Unit 6: Gases Section 1: Combined Gas Law

Overview Gases provide the breath of life, inflate tires, power hot-air balloons, dissolve in our blood, heat our homes, inflate air bags, etc. Gases span from necessity to usefulness to extreme toxicity

Introduction Looks at how molecules of a gas behave  Kinetic molecular theory: the model for the action of gas molecules in a confined space Kinetic means moving, so the theory focuses on how gas molecules behave as a result of their motion Pressure, temperature, and volume are all factors that affect the behavior of gases

Pressure When the molecules of a gas in a container collide with the inside surfaces of the container, causing their speed and mass to push against the walls Atmospheric Pressure  Has weight and exerts pressure on everything  We don’t notice this pressure much because it’s the same inside and outside our homes, the same inside and outside our body, etc.  We notice the pressure change when riding on an airplane  Also known as barometric pressure Units of pressure  1 atm = 14.7 inches = 760 mm = 760 torr = 101,325 pascals

Temperature Measure of the speed at which molecules and atoms are moving  The higher the temperature, the faster the speed Units of temperature  Fahrenheit (ºF), Celsius (ºC), and Kelvin (K)  Gases uses the Kelvin temperature scale, since it’s based on the idea of absolute zero Absolute zero (0 K) is where all movement stops Temperature conversion  To change from ºC to K, add 273  To change from K to ºC, subtract 273

Volume Describes an amount of space Volume units include gallons, quarts, liters, cm 3, and ounces Can be either fixed or elastic  Fixed: volume is contained and has a definite shape Drink can, box, Tupperware  Elastic: volume can change Balloon, raft, basketball

Mathematical Approach to Gases Majority of gas behavior can be described mathematically by two equations: the combined gas law and the ideal gas law Combined gas law is used for situations involving change  P 1 V 1 = P 2 V 2 T 1 T 2 P = pressure V = volume T = temperature (in kelvins)

Combined Gas Law This equation can be used to consider just pressure and volume, just pressure and temperature, just volume and temperature, or all three, without having to remember different equations for each situation  P 1 V 1 = P 2 V 2  P 1 = P 2 T 1 T 2  V 1 = V 2 T 1 T 2  P 1 V 1 = P 2 V 2 T 1 T 2

Boyle’s Law Named after Robert Boyle, a 17 th century Irish scientist who studied the relationship between pressure and volume in gases, keeping temperature constant Boyle’s Law states that volume and pressure are inversely proportional  As volume increases, pressure decreases P 1 V 1 = P 2 V 2 Example: How many liters in size will a balloon become at a pressure of 700 mm if it has a volume of 4 liters at a pressure of 600 mm?  P 1 V 1 = P 2 V 2  (600 mm)(4 L) = (700 mm)(V 2 )  (600)(4) = V  3.43 L = V 2

Charles’ Law Named after Jacques Charles, an 18 th century French physicist who studied the relationship between temperature and volume with respect to gases, keeping pressure constant Charles’ Law states that temperature and volume are directly proportional  As temperature increases, volume increases V 1 = V 2 T 1 T 2 Example: What is the volume of a helium-filled balloon at 200 K if it has a volume of 8 L at 100 K?  V 1 = V 2 T 1 T 2  8 L = V K 200 K  (8)(200) = V 2 (100)  1,600 = 100 V 2  16 L = V 2

Gay-Lussac’s Law Gay-Lussac understood what happens to the pressure of an enclosed gas when heat is applied  Knew that intense pressure builds up as the gas molecules move faster and strike the walls of the container more often and with more force Gay-Lussac’s Law states that temperature and pressure are directly proportional  As temperature increases, pressure increases P 1 = P 2 T 1 T 2 Example: Calculate the pressure that results when the temperature becomes 100ºC if the pressure at 25ºC is 750 torr.  P 1 = P 2 T 1 T 2  750 = P 2 Convert ºC to K first!!!  P 2 = (750)(373) 298  P 2 = torr

Combination Theory Most real applications of gas theory involve varying the temperature, pressure, and volume P 1 V 1 = P 2 V 2 T 1 T 2 Example: What pressure is expected to develop at a volume of 10 L and a temperature of 25ºC if the volume is 5 L, the temperature is 50ºC, and the pressure is 30 inches of mercury?  P 1 V 1 = P 2 V 2 T 1 T 2  (30 inches)(5 L) = (P 2 )(10 L)  (30)(5) = (10)(P 2 )  (30)(5)(298) = (10)(P 2 )(323)  (30)(5)(298) = P 2 (10)(323)  inches = P 2