The Gas Laws Chapter 13

Kinetic Molecular Theory Gas molecules behave differently than those of solids and liquids. To explain their behavior, the Kinetic Molecular Theory provides a model and a special set of assumptions about gases. 1. Gas particles do not attract or repel each other.

Kinetic Molecular Theory 2. Gas particles are much smaller than the distances between them. This is why gases are compressible.

Kinetic Molecular Theory 3. Gas particles are in constant, random motion and they quickly become thoroughly mixed in a closed container. This phenomena is called dispersion and is the reason why women wear perfume and men wear cologne. When a person with Channel or Axe enters a room, it doesn’t take long before everyone looks around to see where the smell is coming from.

Kinetic Molecular Theory 4. Collisions between gas particles or the sides of their containers are completely elastic. There is no kinetic energy lost.

Kinetic Molecular Theory 5. All gases have the same average kinetic energy at a given temperature.

The Nature of Gases The assumptions of the Kinetic Molecular Theory are based on 4 variables: Temperature Pressure Volume The Number of Gas Particles Present These four variables work together to determine the behavior of gases and when one variable changes, it affects the other three. Also, the explanations as to what happens when one of the variables changes is explained by the Gas Laws

The Gas Laws There are five gas laws that we will study: Boyle’s Law – Pressure/Volume Charles’ Law – Volume/Temperature Gay-Lussac’s Law – Pressure/Temperature Combined Gas Law – Pressure/Volume/Temperature Graham’s Law of Diffusion – MM/Diffusion Rate

Boyle’s Law In the 1600’s Robert Boyle determined that if the pressure on a volume of gas was doubled, the volume of gas decreased by half. More precisely, Boyle’s Law states that the volume of a gas varies inversely with the pressure, provided the temperature and the number of air particles do not change.

Ouch! I hate when my ears pop!! Boyle’s Law explains why we need to wear oxygen at high elevations. There is less pressure the higher we are and as a result, fewer oxygen molecules to breathe. Also, Boyle’s Law explains why our ears pop when we go up in an elevator or airplane. The pressure in our middle ear must be equalized as the air pressure is decreased.

Measurement of Air Pressure Air pressure is measured using several different systems: 1. The Non SI System of pressure is pounds per square inch (psi) 2. The Metric System of pressure is the kilopascal (kPa) 3. The Non SI System Meteorologists use is inches of mercury (inHg) 4. The Metric System of pressure uses mm of mercury (mmHg) All of these systems are based on the pressure the atmosphere exerts at sea level which is the atmosphere (atm).

STP To ensure uniformity worldwide in the measurement and calibration of pressure, a set of standard conditions called STP (Standard Temperature and Pressure) has been established as One Atmosphere @ 0°C. However, in recent years there has been a departure from STP by different scientific disciplines. Whenever pressure measurements are stated, the standard that is used must be referenced.

Pressure System Measurements These are the equivalents between the different pressure system measurements: @ STP One Atmosphere = 14.7 psi @ STP One Atmosphere = 101.3 kPa @ STP One Atmosphere = 29.92 inHg @ STP One Atmosphere = 760 mmHg

Boyle’s Law Calculations Now that you have an understanding of pressure systems let’s get back to Boyle’s Law. Since Boyle’s Law is an inverse relationship (increase the pressure, decrease the volume) the formula is: P1V1 = P2V2 A typical Boyle’s Law Problem would look like this: If a gas occupies 2 L at 1 atm, what will be the volume of this gas at 4 atm? (2L)(1 atm) = (4 atm)V2 V2 =

Boyle’s Law Calculations The greatest difficulty students have with Boyle’s Law is moving from one pressure system to another. Look at this problem. Notice that there are two different pressure systems (kPa and psi). The system must have the same units on each side of the equation, so you must change either kPa or psi. A gas occupies a volume of 5 L at 100 kPa. What volume will it occupy at 100 psi? 100 psi x 101.3 kPa = 689.1 kPa 14.7 psi P1V1 = P2V2 (5 L)(100 kPa) = (689.1 kPa)V2 V2 = .752 L