Kinetic Molecular Theory Making Macroscopic Sense out of

Kinetic Molecular Theory Making Macroscopic Sense out of a Microscopic World

What is Kinetic Theory? • Explains what causes pressure. • Explains WHY the individual gas laws are true. • Is theory behind the mathematics of the Ideal Gas Law. • Makes some assumptions…this is why it is called the Ideal Gas Law.

The Tenets of Kinetic Theory • Gases consist of large numbers of molecules moving randomly. • These molecules have negligible volume compared to the container. • The attractions and repulsions between molecules is negligible. • All collisions are elastic. • Average kinetic energy of the molecules is related to the absolute temperature.

Large Numbers of Random Motion • This must be true for statistics reasons. • This means that there are constant collisions with each other and the side of the container. • These collisions exert a force on the container. We call it pressure!!!

Pressure Defined • If pressure is the force per area of these collisions, then what happens if we increase the number of collisions? • How can we do that? – Increase the number of molecules (P~n) – Decrease the area for collisions (P~1/V) • This is exactly what we observe!

Volume is Negligible • The molecules must be thought of as points in space. • It throws off the physics calculations. • Besides, molecules are really small anyway!

Interactions are Negligible • The basis of theory is on collisions. • If outside forces are involved, it throws off the physics calculations. • Gases are really far apart anyway and attractions and repulsions decrease with distance.

Collisions are Elastic • In physics, this means that no energy is lost when things collide. • If this were not true, gases would lose energy during collisions. • This would make the gas freeze on its own!!

Temperature is Defined • If temperature is defined as the average kinetic energy of all the molecules, what would be effect of increasing the temperature on the pressure? • More intense collision would result in more force and an increase in pressure (P~T)

Average Kinetic Energy • Not all molecules are going the same speed! • It is like a freeway. • Since there are lots of them, this is a special statistical state called “normal. ”

Speed and Kinetic Energy • Kinetic Energy = ½ mass * velocity 2 • If KE is constant and mass goes up, velocity must go down by the square root • If mass is the same, velocity is higher for things with higher kinetic energy. • Kinetic Energy is related to temperature! • Temperature measures molecular speed!

Some Examples • In light of KMT, why will an increase in the number of molecules increase the pressure? • In light of KMT, why will a decrease in temperature create a decrease in pressure? • In light of KMT, who is moving faster, H 2(g) or CO 2(g) at STP?

What if the Theory is NOT Right? • We did make assumptions… – Volume is negligible – Attractions/repulsions are negligible • Are these true!? – So there will be some error in what we base off of Kinetic Theory. • What law is based on KMT?

The Real (Non-Ideal) Gas Law • We must correct for the assumptions made: – Volume is NOT negligible – Attraction/repulsions are NOT negligible • n. RT P= V – nb n 2 a Corrects for the attractions and Repulsions between molecules. V 2 Corrects for the volume of the molecules.

Why don’t we use this then? . . . • It is definitely more accurate, but the amount of accuracy gained for the math involved is not beneficiary. • Especially at normal conditions, the Ideal Gas Law gives sufficient accuracy.

So when should we use it? • When the tenets that fail are no longer negligible. – When is volume of molecules not negligible? • When the volume of container is small or there are lots of molecules. – So at large n values and small V values! – When are the interactions not negligible? • When the molecules are moving slowly and are close together. – So at small T values and large P values.