Unit 14 Gas Laws

Properties of Gases Gas properties can be modeled using math. Model depends on— 1.V = volume of the gas (L) 2.T = temperature (Kelvin, K) 3.n = amount (moles, mol) 4.P = pressure (atmospheres, atm)

STP STP = standard temperature and pressure Standard temperature = 0°C = 273 K Standard pressure = 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

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 in Real Life 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 in Real Life Operating a water gun/syringe  As you pull back on the plunger, are you increasing or decreasing the volume? How does the pressure change?  Are P and V directly or inversely proportional? P V

Boyle’s Law in Real Life 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? 400 Marshmallows in a Vacuum P V

Boyle’s Law When temperature is held constant, pressure and volume increase and decrease as opposites Pressure & volume are inversely or indirectly related  If pressure increases, volume decreases  If pressure decreases, volume increases P 1 V 1 = P 2 V 2

Practice with Boyle’s Law A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume temperature is held constant) P 1 V 1 = P 2 V 2 P 1 = V 1 = P 2 = V 2 =

Practice with Boyle’s Law 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

Practice with Boyle’s Law 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 =

CHARLES’ LAW: Relating Volume and Temperature

Charles’ Law in Real Life  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’ Law in Real Life  A ball outside on a cold day  You pump the ball up indoors. After going outside where it’s colder, what happens to the volume of the ball?  Are volume and temperature directly or inversely proportional? V T

Charles’ Law in Real Life  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’ Law  If pressure is held constant (doesn’t change), volume and temperature increase or decrease together  If volume increases, so does the temperature  If temperature decreases, so does the volume ***T must be in Kelvin!!!

Practice with Charles’ Law  A balloon inflated in a room at 24 ºC has a volume of 4.00 L. The balloon is then heated to a temperature of 58 ºC. What is the new volume if the pressure remains constant? V 1 = T 1 = V 2 = T 2 =

Practice with Charles’ Law  Exactly 5.00 L of air at -50 ºC is warmed to some temperature so that the volume was 8.36 L. What temperature was the system warmed to? V 1 = T 1 = V 2 = T 2 =

Practice with Charles’ Law  A 50.0 mL sample of a gas is cooled from 119 ºC to 353 K. If the pressure remains constant, what is the final volume of the gas? V 1 = T 1 = V 2 = T 2 =

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

Gay-Lusaac’s Law in Real Life Warnings on aerosol cans  What do the warnings say regarding putting them near flames?  As the temperature of the can increases, what happens to the pressure in the can? Are pressure and temperature directly or inversely proportional? P T

Gay-Lusaac’s Law in Real Life Warm soda fizzing vs. cold soda fizzing  When opened, which one fizzes more, cold soda or warm soda?  Does more fizzing mean there was higher pressure inside or lower pressure? Are pressure and temperature directly or inversely proportional? P T

Gay-Lusaac’s Law in Real Life 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 If volume is held constant, pressure and temperature increase and decrease together  If pressure increases, so does the temperature  If temperature decreases, so does the pressure

Practice with Gay-Lusaac’s Law 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 =

Practice with Gay-Lusaac’s Law A sample of nitrogen has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K? P 1 = T 1 = P 2 = T 2 =

Practice with Gay-Lusaac’s Law 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

Examples with Combined Gas Law A 200 mL sample of gas is collected at 50 kPa and a temperature of 271 o C. What volume would this gas occupy at 100 kPa and a temperature of -14 o C?

Examples with Combined Gas Law 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 o C to 15 o C?

Examples with Combined Gas Law A certain sample of gas has a volume of L measured at 87 o C and atm. What is its volume at 1 atm and 0 o 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)  R = = = The Ideal Gas Law Ideal Gas Constant

Sample Problem – Ideal Gas Law How many moles are in a sample of gas 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

Sample Problem – Ideal Gas Law What is the volume occupied by 36.0 grams of water vapor at 125  C and 102 kPa? PV = nRT

Sample Problem – Ideal Gas Law What mass of carbon dioxide will occupy 5.5 L at 5  C and 0.74 atm? PV = nRT

Sample Problem – Ideal Gas Law 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

Ideal Gases vs. Real Gases  Real gases behave like ideal gases under the following conditions: At high temperature At low pressure When the gas itself has small, non-polar molecules Why??