The Gas Law Equations

Kinetic Molecular Theory We will use pressure instead of force to describe gases. This is because of the nature of gases which is described by the Kinetic Molecular Theory. 1. Gases are made of tiny particles. 2. These particles are always in high speed random motion.

Kinetic Molecular Theory Image by Becarlson 3. The particles of gas collide with the wall of their container without losing any momentum. The force of the gas that is exerted over the surface of the container is what we measure as pressure.

Which of the molecules below would have the greatest temperature? 4. The speed of these particles is related to the temperature of the system. Temperature is the measure of the average kinetic energy of the particles in a system. Which of the molecules below would have the greatest temperature? Warm Cold Hot

This temperature is known as absolute zero. Celsius and Kelvin are the temperature scales used by most scientists. While you are familiar with Fahrenheit, it is not a widely used scale for science. Since temperature is related to the motion of particles, the coldest possible temperature describes when all of the particles have stopped moving. This temperature is known as absolute zero. 5

Converting Between Temperature Scales Absolute Zero 0 K = -273 oC Kelvin = oC + 273 oC = K - 273 Important Fact: For EVERY gas law, your temperature must be reported in KELVIN! 6

Convert the temperatures on your notes between Celsius and Kelvin. Notice that for any given temperature, the Kelvin measurement is ALWAYS LARGER. 7

This is Dalton’s Law of Partial Pressures Sometimes more than one type of gas will be inside a container. Each one of these gases exerts part of the total pressure. If you add up each of the gases individual pressures, you will get the total pressure inside of a container. This is Dalton’s Law of Partial Pressures 8

Dalton’s Law of Partial Pressures What is the pressure inside a container if it contains neon gas at a pressure of 5 atm, helium gas at a pressure of 3 atm and nitrogen gas at a pressure of 1.5 atm? PTotal = 5 atm + 3 atm + 1.5 atm = 9.5 atm 9

Dalton’s Law of Partial Pressures A container holding neon, helium and nitrogen gas has a total pressure of 20.0 kPa. What is the partial pressure being exerted by helium if the neon gas exerts a pressure of 5.0 kPa and the nitrogen gas exerts a pressure of 1.5 kPa? 20.0 kPa = 5.0 kPa + 1.5 kPa + PHe 20.0 kPa – 5.0 kPa – 1.5 kPa = PHe PHe = 13.5 kPa 10

Complete the questions on your notes using Dalton’s Law of Partial Pressures. 11

Boyle’s Law Robert Boyle published his findings on the relationship between the pressure and volume of a gas in 1662. He determined that they were inversely proportional and behaved according to the equation found on your reference sheet.

Charles’ Law Jacques Charles discovered the relationship between the volume and temperature of a gas during the 1780s. He determined that they were directly proportional and behaved according to the equation found on your reference sheet.

Avogadro’s Law 1 mole 2 mole Amedeo Avogadro hypothesized the relationship between the volume and number of moles of a gas in 1811. He determined that they were directly proportional and behaved according to the equation found on your reference sheet.

= = Combined Gas Law P1 P2 n1 n2 150 kPa P2 (7.5)P2 = 1950 While the gas laws describe several relationships between variables, you may still need to derive a relationship from the combined gas law. P1 P2 n1 n2 = Example: 7.5 moles of helium gas are in a container at a pressure of 150 kPa. What would the pressure be if 13.0 moles were in a container with the same volume at the same temperature? 150 kPa P2 7.5 mol 13.0 mol = (7.5)P2 = 1950 P2 = 260 kPa 15

Complete the practice problems on your notes over the gas law equations. 16