Particle motion in gases

Animations help us understand how particles interact

Moving particles Imagine we could see air particles moving around in a box. Each particle would be moving in a different random direction. Each time a particle hit the sides of the box they would exert a tiny force.

Pressure All of the particles in the box exert a force over the area of the inside of the box. The force divided by the area of the side of the box can be used to calculate the pressure of the gas.

Particles in a gas The particles in a gas move randomly in all directions. Their motion can be described by an average speed, but some will move slightly faster and some slightly slower. When each particle hits the walls of its container it will change direction, when this happens the particle exerts a tiny force on the wall of the container. The action of all of the particles hitting the walls of the container exerts a force over this area – this is a pressure and this is why we have gas pressure.

But how is kinetic energy related to temperature? Particles move; they have mass and speed, hence they must have kinetic energy – this much is easy! But how is kinetic energy related to temperature?

All particles move Temperature is a way of describing the kinetic energy of the particles around us. When we increase the temperature we are increasing the kinetic energy of the particles in a gas. When we increase the kinetic energy they must be going faster.

Particle movement Cool Hot

Kinetic energy of particles Tk KEave At absolute zero (0 K), particles cannot move any slower and so have the minimum kinetic energy possible.

Pressure The impact of the particles on the box creates the pressure of the gas. If the particles are moving faster there are more collisions and so more pressure in the gas.

What causes pressure in a gas? It  was also shown that the pressure the gas exerts is a measure of  the  number  of  times  per  second  that  the  molecules strike the walls of the container and the speed at which they strike it.  What happens to the pressure of a gas, if the temperature is increased? The gas gets hotter… …the gas particles have more kinetic energy… …there are more collisions at greater speed… …so the pressure of the gas increases.

Pressure and temperature

p1/T1 = p2/T2 (at a constant volume) For a fixed mass of a gas at a constant volume, the temperature (T) is directly proportional to the pressure (p). pressure (p/Pa) temperature/K The link between pressure and temperature can be written as an equation. If the pressure of a gas changes from p1 to p2, when the temperature changes from T1 to T2: p1/T1 = p2/T2 (at a constant volume) Pressure law

Pressure law- Example A compressed gas cylinder at a pressure of 300 kPa and room temperature of 22 ºC is heated in a fire to 300 ºC. Calculate the new pressure in the container. P1 / T1 = P2 / T2 T1 = 22 + 273 = 295 K T2 = 300 + 273 = 573 K P2 = (P1 / T1 ) × T2 P2 = (300,000  295) × 573 P2 = 583,000 Pa = 583 kPa

Relationship of P and V we will look at the relationship between changing values of volume and pressure. In this instance the temperature, mass and number of particles will remain the same.

Think about how the particles move

Smaller volume = more collisions First of all this experiment occurs when the temperature of the gas stays the same. If the temperature is the same then the kinetic energy of the particles is the same, which means that their speed remains the same. In a smaller volume there is less time between collisions of the particles and the walls of the container. More collisions means, more forces are exerted and this results in a greater pressure.

Boyles law apparatus Column of air Pressure gauge Foot pump to pressurise the oil Coloured oil makes it easier to see

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Manometer

Boyles law data 62 64 63 Pressure (Atm) Volume (cm3) Pressure × volume 3.1 20 2.7 23 2.2 28 1.6 39 1.3 48 1.1 58 1.0 63

Pressure versus Volume graph

Boyle’s law – Example A gas initially has a volume of 450 cm3 at a certain pressure. After a change the new pressure is 2.5 atm and the new volume is 250 cm3. What was the initial pressure ? P1 × V1 = P2 × V2 P1 × 450 = 2.5 × 250 P1 = (250 × 2.5)  450 P1 = 1.4 atm

Charles’s Law As the temperature of a gas increases, the volume increases proportionally, provided that the pressure and amount of gas remain constant, V1/T1 = V2/T2

How Volume Varies With Temperature If we place a balloon in liquid nitrogen it shrinks: So, gases shrink if cooled. Conversely, if we heat a gas it expands (as in a hot air balloon). Let’s take a closer look at temperature before we try to find the exact relationship of V vs. T.

Explanation in term of molecules By increasing T we increase the average energy of all the molecules. Yet, we are forcing the pressure to remain fixed, which must mean that the molecules are not colliding with the walls as often. So an increase in V is necessary to decrease the number of collisions per unit time

p1/T1 = p2/T2 (at a constant volume) The Ideal Gas Law PV=P1 × V1 = P2 × V2 = constant p1/T1 = p2/T2 (at a constant volume) V1/T1 = V2/T2=constant From combined gas law: P1V1/T1 = P2V2/T2 or PV/T = constant