Copyright Sautter 2003

THE KINETIC MOLECULAR THEORY

UNDERSTANDING SUBSTANCES ON A MOLECULAR LEVEL

WHAT IS THE DIFFERENT BETWEEN SOLIDS, LIQUIDS AND GASES ON A MOLECULAR LEVEL?

• THE ENERGY STATE OF THE MOLECULES

• SOLIDS CONTAIN THE LEAST ENERGY

• LIQUIDS ARE AT AN INTERMEDIATE ENERGY STATE

• GASES ARE AT THE HIGHEST ENERGY STATE

WHAT DOES ENERGY STATE MEAN AT A MOLECULAR LEVEL ?

• THE ENERGY CONTENT OF A MOLECULE RELATES TO THE TOTAL ENERGY OF ITS:

• (1) MOTION THROUGH SPACE (TRANSLATIONAL ENERGY)

• (2) SPINNING (ROTATIONAL ENERGY)• (3) “SPRINGINESS” OF BONDED ATOMS

(VIBRATIONAL ENERGY)• (4) MOTION OF THE ELECTRONS IT CONTAINS

(ELECTRONIC ENERGY)• AT A TEMPERATURE CALLED ABSOLUTE ZERO (-

273 DEGREES CELSIUS) NO ENERGY IS PRESENT IN THE SYSTEM (EXCEPT ELECTRONIC)

MOLECULAR MOTIONS• MOTION OF GAS MOLECULES (TRANSLATION, ROTATION & VIBRATION)

• MOTION OF LIQIUD MOLECULES (ROTATION & VIBRATION)

• MOTION OF SOLID MOLECULES (VIBRATION)

RANDOM MOTIONOF GAS MOLECULES

MOLECULES MOVE MOST RAPIDLY

IN THE GAS PHASE

THE KINETIC MOLECULAR THEORY PRIMARY DESCRIBES GASES

• THIS THEORY CONTAINS FIVE BASIC STATEMENTS ABOUT GASES MOLECULES AND HELPS US TO BETTER UNDERSTAND THE BEHAVIOR OF GASES

POSTULATES OF THE KMT(POSTULATES MEANS IDEAS OF PROPOSALS)

• (1) THE MOLECULES OF A GAS ARE IN CONSTANT, RANDOM, STRAIGHT LINE MOTION. AT ABSOLUTE ZERO (-273 DEGREES C) MOLECULAR MOTION CEASES. (RANDOM MEANS WITHOUT PATTERN, LIKE THE PING PONG BALLS IN THE LOTTO MACHINE)

• (2) TEMPERATURE MEASURES THE AVERAGE KINETIC ENERGY OF THE MOLECULES IN THE SYSTEM. (KINETIC ENERGY IS THE ENERGY OF MOTION. THE HIGHER THE TEMPERATURE THE FASTER THE AVERAGE MOLECULE IS MOVING HOWEVER, ALL THE MOLECULES ARE NOT MOVING AT THE SAME SPEED)

MORE ABOUT TEMPERATURE AND KINETIC ENERGY

• THE KINETIC ENERGY OF AN OBJECT IS RELATED TO ITS MASS AND ITS SPEED. LARGE, FAST MOLECULES HAVE MORE ENERGY THAN SMALL, SLOW ONES!

• HOWEVER, LARGE, SLOW MOLECULES CAN HAVE THE SAME ENERGY AS SMALL, FAST ONES. WHAT THE LARGE ONES LACK IN SPEED THEY MAKE UP FOR WITH MASS AND WHAT THE SMALL MOLECULES LACK IN MASS THEY MAKE UP FOR WITH SPEED. IN BOTH MASS AND SPEED COUNT KINETIC ENERGY!!

• IN ANY GAS AT A PARTICULAR TEMPERATURE THERE IS A DISTRIBUTION OF KINETIC ENERGIES. SOME MOLECULES HAVE LOW KINETIC ENERGY, SOME HAVE HIGH KINETIC ENERGY, MOST HAVE AN AVERAGE AMOUNT ! (THIS IS LIKE THE SPEED OF CARS ON A HIGHWAY, SOME TRAVEL FAST, SOME TRAVEL SLOWLY, MOST TRAVEL AT AN AVERAGE SPEED NEAR THE SPEED LIMIT !)

KINETIC ENERGY DISTRIBUTION CURVE

TEMPERATURE = T1

TEMPERATURE = T2

KINETIC ENERGY

NUMBER

OF

MOLES

TEMP 2 > TEMP 1AT HIGHER

TEMPERATURES, MOLECULES HAVE HIGHER ENERGIES

ON AVERAGE

POSTULATES OF THE KMT (CONT’D)

• (3) THE MOLECULES OF A GAS ARE SO TINY COMPARED TO THE SPACE THEY OCCUPY THAT THEIR VOLUME CAN BE CONSIDERED TO BE ZERO.(IN REALITY IT IS IMPOSSIBLE FOR ANY OBJECT TO HAVE ZERO VOLUME !)

• (4) THE MOLECULES OF A GAS NEVER ATTRACT EACHOTHER. (IN ACTUALITY, ALL MOLECULES ATTRACT EACHOTHER BUT IN GASES ONLY SLIGHTLY)

• (5) WHEN MOLECULES COLLIDE WITH EACHOTHER OR THE WALLS OF A CONTAINER THE COLLISIONS ARE PERFECTLY ELASTIC. THIS MEANS THAT ENERGY IS EVER LOST FROM THE SYSTEM DUE THE MOLECULES HITTING EACHOTHER OR THE CONTAINER WALLS. ENERGY OF MOTION IS MERELY TRANSFERRED BETWEEN MOLECULES

IDEAL GASES AND REAL GASES

• WHAT DOES THE WORD “IDEAL” MEANS ?• IDEAL – “PERFECT, OF HIGHEST

STANDARD”• IDEAL GASES THEN ARE THOSE THAT

CONFORM PERFECTLY TO THE POSTULATES OF THE KINETIC MOLECULAR THEORY. NO GAS IS IDEAL. AN IDEAL GAS IS A THEORETICAL GAS WHICH REAL DOESN’T EXIST !

IDEAL GASES AND REAL GASES (CONT’D)

• IF AN IDEAL GAS DOES NOT EXIST, WHY DO WE TALK ABOUT IT ?

• MANY GASES UNDER THE RIGHT CONDITIONS ACT SIMILARLY TO AN IDEAL GAS SO IT GIVES US A GOOD IDEA OF “REAL GAS” BEHAVIOR.

IDEAL GASES AND REAL GASES (CONT’D)

• A REAL GAS IS ONE THAT DOES NOT CONFORM EXACTLY TO THE KINETIC MOLECULAR THEORY AND DOES NOT FOLLOW THE GAS LAWS EXACTLY (THE GAS LAWS WILL BE DISCUSSED LATER)

IDEAL GASES AND REAL GASES (CONT’D)

• IN WHAT WAYS DO REAL GASES DIFFER FROM AN IDEAL GAS ?

• (1) IN REAL GASES THE MOLECULES DO HAVE A VOLUME. IN AN IDEAL GAS THE MOLECULES DON’T HAVE VOLUME

• (2) IN REAL GASES, THE MOLECULES ATTRACT EACHOTHER. IN IDEAL GASES THE MOLECULES HAVE ZERO ATTRACTION FOR EACHOTHER.

IDEAL GASES AND REAL GASES (CONT’D)

• AS A RESULT OF MOLECULAR VOLUME AND ATTRACTION, WHAT WILL REAL GASES DO THAT IDEAL GASES WILL NOT ?

• (1) REAL GASES WILL NOT GIVE ALL THE VALUES OF PRESSURE, TEMPERATURE AND VOLUME THAT ARE PREDICTED BY THE GAS LAWS

• (2) REAL GASES WHEN COOLED AND PRESSURIZED WILL CONDENSE TO LIQUIDS AND SOLIDS. AN IDEAL GAS WOULD NEVER CONDENSE BUT WOULD REMAIN A GAS TO ABSOLUTE ZERO AT WHICH POINT IT WOULD SHRINK TO ZERO VOLUME. (AN IMPOSSIBLE RESULT!)

No Gas is Ideal

real gases liquefy before

absolute zero

Volume

T

E

M

P

E

R

A

T

U

R

E

- 273 0C

Absolute Zero

An ideal gas would

shrink to zero volume

at absolute zero

WHAT IS PRESSURE AND WHAT CAUSES IT ?

• PRESSURE IS THE PUSH OF GAS MOLECULES ON THE WALLS OF A CONTAINER AS THEY BOUNCE OFF THE SURFACE. IT IS DEFINE AS FORCE DIVIDED BY AREA.

• IF MOLECULES HIT HARDER AND/ OR MORE OFTEN, THEY PUSH HARDER AND PRESSURE INCREASES.

WHAT MAKES MOLECULES HIT THE WALLS OF A CONTAINER HARDER AND / OR MORE OFTEN ?

• (1) INCREASING MOLECULAR SPEED (AS TEMPERATURE INCREASES, THE AVERAGE KINETIC ENERGY INCREASES AND MOLECULES MOVE FASTER)

• (2) SHORTER DISTANCES BETWEEN COLLISIONS WITH THE WALLS OF THE CONTAINER (IF THE VOLUME OF THE CONTAINER IS REDUCED, THE MOLECULES MOVE A SHORTER DISTANCE AND HIT THE WALL MORE FREQUENTLY)

• (3) MORE MOLECULES IN THE CONTAINER (MORE MOLECULES ALLOW MOLECULES TO STRIKE THE CONTAINER WALLS MORE OFTEN)

GRAHAM’S LAW OF DIFFUSION (ANOTHER APPLICATION OF THE KMT)

WHY DO MOLECULES OF SOME GASES MOVE FASTER THAN OTHERS AT THE SAME TEMPERATURE

?• GRAHAM’S LAW – AT ANY SPECIFIC TEMPERATURE, THE

SPEED OF A MOLECULE IS INVERSELY PROPORTIONAL TO ITS MASS (AS MASS INCREASES, MOLECULAR SPEED DECREASES)

• LIGHTER MOLECULES LIKE HELIUM MOVE MUCH FASTER THAN HEAVIER ONES LIKE CARBON DIOXIDE AT THE SAME TEMPERATURE.WHY ?

• BECAUSE AT THE SAME TEMPERATURE EACH GAS HAS THE SAME AVERAGE KINETIC ENERGY, WHAT HELIUM LACKS IN MASS IT MUST MAKE UP IN SPEED. THE MORE MASSIVE CARBON DIOXIDE CAN MOVE MORE SLOWLY AND STILL HAVE THE SAME KINETIC ENERGY AS THE HELIUM.

SUMMARY OF THE KINETIC MOLECULAR THEORY (KMT) AND ITS CONSEQUENCES

• TYPE OF ENERGY (1) TRANSLATIONAL (2) ROTATIONAL (3) VIBRATIONAL (4) ELECTRONIC

• FIVE POSTULATES OF KMT (1) CONSTANT, RANDOM MOTION (2) TEMPERATURE MEASURES AVERAGE KE (3) MOLECULES HAVE NO VOLUME (4) MOLECULES NEVER ATTRACT EACHOTHER (5) MOLECULAR COLLISIONS ARE ELASTIC

SUMMARY OF THE KINETIC MOLECULAR THEORY (KMT) AND ITS CONSEQUENCES

(CONT’D)

• PRESSURE = FORCE / AREA

• AS TEMPERATURE INCREASES, PRESSURE INCREASES

• AS VOLUME DECREASES, PRESSURE INCREASES

• AS THE NUMBER OF MOLES INCREASES, PRESSURE INCREASES

• AS TEMPERATURE INCREASES, AVERAGE MOLECULAR SPEED INCREASES

• AS MOLECULAR MASS INCREASES AT A GIVEN TEMPERATURE, THE AVERAGE MOLECULAR SPEED DECREASES

SUMMARY OF THE KINETIC MOLECULAR THEORY (KMT) AND ITS CONSEQUENCES

(CONT’D)

• AN IDEAL GAS CONFORMS EXACTLY TO KMT AND THE GAS LAWS

• REAL GASES ARE NOT DESCRIBED EXACTLY BY THE KMT AND THE GAS LAWS BECAUSE THEY HAVE MOLECULAR VOLUME AND ATTRACTIVE FORCES

• REAL GASES WILL FORM LIQUIDS AND SOLIDS UPON COOLING. AN IDEAL GAS NEVER WOULD CONDENSE.

UNDERSTANDING THE KINETIC MOLECULAR THEORY WILL GREATLY

INCREASE YOUR UNDERSTANDING OF THE GAS LAWS AND CHEMISTRY IN GENERAL !!