chapter 18kinetic theory of gases • vol. of gas, # of gas particles, press. of gas, & temp. of...

CHAPTER 18

GASES

KINETIC THEORY OF GASES

•  A given amt. of gas will occupy the entire volume of its container. – Changes in temp. have a greater effect on the

vol. of a gas than on a liquid or solid


•  Gas particles are in constant random motion. –  not held in fixed position by attractive forces –  size of gas molec. is insignificant in comparison

w/ the dist. betw. molecs. ∴ we assume gas particles have no effect on ea.

other


•  Gas particles are treated as Point Masses –  considered to have no vol. or diameter

•  Ideal Gas - imaginary gas composed of molecs. w/ mass but no vol. and no mutual attraction betw. particles


•  Vol. of gas, # of gas particles, press. of gas, & temp. of gas are variables that depend on ea. other. – The # of particles in a vol. of gas depends on

the press. & temp. of the gas ∴ it’s necessary to give temp. & press. of gas

along w/ vol. when discussing quantity of a gas.


•  Standard Pressure - 101.325 kPa •  Standard Temp. - 0 oC •  STP - Standard temp. & press.

BOYLE’S LAW

•  Gas press. depends on 2 factors: 1. # of molecs. per unit volume 2. Avg. kinetic energy of the molecs - temp.

– A change in either will change the press. of a gas

BOYLE’S LAW

•  If the # of molecs. in a constant vol. incr., press. incr.

•  If # of molecs. & vol. remain constant, but K.E. of molecs. incr., press incr.

•  If temp. & # of molecs. remain constant, but vol. is decr., press. is incr.

BOYLE’S LAW

•  What happens when volume is decr. by half? –  press. doubles

•  same # of molecs. in 1/2 the volume •  molecs. hit the wall of container twice as often & w/

same force per collision

∴ @ constant temp., press. varies inversely as vol. –  the product of press. & vol. is constant

BOYLE’S LAW

•  BOYLE’S LAW - If the amt. & temp. of a gas remains constant, the press. exerted by the gas varies inversely as the vol. – PV = k

•  k - constant - takes into account # of molecs. & temp.

•  Press. varies directly w/ # of molecs.

APPLYING BOYLE’S LAW

•  Not all experiments can be carried out @ STP

•  In order to compare vols., we adjust them to standard conditions

•  V1P1 = V2P2 – V1, P1 - original conditions – P2, V2 - new conditions

Dalton’s Law of Partial Pressure

•  Gas is often obtained by bubbling it through water –  collecting gas over water or by water

displacement •  gases collected must be practically insoluble in

water – Water vapor will be present in the gas


•  Dalton’s Law of Partial Pressure - The total pressure in a container is the sum of the partial pressures of the gases in the container –  ea. gas exerts the same press. it would if it

alone were present @ the same temp. – Press. exerted by an indiv. gas in a mixture is

its Partial Pressure.


•  Air contains ~ 78% nitrogen ∴ 78% of press. is due to nitrogen

–  partial press. of N in air @ std. conditions is 78% x 101.325 = 79 kPa


•  If gas is collected over water, the press. in the container = the sum of the partial press. of the gas & the water vapor ∴ to find the press. of the gas alone (dry gas),

subtract the water vapor press. for that temp.

CHARLES’ LAW

•  Jacque Charles found a relationship betw. vol. & temp. – For ea. C o incr. in temp., the vol. of a gas is

incr. by 1/273 of its vol. @ 0 oC. •  Examples?

CHARLES’ LAW

•  Suggests that @ -273 oC (0 K) a gas will have no volume – Not true - all gases liquefy before this temp. –  relationship holds true only for gases

CHARLES’ LAW

•  CHARLES’ LAW - The vol. of a quantity of gas @ constant press. varies directly w/ the kelvin temp. –  experimental info led to formation of the

Kelvin Scale K = oC + 273 – Zero pt. of Kelvin scale is absolute zero –  triple pt. of water is 273.16 K

APPLYING CHARLES’ LAW

•  For a direct proportion, the quotient is constant

•  V/T = k •  Temperature must be in Kelvin •  If temp. goes up, vol. goes up •  V1 = V2 T1 T2

COMBINED GAS LAW

•  Usually need to correct for both temp. & press. of a gas – Can do this by applying Boyle’s Law, then

taking new vol. & putting it into Charles’ Law •  Can also be done in one step •  Temp. must be in Kelvin •  P1 V1 = P2 V2 T1 T2

Diffusion & Graham’s Law

•  Gas molecs. travel in straight lines betw. collisions –  If NH3 is opened in back of room, can soon be

detected in front of room. •  Molecs. travel from back to front of room in straight

lines betw. collisions –  collide w/ air molecs.


•  Diffusion - random scattering of gas molecs. –  as gas molecs. diffuse, they become more

evenly distributed throughout the room or container


•  All gases do not diffuse @ the same rate –  rate varies w/ velocity – @ same temp. molecs. w/ lower mass diffuse

faster than molecs. w/ larger mass bec. they travel faster.

•  They also pass thru a sm. hole - effuse - more rapidly than higher mass molecs.


•  @ the same temp: V1 = M2 V2 M1 ∴ relative rates of diffusion of 2 gases vary

inversely w/ the square root of their molecular masses


•  Graham’s Law - the relative rates @ which 2 gases under identical conditions of temp. & press. will diffuse vary inversely as the square roots of the molecular masses of the gases.

Gas Density

•  Usually expressed in g/dm3 •  May calculate density of a gas @ any temp.

& press. – A decr. in temp. will decr. vol. & incr. density – D2 = D1 x T1 x P2 T2 P1

Deviations of Real Gases

•  @ low press., real gases behave like ideal gases – molecs. are far apart - vol. molecs. occupy is

small compared to total vol. •  vol. is mostly empty space


•  @ higher press., real gas molecs. are forced closer together. – molecs. begin to occupy a significant portion of

total vol. –  If molecs. have slowed down enough, van der

Waals forces will have an effect.


∴ Assumption that there’s no attractive forces betw. gas molecs. is not always true. –  If gas molecs. are polar, gas behaves

significantly diff. than an ideal gas would •  weak forces will cause some diff.


•  For most common gases, ideal gas laws are accurate to 1% @ normal lab temps. & press. ∴ assume these gases have ideal gas properties •  He approaches ideal behavior closer than any other


•  A property of real gases which depends upon the attractive forces betw. molecs. –  Joule-Thomson Effect - If a highly

compressed gas is allowed to escape through a sm. opening, its temp. decr.

•  In order to expand, the molecs. must do work to overcome attractive forces betw. molecs.

–  this energy comes from their kinetic energy

∴ as K.E. decr., temp. decr.


•  This can be seen when spraying an aerosol can. – As product & propellant are released through

nozzel, can & contents become cooler •  Adiabatic System - a syst. completely

insulated so no heat exchange can take place w/ surroundings.

chapter 18kinetic theory of gases • vol. of gas, # of gas particles, press. of gas, & temp. of...

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