseph Gay-Lussac, French chemist)

“The pressure exerted by a gas at constant volume is directly proportional to its absolute temperature.”

P α T (constant moles and V)

i

i

f

f

TP

TP

A Problem to Consider

An aerosol can has a pressure of 1.4 atm at 25°C. What pressure would it attain at 1200°C, assuming the volume remained constant?

i

i

f

f

TP

TP

using

)K298()K1473)(atm4.1(

TTP

fi

fiP

atm9.6Pf

Combined Gas LawsIn the event that all three

parameters, P, V, and T, are changing, their combined relationship is defined as follows:

f

ff

i

ii

TVP

TVP

A Problem to ConsiderA sample of carbon dioxide

occupies 4.5 L at 30°C and 650 mm Hg. What volume would it occupy at 800 mm Hg and 200°C?

f

ff

i

iiTVP

TVP

using

)K 303)(Hg mm 800()K 473)(L 5.4)(Hg mm 650(

TPTVP

Vif

fiif

L7.5Vf

Avogadro’s Law(Amadeo Avogadro, Italian chemist)

“Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules.”

V α n (constant T and P)

Vi = Vf

ni nf

Some Definitions…

STP – standard temperature and pressure: 0° C and 1 atm

Molar gas volume, Vm – volume of 1 mole of gas

At STP, Vm is 22.4 L

Ideal Gas Equation

V α 1 Boyle’s Law

PV α Tabs Charles’ LawV α nAvogadro’s Law

Ideal Gas Equation

R – ideal gas constant- 0.0821 L-atm

mol K

)( PnTabs R""V

The Ideal Gas Law

The numerical value of R can be derived using Avogadro’s law, which states that one mole of any gas at STP will occupy 22.4 liters.

nTVP R

K) mol)(273 (1.00atm) L)(1.00 (22.4 R

KmolatmL 0.0821

The Ideal Gas Law

Thus, the ideal gas equation, is usually expressed in the following form:

P - pressure (atm)V - volume (liters)n - number of atoms (moles)R - universal gas constant (0.0821 L.atm/K.mol)T - temperature (Kelvin)

nRT PV

A Problem to Consider

An experiment calls for 3.50 moles of chlorine, Cl2. What volume would this be if the gas volume is measured at 34°C and 2.45 atm?

PnRT V since

atm 2.45K) )(307 1mol)(0.082 (3.50 Kmol

atmL

V then

L 36.0 V then

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. Calculate the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

A sample of oxygen gas initially at 0.97 atm is cooled from 21°C to -68°C at constant volume. What is its final pressure (in atm)?

A 36.4-L volume of methane gas is heated from 25°C to 88°C at constant pressure. What is the final volume of the gas?

A sample of 15.0 moles CH4 occupies a volume of 5.80 L. What is the final volume of the gas if 0.95 mole CH4 was added? Assume that temperature and pressure do not change.

Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.82 moles of the gas in a steel vessel of volume 5.43 L at 69.5°C.

A small bubble rises from the bottom of a lake, where the temperature and pressure are 8°C and 6.4 atm, to the water’s surface, where the temperature is 25°C and the pressure is 1.0 atm. Calculate the final volume (in mL) of the bubble if its initial volume was 2.1 mL.

1. An inflated helium balloon with a volume of 0.55 L at sea level (1.0 atm) is allowed to rise to a height of 6.5 km, where the pressure is about 0.40 atm. Assuming that the temperature remains constant, what is the final volume of the balloon?

2. Argon is an inert gas used in lightbulbs to retard the vaporization of the tungsten filament. A certain lightbulb containing argon at 1.20 atm and 18°C is heated to 85°C at constant volume. Calculate its final pressure (in atm).

3. Calculate the volume (in liters) occupied by 7.40 g of NH3 at STP.

4. Under constant pressure conditions a sample of hydrogen gas initially at 88°C and 9.6 L is cooled until its final volume is 3.4 L. What is its final temperature?

5. A gas-filled balloon having a volume of 2.50 L at 1.2 atm and 25°C is allowed to rise to the stratosphere (about 3 km above the surface of the Earth), where the temperature and pressure are -23°C and 3.0x10-3 atm, respectively. Calculate the final volume of the balloon.

Dalton’ Law of Partial Pressures(John Dalton, English chemist)

“The sum of all the pressures of all the different gases in a mixture equals the total pressure of the mixture.”

.... cbatot PPPP

Pa = naRT V

Ptot = ntotRT V

Xa = na

ntot

Pa = naPtot

ntot

Pa = XaPtot

A mixture of gases contains 4.46 moles of Ne, 0.74 mole of Ar and 2.15 moles of Xe. Calculate the partial pressures of the gases if the total pressure is 2.00 atm at a certain temperature.

A mixture of gases contains 0.31 mol CH4, 0.25 mol C2H6 and 0.29 mol C3H8. The total pressure is 1.50 atm. Calculate the partial pressures of the gases.

Amagat’s Law of Partial Volumes(Emile Hilaire Amagat, French physicist)

“The volume of a gas mixture is equal to the sum of the volumes of all constituents at the same temperature and pressure as the mixture. ”

.... cbatot VVVV

Molecular Speeds

The root-mean-square (rms) molecular speed, u, is a type of average molecular speed, equal to the speed of a molecule having the average molecular kinetic energy

MM

3RT u

Graham’s Law of Diffusion/ Effusion(Thomas Graham, Scottish physical chemist)

the rate of effusion or diffusion is inversely proportional to the square root of its molecular mass

A gas of M

B gas of M

B"" gas ofeffusion of Rate

A"" gas ofeffusion of Rate

m

m

Diffusion vs. Effusion

Diffusion – process by which molecules intermingle as a result of their kinetic energy of random motion

Diffusion vs. Effusion

Effusion is where a gas escapes through a small hole

A Problem to Consider

How much faster would H2 gas effuse through an opening than methane, CH4?

)(HM)(CHM

CH of RateH of Rate

2m

4m

4

2

8.2g/mol 2.0g/mol 16.0

CH of RateH of Rate

4

2

So H2 effuses 2.8 times faster than CH4

A flammable gas made up only of carbon and hydrogen is found to effuse through a porous barrier in 1.50 min. Under the same conditions of temperature and pressure, it takes an equal volume of bromine vapor 4.73 min to effuse through the same barrier. Calculate the molar mass of the unknown gas.

Real Gases: van der Waals equation

Real gases do not follow PV = nRT perfectly.

The van der Waals equation corrects for the nonideal nature of real gases

a corrects for interaction between atoms

b corrects for volume occupied by atoms

nRT nb)-V)( P( 2

2

Van

where “nb” representsthe volume occupied by “n” moles of molecules

nb)-V( becomesV

Real Gases: van der Waals equation

where “n2a/V2” representsthe effect of pressure tointermolecular attractions or repulsions

)P( becomes P 2

2

Van

Real Gases: van der Waals equation