the kinetic theory of gases

how does the development of the gas laws differ from that of the kinetic theory?

* gas laws are empirical so developed from experiments on gas
* kinetic theory was developed from theory so models of gas

state the assumptions made in the kinetic theory

* gases are made up of large numbers of small particles called molecules
* volume of molecules is negligible compared to volume of gas
* molecules move in continual random motion
* molecules move in straight lines between collisions
* all collisions are elastic
* time spent in collisions in negligible compared to time spent between collisions

how do you calculate root mean square speed

* calculate the mean of the SQUARED values
* then square root that mean

derive the kinetic theory equation

1. set up
* assume gas container is a cube of side length l
* in container is ideal gas made up of N molecules each with m mass and speed cₙ
* molecules move only in x, y, or z direction with a 1/3 in each
2. change in momentum of one molecule
* (mc₁)-(-mc₁) = 2mc₁
3. time between collisions
* time = distance ÷ speed = 2l ÷ c₁
4. average force of one molecule
* force = change in mom ÷ time = 2mc₁ ÷ (2l÷c₁) = m(c₁)²÷l
5. area of the wall
* l x l =l²
6. pressure of one molecule on wall
* pressure = force÷area = m(c₁)²÷l ÷ l² = m(c₁)²÷l³
* l³ = V so pressure = m(c₁)²÷V
7. pressure
* multiply by N since there are N molecules
* divide by 3 since only 1/3 are moving in the x direction
* change c₁ to cᵣₘₛ

why can kinetic gas theory be used to predict how gases work in reality?

because when you sub the average kinetic molecular energy into the kinetic theory model equation, you get the gas law equation

what is Brownian motion?

caused by collisions between air molecules and smoke particles

can conclude:

* motion of air molecules is random
* air molecules are much smaller than smoke particles

explain why increasing T increases P

* increase in temperature causes average kinetic energy of each molecule to increase
* average speed and average momentum of molecules increases
* so collisions between the molecules and the walls are more frequent and result in a greater change in momentum
* so the force imparted on the walls increases while area stays the same
* as pressure = force÷area, pressure increases

explain why decreasing V increases P

* decreasing V means less space for molecules to move around in
* this means collisions between molecules and walls occur more frequently
* so more force imparted on the walls
* pressure = force/area