X Unit 14 – GAS LAWS

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?

RELATIONSHIP BETWEEN PRESSURE AND VOLUME Boyle’s Law

Boyle’s Law Demos Pushing a syringe  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? P V

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  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  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 to some temperature so that the volume was 8.36 L. What temperature was the system warmed to in °C? V 1 = T 1 = V 2 = T 2 =

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

Gay-Lusaac’s Law Tire Pressure in the Winter  Think about what happens to your tire pressure on the first cold day of winter…  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 (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 #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