X Unit 13 – GAS LAWS

Importance of Gases  Airbags fill with N 2 gas in an accident.  Gas is generated by the decomposition of sodium azide, NaN 3 according to the reaction: 2 NaN 3 ---> 2 Na + 3 N 2

Properties of Gases Gas properties are affected by certain variables. Those variables are: 1. V = volume of the gas (L) 2. T = temperature (Kelvin, K) 3. n = amount (moles) 4. P = pressure (atmospheres, atm) STP = Standard Temperature and Pressure 0 °C (273 K) and 1 atm

Pressure of a Gas  SI unit of pressure: pascal (Pa)  Other common pressure units:  Millimeters of mercury (mm Hg)  Atmospheres (atm) 1 atm = 760 mmHg = kPa = 760 torr  Other common units: psi, bar, N/m 2, etc.

Example #1: Practice Converting Units 1 atm = 760 mmHg = kPa A tire pressure gauge records a pressure of 450 kPa. What is the pressure in atmospheres? In mm Hg?

Example #1: Practice Converting Units 1 atm = 760 mmHg = kPa A tire pressure gauge records a pressure of 450 kPa. What is the pressure in atmospheres? In mm Hg?

RELATIONSHIP BETWEEN PRESSURE AND VOLUME Boyle’s Law

Boyle’s Law Demos Popping a balloon  As you squeeze the balloon, what happens to the pressure and volume inside the balloon?  Are pressure and volume directly proportional or inversely proportional? P V

Boyle’s Law Demos Marshmallow/balloon in a vacuum  As we evacuate the chamber, what do you think will happen to the pressure? What do you think will happen to the volume of the marshmallow?  Are P and V directly or inversely proportional? Video Clip Marshmallows in a Vacuum P V

Boyle’s Law in Real Life For homework tonight, think of something in real life that illustrates Boyle’s Law in action. It can be anything that shows the inverse relationship between pressure and volume! Fill in this example in the blank spot in your notes!!

Boyle’s Law When temperature is held constant, pressure and volume increase and decrease as opposites (they are inversely proportional)  If pressure increases, volume decreases  If pressure decreases, volume increases P 1 V 1 = P 2 V 2

Example #2 Nitrous oxide (N 2 O) is used as an anesthetic. The pressure on 2.50 L of N 2 O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be? P 1 V 1 = P 2 V 2 P 1 = V 1 = P 2 = V 2 =

Example #3 At room temperature, L of a gas is found to exert 97.0 kPa. What pressure (in atm) would be required to change the volume to 5.00 L? P 1 V 1 = P 2 V 2 P 1 = V 1 = P 2 = V 2 = 1 atm = kPa

CHARLES’ LAW: Relating Volume and Temperature

Charles’ Law Demos  Balloons popping when kept outdoors  As the balloons sits outside, what happens to the temperature of the gas inside the balloon? What happens to the volume of the balloon?  Are volume and temperature directly proportional or inversely proportional? V T

Charles’ Demos  Liquid Nitrogen demo video Liquid Nitrogen demo video  When the balloon is placed in the liquid nitrogen, what happened to the temperature of the gas inside the balloon? What happened to the volume?  Are volume and temperature directly or inversely proportional? V T

Charles’s Law in Real Life For homework tonight, think of something in real life that illustrates Charles’s Law in action. It can be anything that shows the directly proportional relationship between volume and temperature! Fill the blank spot in your notes with your example!

Charles’ Law  If pressure is held constant (doesn’t change), volume and temperature increase or decrease together (they are directly proportional)  If volume increases, so does the temperature  If temperature decreases, so does the volume Temperatures must be in Kelvin!!!!

Example #4 A balloon inflated in a room at 24 °C has a volume of 4.00 L. The balloon is then heated to a temperature of 58 °C. What is the new volume if the pressure remains constant? V 1 = T 1 = V 2 = T 2 =

Example #5 Exactly 5.00 L of air at -50 °C is warmed until the volume is 8.36 L. What temperature is the system warmed to? V 1 = T 1 = V 2 = T 2 =

Gay-Lusaac’s Law: The Relationship Between Pressure and Temperature

Gay-Lusaac’s Law Demo Egg and flask demo  When the boiling water gets dumped goes out, what happens to the temperature of the gases inside the flask?  Do the gas particles have more kinetic energy or less? Are they creating more pressure or less? Are pressure and temperature directly or inversely proportional? P T

Gay-Lusaac’s Law in Real Life For homework tonight, think of something in real life that illustrates Gay-Lusaac’s Law in action. It can be anything that shows the directly proportional relationship between pressure and temperature! Fill this in as the second example in your notes!

Gay-Lusaac’s Law If volume is held constant, pressure and temperature increase and decrease together (they are directly proportional)  If pressure increases, so does the temperature  If temperature decreases, so does the pressure Temperatures still must be in Kelvin!!!!

Example #6 The gas in a used aerosol can is at a pressure of 103 kPa at 25 ºC. If the can is thrown onto a fire, what will the pressure be when the temperature reaches 928 ºC? P 1 = T 1 = P 2 = T 2 =

Example #7: A L sample of a gas is found to exert 97.0 kPa at 25 ºC. What temperature (in celsius) would be required to change the pressure to 1.00 atm? P 1 = T 1 = P 2 = T 2 =

The Combined Gas Law Taking Into Account Pressure, Volume, AND Temperature

In Review Boyle’s Law looked at which 2 factors? Charles’ Law? Gay Lusaac’s?

Imploding Can Demo What happened to the volume of the can? What happened to the temperature of the gas inside the can? How did pressure play a role in the can imploding?

The Combined Gas Law The combined gas law considers the effect of all 3 factors at the same time All 3 of the gas laws can be derived from the combined gas law

Example – Boyle’s Law from Combined Gas Law If temperature is constant, T 1 = T 2 Rearrange the equation to get both temperatures together

Example #8 A 200 mL sample of gas is collected at 50 kPa and a temperature of 271°C. What volume would this gas occupy at 100 kPa and a temperature of -14°C?

Example #9 Helium in a 100 mL container at a pressure of 66.6 kPa is transferred to a container with a volume of 250 mL. What is the new pressure if the temperature changes from 20°C to 15°C?

Example #10 A certain sample of gas has a volume of L measured at 87°C and atm. What is its volume at 740 mmHg and 0°C?

The Ideal Gas Law P, V, T, and n

The Combined Gas Law  Takes into account P, T, and V but not the amount of gas present Amount of gas = moles of gas present (n)

 Takes into account all 4 variables – pressure (P), volume (V), temperature (T), AND the amount of moles (n) The Ideal Gas Law

IDEAL GAS LAW P = pressure V = volume n = # of moles R = Ideal gas constant T = temperature (in Kelvin) P V = n R T

Ideal Gas Constant (R) R : Ideal Gas Constant You must make sure the units in the constant match up with the units you plug into the Ideal Gas Law (PV = nRT)!!!

Example #11 How many moles of gas are in a sample occupying 12 L at a temperature of 15˚C and a pressure of 2.4 atm? PV = nRT

The Ideal Gas Law  Once you calculate the moles of gas you can convert this to a mass (in grams, kilograms, etc.) using what?  You may also be given the amount of gas in grams and have to convert it to moles in order to plug into the ideal gas law

Example #12 What is the volume occupied by 36.0 grams of water vapor at 125  C and 102 kPa? PV = nRT

Example #13 What mass of carbon dioxide will occupy 5.5 L at 5  C and 0.74 atm? PV = nRT

Example #14 A deep underground cavern contains 2.24 x 10 6 L of methane gas (CH 4 ) at a pressure of 1500 kPa and a temperature of 315 K. (a) How many moles of CH 4 does the cavern contain? (b) How many kilograms does the cavern contain? PV = nRT

Ideal Gases vs. Real Gases  Ideal Gas – a gas which behaves according to the gas laws and KMT at all pressures and temperatures Gas particles have no volume and no attraction to one another  No such thing as an ideal gas; just real gases which behave like ideal gases under certain conditions

Deviations from Ideal Gas Law (Real Gases) The ideal gas law is a great tool for most gases. However, the ideal gas laws ignores these two facts: 1. Real molecules have volume. 2. There are attractive forces between molecules. These factors become relevant at HIGH pressures and LOW temperatures! (In general, the closer a gas is to the liquid state, the more it will deviate from the Ideal Gas Law)

Deviations from Ideal Gas Law Deviations from Ideal Gas Law At High Pressures: (a) At low pressures, the volume occupied by the molecules themselves is negligible compared to the volume of the container. (b) At high pressures, the molecules occupy a large portion of the volume of the container, resulting in significantly decreased space in which the molecules can move & increased attraction.

Deviations from Ideal Gas Law Deviations from Ideal Gas Law At Low Temperatures: Molecules are not moving as fast (they have less kinetic energy) and they cannot overcome the attractive intermolecular forces. This results in gases being liquefied. Liquefied Natural Gas Halon Fire Extinguishers