Honors Unit 8 – 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

Reviewing States of Matter 2) 1) 3)

States of Matter  Solid  Has definite shape & volume  Particles are tightly packed  Can expand when heated

States of Matter  Liquid  Has constant volume but takes the shape of its container  Fluid (can flow)  Less closely packed particles than solid particles  Can expand when heated

States of Matter  Gas  Expands to fill its container & takes the shape of its container No definable shape or volume  Expands when heated – wants to escape container!  Lots of “free space” between molecules = low density

Gases & the Kinetic Molecular Theory  The KMT describes the behavior of gases (and sol./liq. to some extent) in terms of particles in motion  Kinetic = movement  Assumptions: 1. Gas particles have negligible volume compared to the volume of their container 2. Particles move in constant, random, straight line motion 3. Particles collide with themselves and walls without losing energy (elastic collisions) 4. There are no intermolecular forces between gas molecules

Kinetic Molecular Theory  If gas particles are always in this constant, random motion, what keeps them going? ENERGY!! (Kinetic Energy to be exact)  Temperature is a measure of the average kinetic energy in a substance.  Higher temp. = more kinetic energy = particles move faster!

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)

Gas Pressure  Pressure of a gas = the force of a gas exerted on the surface of a container  As gases bounce around in a container, each collision with a container wall exerts a force More collisions = higher pressure Less collisions = lower pressure  Vacuum = Empty space with no particles (no pressure)

Pressure of a Gas  Atmospheric pressure – due to collisions of air molecules with objects  As elevation increases, air density and therefore pressure decrease  Barometers measure atmospheric (barometric) pressure  Column height measures the barometric pressure of the atmosphere

Gravity When baking, there are different instructions for baking at high altitudes…why?  Boiling point of water decreases due to less atmospheric pressure  Liquid leaves faster so food must bake longer

Pressure of a Gas  Vapor pressure – pressure due to force of gas particles above a liquid colliding with walls of container  Higher temp. = higher vapor pressure!!

Collecting a Gas Over Water  When a gas is collected over water, the total pressure is the pressure of the gas plus the vapor pressure of water

Units of Pressure  SI unit of pressure: pascal (Pa)  Other common pressure units:  Millimeters of mercury (mm Hg)  Atmospheres (atm)  Kilopascals (kPa)  Torr (torr)  Pounds per square inch (psi) 1 atm = 760 mmHg = kPa = 760 torr = psi STP = Standard Temperature and Pressure 0 °C (273 K) and 1 atm

Manometers Barometers: Measure air pressure (atmospheric pressure) Manometers: Measure the pressure of a gas in a container or system

Manometer: Two Cases Manometer – used to measures the pressure of a gas in a container or system.

Manometer Problem An open manometer is filled with Hg and connected to a container of hydrogen. The mercury level is 40.0 mm lower in the arm of the tube connected to the air. Air pressure is 1.00 atm. What is the pressure of the hydrogen gas in millimeters of mercury (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 Demos Operating a 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 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

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!

Example #1 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

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 =

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’ Law Demos  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’ 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’ 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!!!!

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!

Example #3 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 #4 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 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 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!!!!

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!

Avogadro’s Hypothesis Equal volumes of gases (V) at the same T and P have the same number of molecules (n). V = kn V and n are directly related. twice as many molecules

1 mol STP = 22.4 L (a new conversion factor for stoichiometry!!) Avogadro’s Hypothesis & Molar Volume

Combined Gas Law  If any one of these variables does not change in the problem, you can eliminate it from the equation before starting!

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 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 #5

Example #6 A gas cylinder is filled with 100 g of CO 2 at 25 o C and a pressure of 1000 mmHg. If 50 more grams of CO 2 are added and the cylinder is stored at a temperature of 50 o C, calculate the new pressure inside the cylinder.

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

Gas Law Constant (R) 

Example #7 If g of ethane, C 2 H 6, is introduced into an evacuated milliliter container at 23 ° C, what is the pressure, in atmospheres, in the container?

Example #8 How much N 2 (in grams) is required to fill a small room with a volume of 960 cubic feet (27,000 L) to a pressure of 745 mm Hg at 25°C?

Ideal Gas Law: Molar Mass and Density  Density = mass/volume  Recall that the molar mass has units of grams per mole (MM = m/n)  Now, look at the ideal gas law: Substitute m/MM for n PV = mRT MM Substitute Density for m/V P=mRTP=DRTD=P MM V MM MM RT

Density Problems  Example #9: A sample of phosgene (a highly toxic gas) is collected in a flask with a volume of 247 mL at a pressure of 751 mmHg and a temperature of 21 ° C. If the mass of the gas is 1.00 g, what is the molar mass of phosgene?

Sample Problem Example #9: A sample of phosgene (a highly toxic gas) is collected in a flask with a volume of 247 mL at a pressure of 751 mmHg and a temperature of 21 ° C. If the mass of the gas is 1.00 g, what is the molar mass of phosgene?

Example #10: Acetone is widely used as a nail polish remover. A sample of liquid acetone is placed in a 3.00-L flask and vaporized by heating to 95 °C at 1.02 atm. The vapor filling the flask at this temperature and pressure weighs 5.87 g. (a)Calculate the molar mass of acetone. (b)What is the density of acetone vapor under these conditions?

Stoichiometry Review! Steps in a Stoichiometry Problem: 1. Balance equation & convert to moles of known. 2. Convert moles of known to moles of desired compound using mole ratio.  Mole ratio comes from coefficients in balanced equation! 3. Convert moles of desired compound to required unit (g, L, etc.)

(22.4 L only STP!!)

Example #11:

Example #12: ° What is the mass, in grams, of potassium chlorate that must be used to produce 1.50 L of oxygen gas measured at 18 ° C and atm? ____ KClO 3 (s)  ____ KCl (s) + ____ O 2 (g)

G RAHAM ’ S L AW & D ALTON ’ S LAW

Racing Gases Demo: If concentrated HCl is at one end of the tube and concentrated NH 3 is at the other end, which gas do you think will move farthest and fastest down the tube? Why? Video Clip - Racing Gases Demo HCl (g) NH 3 (g)

RACING GASES DEMO The gases will diffuse down the tube Diffusion – tendency of molecules to move from areas of higher concentration towards areas of lower concentration Example: spraying perfume and smelling it across the room

DIFFUSION Originally Over Time

RACING GASES DEMO The gases diffused at different rates If the white ring forms closer to the HCl end of the tube, which gas moved farthest and fastest? What if it was closer to the NH 3 end?

RACING GASES DEMO What happened in the tube? Was the reaction closer to the HCl or NH 3 end of the tube? Calculate the molar mass of NH 3 (g) and HCl(g). Did the lighter or heavier gas move faster?

GRAHAM’S LAW OF EFFUSION The demo is related to Graham’s Law of Effusion – gases of lower molar masses effuse faster than gases with higher molar masses Effusion – when a gas escapes through a tiny hole in its container Example: Helium balloons shrinking compared to normal balloons

GRAHAM’S LAW Graham’s Law can also be applied to the diffusion of a gas Gases with lower molar masses (lighter gases) diffuse faster than gases with higher molar masses (heavier gases) The lighter the gas, the faster it moves!!

Example #13: Which gas would both diffuse and effuse faster… Methane (CH 4 ) or carbon dioxide (CO 2 )? Chlorine (Cl 2 ) or oxygen (O 2 )? Hydrogen sulfide (H 2 S) or carbon monoxide (CO)?

Graham’s Law Formula The rates are simply the speed or velocity at which the gas is traveling. So, this formula will compare the speed of one gas to the speed of the other gas. Rate of effusion is inversely proportional to its molar mass!

Example #14: The rate for some volume of an unknown gas to effuse through a pinhole was 4.00 moles/sec. The rate calculated for the same volume at the same temperature and pressure for oxygen was 2.00 moles/sec. Calculate the molar mass of the unknown gas.

Example #15: If they are compared under the same conditions, how much faster than helium does hydrogen effuse through a tiny hole?

REVIEW - PRESSURE OF A GAS If the gas molecules in a sample collide more with the walls of the container, will the pressure increase or decrease? If the number of gas molecules increases, what will happen to the pressure?

DALTON’S LAW

Partial pressure – the contribution of each gas in a mixture to the total pressure Dalton’s Law of Partial Pressures – for a mixture of gases, the total pressure is the sum of the partial pressure of each gas in the mixture P total = P 1 + P 2 + P 3 + … (at constant volume and temperature)

Collecting a Gas Over Water When a gas is collected over water, the total pressure is equal to the pressure of the gas plus the vapor pressure of water

Example #16:

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