gases (chapter 10) rather than considering the atomic nature of matter we can classify it based on...

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Gases (Chapter 10) Rather than considering the atomic nature of matter we can classify it based on the bulk property: gaseous, liquid or solid. Gases are the most easily understood form of matter (we shall see why). Air is an example of a complex mixture of gases: gases form homogeneous mixtures regardless of identities or proportions (unlike liquids and solids). Gases expand to fill any container, and are highly compressible (unlike liquids and solids) These characteristics arise because the molecules of gas are very far apart and don’t (mostly) interact. Different gases thus behave similarly. Component Symbol Volume Nitrogen N 2 78.084% 99.998% Oxygen O 2 20.947% Argon Ar 0.934% Carbon Dioxide CO 2 0.033% Neon Ne 18.2 parts per million Helium He 5.2 parts per million Krypton Kr 1.1 parts per million Sulfur dioxide SO 2 1.0 parts per million Methane CH 4 2.0 parts per million Hydrogen H 2 0.5 parts per million Nitrous Oxide N 2 O 0.5 parts per million Xenon Xe 0.09 parts per million Ozone O 3 0.07 parts per million Nitrogen dioxide NO 2 0.02 parts per million

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Gases (Chapter 10)• Rather than considering the atomic

nature of matter we can classify it based on the bulk property: gaseous, liquid or solid.

• Gases are the most easily understood form of matter (we shall see why).

Air is an example of a complex mixture of gases: gases form homogeneous mixtures regardless of identities or proportions (unlike liquids and solids).

Gases expand to fill any container, and are highly compressible (unlike liquids and solids)

These characteristics arise because the molecules of gas are very far apart and don’t (mostly) interact. Different gases thus behave similarly.

Component Symbol Volume

Nitrogen N2 78.084%

99.998%Oxygen O2 20.947%

Argon Ar 0.934%

Carbon Dioxide CO2 0.033%

Neon Ne 18.2 parts per million

Helium He 5.2 parts per million

Krypton Kr 1.1 parts per million

Sulfur dioxide SO2 1.0 parts per million

Methane CH4 2.0 parts per million

Hydrogen H2 0.5 parts per million

Nitrous Oxide N2O 0.5 parts per million

Xenon Xe 0.09 parts per million

Ozone O3 0.07 parts per million

Nitrogen dioxide NO2 0.02 parts per million

Iodine I2 0.01 parts per million

Carbon monoxide CO trace

Ammonia NH3 trace

Pressure• Pressure is the force that acts on a given area (P=F/A).

• Gravity on earth exerts a pressure on the atmosphere: atmospheric pressure.

• We can evaluate this by calculating the force due to acceleration (by gravity) of a 1m2 column of air extending through the atmosphere (this has a mass of ~10,000kg).

252

5

22

/1011

101/

/000,100/8.9000,10

.

mNm

NAFP

skgmsmkgF

amF

This unit is a Newton (N)

This unit is a Pascal (Pa)

Units of PressureS.I. unit of pressure is the N/m2, given the name Pascal (Pa).

A related unit is the bar (1x105 Pa) used because atmospheric pressure is ~ 1x105 Pa (100 kPa, or 1bar).

Torricelli (a student of Galileo) was the first to recognise that the atmosphere had weight, and measured pressure using a barometer

Standard atmospheric pressure was thus defined as the pressure sufficient to support a mercury column of 760mm (units of mmHg, or torr).

Another popular unit was thus introduced to simplify things, the atmosphere (atm = 760mmHg).

Pressure• Atmospheric pressure and relationship between units

1 atm = 760 mmHg = 760 torr = 101.325kPa = 1.01325 bar)

Measuring Pressure: the manometer

Exercise:

On a certain day a barometer gives the atmospheric pressure as 764.7 torr. If a metre stick is used to measure a height of 136.4mm in the open arm, and 103.8mm in the gas arm of a manometer, what is the pressure of the gas sample? (give in torr, atm, kPa and bar).

ResultDifference in height is 32.6 mm. Gas inside

has greater pressure than prevailing atmospheric pressure: 764.7 + 32.6 mmHg = 797.3 mmHg (Torr)

Convert to atm: divide by 760 = 1.049 atmConvert to kPa: multiply by 101.325 = 106.3

kPaConvert to bar: divide by 100 = 1.063 bar

Gas Laws• A large number of experiments have determined that 4

variables are sufficient to define the physical condition (or state) of a gas: the gas laws.

Boyle’s Law, Charles’ Law, Avogadro’s hypothesis

Robert Boyle: (1627-1691) the first modern chemist, known as the father of chemistry.

His 1661 book The Sceptical Chymist marks the introduction of the scientific method, a definition of elements and compounds and a refutation of alchemy and magic potions.

Boyle biography

Boyle’s Law

• Boyle investigated the variation of the volume occupied by a gas as the pressure exerted upon it was altered and noted that the volume of a fixed quantity of gas, at constant temperature is inversely proportional to the pressure

constantor 1

constant PVp

V

Charles’ Law• A century later, a French scientist, Jacques Charles discovered that the

volume of a fixed amount of gas, as constant pressure, is proportional to the absolute temperature. Cool a balloon, or a sealed plastic bottle, to verify this!

constantor constant T

VTV

It was recognised (by William Thomson, Lord Kelvin, a Belfast born physicist) that if the graph was extrapolated to zero volume, an absolute zero of -273.15 oC is obtained.

Avogadro’s Law• Relationship between quantity of gas and volume established by

Gay-Lussac (balloon science!) and Avogadro in the 19th Century.Result was Avogadro’s hypothesis: equal volumes of gases at the

same temperature and pressure contain equal numbers of molecules

Experiments show that 22.4L of gas at 0oC and 1atm (STP), or 24.8L of gas at 298.15 K and 1 bar (SATP), contains 6.022 x 1023 molecules (Avogadro’s number, NA)Avogadro’s law: volume of gas at constant temperature and pressure is proportional to the number of moles of gas (n)

constant nV Remember:

1 mole = Avogadro’s number of objects

Putting it all together

nRTPV

P

nTRV

P

nTV

nVTVP

V

, ,1

Boyle, Charles, Avogadro

Combine

Call proportionality constant R

(gas constant)

Ideal Gas Equation

A note on units and dimensional analysisSI unit for R is J/mol.K or m3.Pa/mol.K (R=8.315 of these units)Need to use the units of Pa for pressure and m3(=1000L) for volume in any

calculation.

Alternatively you can use units of kPa and L.

If you wish to use atm and L (as in USA and Textbook) R=0.0826 L.atm/mol/K.

Always use absolute temperature scale (K)

Exercises

• What is the volume of 1 mole of an ideal gas

under standard temperature and pressure (STP)?• How many moles (g) of CO2 is liberated into a

250mL flask when a pressure of 1.3atm is found upon heating calcium carbonate to 31oC?

• If a metal cylinder holds 50L of oxygen at 18.5atm and 21oC, what volume will the gas occupy at 1atm and same T?

Gases in chemical reactions

If an air bag has a volume of 36L and is to be filled with nitrogen gas at a pressure of 1.15atm and 26oC, how many grams of NaN3 must be decomposed?

More ExercisesIf the pressure of a gas in an aerosol can is 1.5atm at 21oC, what would the pressure be if can is heated to 450oC?

What is the density of carbon tetrachloride vapour at 714torr and 125oC?

See student activities

Gas mixtures• Dalton’s Law of partial pressures

The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone

PT=P1+P2+P3+….Pn

Exercise: A gaseous mixture is made from 6.00g oxygen and 9.00g methane placed in a 15L vessel at 0oC. What is the partial pressure of each gas and the total pressure in the vessel?

Aside: A wronged chemist?

John Dalton, is credited with the formulation of the atomic theory. This was disputed by William Higgins, an Irish chemist from Colloney, Sligo, who claimed to have been the first to postulate the theory in his book Comparative view of the phlogistic and anti-phlogistic theories (1789) a work very critical of the Galway chemist Richard Kirwan. (Atkinson, E. R. The Atomic Hypothesis of William Higgins, J. Chem. Ed. 1940, 17(1), 3-11).

Mole Fractions

• The ratio n1/nT is called the mole fraction (denoted x1), a dimensionless number between 0 and 1.

TT

TTT

Pn

nP

n

n

VRTn

VRTn

P

P

11

111

/

/

Mole fraction of N2 in air is 0.78, therefore if the total barometric pressure is 760 torr, the partial pressure of N2 is (0.78)(760) = 590 torr.

Kinetic –Molecular TheoryTheory describing why gas laws are obeyed (explains both pressure and

temperature of gases on a molecular level).• Complete form of theory, developed over 100 years or so, published by

Clausius in 1857. Gases consist of large numbers of molecules that are in continuous,

random motion Volume of all molecules of the gas is negligible, as are

attractive/repulsive interactions Interactions are brief, through elastic collisions (average kinetic energy

does not change) Average kinetic energy of molecules is proportional to T, and all gases

have the same average kinetic energy at any given T.

Because each molecule of gas will have an individual kinetic energy, and thus individual speed, the speed of molecules in the gas phase is usually characterised by the root-mean-squared (rms) speed, u,(not the same though similar to the average speed). Average kinetic energy є = ½mu2

Application to Gas Laws

• Increasing V at constant T:Constant T means that u is unchanged.

But if V is increased the likelihood of collision with the walls decreases, thus the pressure decreases (Boyle’s Law)

• Increasing T at constant V:Increasing T increases u, increasing

collisional frequency with the walls, thus the pressure increases (Ideal Gas Equation).

Molecular speeds and mass• The average kinetic energy of gases has a specific value at

a given temperature. The rms speed of gas composed of light particles, He, is higher than that for heavier particles, Ne, at the same temperature.

• Can derive an expression for the rms speed (from kinetic theory)

M

RTu

3 M is the molar mass

This gives rise to interesting consequences: effusion

See student activities

Effusion• Thomas Graham (1846)

discovered that effusion is inversely proportional to the square root of molar mass.

1

2

2

1

M

M

r

r

Derived from comparison of rms speeds

REAL GASES

Deviations from ideal gas law

WHY?1. Molecules have volume

2. Molecules have attractive forces (intermolecular)

1. V-nb

2. -a(n/V)2

Van der Waals Equation of State2

V

na

nbV

nRTP

Van der Waal’s constantsvan der Waals Coefficients

Gas a (Pa m3) b(m3/mol)

Helium 3.46 x 10-3 23.71 x 10-6

Neon 2.12 x 10-2 17.10 x 10-6

Hydrogen 2.45 x 10-2 26.61 x 10-6

Carbon dioxide 3.96 x 10-1 42.69 x 10-6

Water vapor 5.47 x 10-1 30.52 x 10-6

a correlates with boiling point (see later)

b can be used to estimate molecular radii