X Unit 14 GAS LAWS Properties of Gases

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X Unit 14 – GAS LAWS

X Unit 14 – GAS LAWS

Properties of Gases Gas properties are affected by certain variables. Those variables are: STP

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

Pressure of a Gas SI unit of pressure: pascal (Pa) Other common pressure units:

Pressure of a Gas SI unit of pressure: pascal (Pa) Other common pressure units: Millimeters of mercury (mm Hg) Atmospheres (atm) 1 atm = 760 mm. Hg = 101. 3 k. Pa = 760 torr Other common units: psi, bar, N/m 2, etc.

Example #1: Practice Converting Units 1 atm = 760 mm. Hg = 101. 3

Example #1: Practice Converting Units 1 atm = 760 mm. Hg = 101. 3 k. Pa A tire pressure gauge records a pressure of 450 k. Pa. What is the pressure in atmospheres? In mm Hg?

Boyle’s Law RELATIONSHIP BETWEEN PRESSURE AND VOLUME

Boyle’s Law RELATIONSHIP BETWEEN PRESSURE AND VOLUME

Boyle’s Law Demos Pushing a syringe As you squeeze the balloon, what happens to

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

Boyle’s Law Demos Marshmallow/balloon in a vacuum As we evacuate the chamber, what do

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? P Are V P and V directly or inversely proportional?

Boyle’s Law When temperature is held constant, pressure and volume increase and decrease as

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

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 k. Pa to 40. 5 k. Pa. 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, 10. 01 L of a gas is found to

Example #3 At room temperature, 10. 01 L of a gas is found to exert 97. 0 k. Pa. 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 = 101. 3 k. Pa

CHARLES’ LAW: Relating Volume and Temperature

CHARLES’ LAW: Relating Volume and Temperature

Charles’ Law Balloons popping when kept outdoors As the balloons sits outside, what happens

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? V T Are volume and temperature directly proportional or inversely proportional?

Charles’ Law If pressure is held constant (doesn’t change), volume and temperature increase or

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

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

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: The Relationship Between Pressure and Temperature

Gay-Lusaac’s Law l Tire Pressure in the Winter Think about what happens to your

Gay-Lusaac’s Law l 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? P T l Are pressure and temperature directly or inversely proportional?

Gay-Lusaac’s Law l If volume is held constant, pressure and temperature increase and decrease

Gay-Lusaac’s Law l 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 l The gas in a used aerosol can is at a pressure

Example #6 l The gas in a used aerosol can is at a pressure of 103 k. Pa 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: l A 10. 01 L sample of a gas is found to

Example #7: l A 10. 01 L sample of a gas is found to exert 97. 0 k. Pa 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

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

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

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

Imploding Can Demo l What happened to the volume of the can? l What

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

The Combined Gas Law l The combined gas law considers the effect of all

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

Example #8 A 200 m. L sample of gas is collected at 50 k.

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

Example #9 Helium in a 100 m. L container at a pressure of 66.

Example #9 Helium in a 100 m. L container at a pressure of 66. 6 k. Pa is transferred to a container with a volume of 250 m. L. 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 0. 452 L

Example #10 A certain sample of gas has a volume of 0. 452 L measured at 87°C and 0. 620 atm. What is its volume at 740 mm. Hg and 0°C?

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

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

The Combined Gas Law o Takes into account P, T, and V but not

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

The Ideal Gas Law o Takes into account all 4 variables – pressure (P),

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

IDEAL GAS LAW P V = n R T P = pressure V =

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

Ideal Gas Constant (R) R: Ideal Gas Constant • 0. 0821 • 8. 314

Ideal Gas Constant (R) R: Ideal Gas Constant • 0. 0821 • 8. 314 You must make sure the units in the constant match up with the units you plug into the Ideal Gas Law (PV = n. RT)!!!

Example #11 How many moles of gas are in a sample occupying 12 L

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 = n. RT

The Ideal Gas Law o Once you calculate the moles of gas you can

The Ideal Gas Law o Once you calculate the moles of gas you can convert this to a mass (in grams, kilograms, etc. ) using what? o 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

Example #12 What is the volume occupied by 36. 0 grams of water vapor at 125 C and 102 k. Pa? PV = n. RT

Example #13 What mass of carbon dioxide will occupy 5. 5 L at 5

Example #13 What mass of carbon dioxide will occupy 5. 5 L at 5 C and 0. 74 atm? PV = n. RT

Example #14 A deep underground cavern contains 2. 24 x 106 L of methane

Example #14 A deep underground cavern contains 2. 24 x 106 L of methane gas (CH 4) at a pressure of 1500 k. Pa 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 = n. RT

Ideal Gases vs. Real Gases o Ideal Gas – a gas which behaves according

Ideal Gases vs. Real Gases o Ideal Gas – a gas which behaves according to the gas laws and KMT at all pressures and temperatures n o 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

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 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 At High Pressures: (a) At low pressures, the volume

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 At Low Temperatures: Molecules are not moving as fast

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