Section 3 Behavior of Gases

Essential Questions How does a gas exert pressure on its container? How is a gas affected when pressure, temperature, or volume change?

Review Vocabulary temperature: a measure of the average kinetic energy of all the particles in an object

New Vocabulary Boyle’s law Charles’s law

What is Pressure? Pressure = Force/Area When a gas particle strikes the walls of the container, The force it exerts applies pressure to the container. The sum of all of the forces exerted by all of the collisions of particles with the walls of the container is the pressure of that gas. The SI unit of pressure is the Pascal or kilopascal (Pa or kPa) A more common unit of pressure is the standard atmosphere (atm) Which is the pressure exerted by the atmosphere at sea level. (atmospheric pressure).

What is the Kinetic Theory of Gases? Kinetic means motion! As in Kinetic Energy! Gases are composed of particles in constant, rapid motion. The particles exert pressure when they collide with the walls of the container. When the kinetic energy (speed) of the particles increase, the force of the collisions increase so the pressure increases The Kelvin temperature of the gas is directly proportional to the kinetic energy of the gas.

What is Temperature? Temperature may be thought of as a measure of the kinetic energy of the particles in a system. There are three common temperature scales: Farenheit, Celsius and Kelvins. Specifically, the Kelvin temperature is proportional to the average kinetic energy of the particles in a system. If you double the Kelvin temperature, you double the average kinetic energy.

Why Kelvins? As an object is cooled, kinetic energy is being removed from the particles it is Composed of, so the particles slow down. Once all of the kinetic energy has been removed, the particles will come to rest so There is no more energy left to remove. This Is as cold as a system can get! Wouldn’t it make sense to have a temperature scale where the coldest Possible temperature one can achieve is ‘0’? In addition to the convenient relationship between the Kelvin temperature and The average kinetic energy, Kelvins eliminate other problems that arise from Negative temperature values we shall see later.

Here are three thermometers representing the three temperature scales. The freezing and boiling points of water are shown such that each represents The same amount of ‘hotness’ or ‘coldness’. When we label the Kelvin thermometer with a ‘0’ at absolute zero, then stack Celsius degrees on top until we reach the freezing point of water, we find that water freezes at 273 Kelvins* (or 0 oC ). So to convert between degrees Celsius and Kelvins the formula is K = oC + 273 * It is actually incorrect to say “degrees Kelvin” like we would say “degrees Farenheit or Celsius”!

Boyle’s Law–Volume and Pressure According to Boyle’s law, if you decrease the volume of a container of gas and hold the temperature constant, the pressure from the gas will increase. An increase in the volume of the container causes the pressure to drop, if the temperature remains constant.

Charles’s Law—Temperature and Volume If you’ve watched a hot-air balloon being inflated, you know that gases expand when they are heated. Jacques Charles (1746– 1823), a French scientist, also noticed this. According to Charles’s law, the volume of a gas increases with increasing temperature, as long as the pressure on the gas does not change. As with Boyle’s law, the reverse is also true. The volume of a gas shrinks with decreasing temperature, as shown at the right.

Applications 1. Convert 25oC to Kelvins. Write the formula: K = oC + 273 So, K = 25oC + 273 and K = 298 2. Convert 335 Kelvins to degrees Celsius Write the formula: K = oC + 273 So, 335 = oC + 273 and oC = 335 – 273 = 62oC

Now you try, 3. Convert -45oC to Kelvins Answer = 228 K 4. Convert 200 K to oC Answer = -73oC

IF a gas occupies 25 L in a weather balloon at 1 atm pressure, what volume would it occupy at 5 atm pressure? Write the formula: P1V1 = P2V2 Identify your variables: P1 = 1 atm V1= 25 L P2= 5 atm V2= ? V2 = P1V1/P2 Rewrite the equation for the unknown: V2 = 1 atm x 25 L Now “plug and chug”: = 5 L 5 atm

6. If a gas occupies 2.5 L in a weather balloon at 25oC, what volume would it occupy at 75oC? Write the formula: V1/T1 = V2/T2 Identify your variables: V1 = 2.5 L = 298 K T1= 25oC V2= ? T2= 75oC = 348 K Don’t forget to convert temperatures to Kelvins!!!!! V2 = V1T2/T1 Rewrite the equation for the unknown: V2 = 2.5 L x 348 K = 2.9L Now “plug and chug”: 298 K

Now you try: If a gas exerts 5.0 atm pressure in a 2.0 L cylinder, what pressure would it exert if the volume is increased to 10.0 L? Answer: 1.0 atm If a gas occupies 2.5 L in a weather balloon at 25oC was allowed to float into the upper atmosphere where the temperature was -20oC, what would the new volume be? Answer: 2.9 L What impossible result would you get if you forgot to convert your temperatures to Kelvins?

Assessment 1. Which uses Bernoulli’s principle? hose-end sprayer CORRECT skateboard B piston C snowboard D