Dr. Mihelcic Honors Chemistry Unit 8 – GAS LAWS Dr. Mihelcic Honors Chemistry Dr. Mihelcic Honors Chemistry

Importance of Gases Airbags fill with N2 gas in an accident. Gas is generated by the decomposition of sodium azide, NaN3. 2 NaN3 ---> 2 Na + 3 N2

Three States of Matter Dr. Mihelcic Honors Chemistry

Characteristics of Gases No definable shape or volume Low mass, with a lot of “free” space (leads to low density) Can be expanded infinitely and placed into a container if force is exerted. Occupy containers uniformly and completely. Escape readily from containers, mix rapidly.

KINETIC MOLECULAR THEORY (KMT) Definition: Theory used to explain gas laws. Treats gases as a collection of particles in rapid, random motion. Applies to ALL gases, regardless of chemical identity.

Molecular Model Gas molecules are relatively far apart (mostly empty space). Gas molecules are in continuous, rapid, random motion. All collisions between gas molecules are elastic (no energy lost or gained in a collision). Gas pressure is caused by collisions of molecules with the walls of the container. Average Temperature of a gas sample is related to its kinetic energy.

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

Gas Pressure Caused by gas molecules hitting container walls. Definition: Force per unit area, or Force Area Image from: www.indiana.edu/.../PressGasLaws.html

Pressure Units SI unit: pascal (Pa) (equal to N/m2) 1 kPa = 1000 Pa

Additional Units of Pressure Will also see problems with: atmospheres (atm) millimeters of mercury (mm Hg) inches of Hg (in Hg) torr ( = 1 mm Hg) Less commonly used: pounds per square inch (psi) millibars (mb)

Conversion Factors and STP 1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 29.921 in Hg = 1013.25 mb = 14.969 psi STP – Standard Temperature (0ºC) and Pressure (1 atm)

Pressure BAROMETER (developed by Torricelli in 1643) Use: Measures pressure of air Image from Dr. Walt Volland, all rights reserved 1998-2005

Column height measures the pressure of the atmosphere Barometric Pressure Column height measures the pressure of the atmosphere 1 standard atm = 760 mm Hg = 29.921 inches Hg = about 34 feet of water

Manometers Use: Measures the pressure of a gas in a closed system.

Open Manometer: Two Cases

Sample 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 mm of Hg?

Relationship between pressure and volume Boyle’s Law Relationship between pressure and volume

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 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 If pressure increases, volume decreases If pressure decreases, volume increases P1V1 = P2V2

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) P1V1 = P2V2 P1 = V1 = P2 = V2 =

Practice with Boyle’s Law At room temperature, 10.01 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? P1V1 = P2V2 P1 = V1 = P2 = V2 = 1 atm = 101.3 kPa

Practice with Boyle’s Law Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.50 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be? P1V1 = P2V2 P1 = V1 = P2 = V2 =

Relating Volume and Temperature 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 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? V1 = T1 = V2 = T2 =

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? V1 = T1 = V2 = T2 =

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? V1 = T1 = V2 = T2 =

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

(a new conversion factor for moles!!) Avogadro’s Hypothesis & Molar Volume Image from library.thinkquest.org/12 596/avogadro.html 1 mol gas @ STP = 22.4 L (a new conversion factor for moles!!)

Sample Problem Example 5.3 What is the mass of propane gas, C3H8, that can be held in a 5.0 L container at STP?

Combining all four variables: Combined Gas Law Combining all four variables: P1V1 = P2V2 n1T1 n2T2 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?

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

Can be in different units, depending on units used in the equation! Gas Law Constant (R) R: Universal or ideal gas constant Can be in different units, depending on units used in the equation! 0.082058 L atm/mol K 62.364 L torr/mol K 8.3145 J/mol K

Sample Problem Example 5.4 If a fixed amount of gas occupies 2.53 m3 at -15°C and 191 Torr, what will the volume of the same gas be at 25°C and 1142 Torr?

Sample Problem Example 5.5 A gas cylinder is filled with 100 g of CO2 at 25oC and a pressure of 1000 mmHg. If 50 more grams of CO2 are added and the cylinder is stored at a temperature of 50oC, calculate the new pressure inside the cylinder.

Using PV = nRT How much N2 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?

Sample Problem Example 5.7 If 0.623 g of ethane, C2H6, is introduced into an evacuated 2.00 liter container at 23°C, what is the pressure, in atmospheres, in the container?

Sample Problem Example 5.8 How much gas can be placed in a gas cylinder with a volume of 10.0 L and which is designed to store gas at a maximum pressure of 75.0 atm and at a maximum of 50°C?

Gas Density and Molar Mass PV = nRT and density (d) = m/V d and M proportional

Sample Problem Example 5.9 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 5.10 What is the density of methane, CH4, at 0.940 atm and 23°C?

Gases in Reaction Stoichiometry Review of steps in Stoichiometry Problems: Balance equation & convert to moles for known. Convert moles of known to moles of unknown quantity using coefficient ratio. Convert moles of unknown to required unit (g, L)

Short-cut when dealing with all gases in an equation If have all gases in an equation, can go directly from V of the given to V of the asked for quantity using the coefficients. ONLY works for equations with all gases!

Sample Problem Write the balanced equation for the synthesis of gaseous water from gaseous hydrogen and oxygen. If we start with 5.4 L of oxygen, how much water in Liters is produced?

Sample Problem 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 0.950 atm?

Sample Problem How many liters of oxygen, measured at 725 mmHg and 21°C are required to burn 1.00 g of butane gas, C4H10, to produce water and carbon dioxide?

Graham’s Law & Dalton’s law

Racing Gases Demo: If concentrated HCl is at one end of the tube and concentrated NH3 is at the other end, which gas do you think will move farthest and fastest down the tube? Racing Gases Demo HCl (g) NH3 (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 NH3 end?

RACING GASES DEMO What happened in the tube? Was the reaction closer to the HCl or NH3 end of the tube? Calculate the molar mass of NH3(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

GRAHAM’S LAW Which gas would both diffuse and effuse faster… Methane (CH4) or carbon dioxide (CO2)? Chlorine (Cl2) or oxygen (O2)? Hydrogen sulfide (H2S) or carbon monoxide (CO)?

GAS DIFFUSION AND EFFUSION Graham’s law calculates: rate of effusion and diffusion of gas molecules. M of 1 M of 2 Rate(Gas 2) Rate (Gas 1) Thomas Graham, 1805-1869. Professor in Glasgow and London. Rate of effusion is inversely proportional to its molar mass.

Sample Problem If they are compared under the same conditions, how much faster than helium does hydrogen effuse through a tiny hole?

Sample Problem The rate of a 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 of oxygen was 2.00 moles/sec. Calculate the molar mass of the unknown gas.

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

(at constant volume and temperature) 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 Ptotal = P1 + P2 + P3 + … (at constant volume and temperature)

PRACTICE – DALTON’S LAW Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are: PO2= 20.0 kPa, PN2=46.7 kPa, and PHe=26.7 kPa. Ptotal = P1 + P2 + P3 + …

PRACTICE – DALTON’S LAW Air contains O2, N2, CO2, and trace amount of other gases. What is the partial pressure of oxygen (PO2) if the total pressure of the system is 101.3 kPa and the partial pressures of N2, CO2, and the other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively? Ptotal = P1 + P2 + P3 + …

Vapor Pressure of Water If the total pressure is 788 mm Hg at 25oC, what is the partial pressure of hydrogen collected over water? Ptotal = P(gas) + P(H2O) = 788 mm Hg

Deviations from Ideal Gas Law occur because of two main factors: 1. Real molecules have volume. 2. There are forces between molecules. Otherwise a gas could not become a liquid. These factors are important at HIGH pressures and LOW temperatures.

Deviations from Ideal Gas Law occur because of two main factors: 1. Real molecules have volume. 2. There are forces between molecules. Otherwise a gas could not become a liquid. 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 Account for volume of molecules and intermolecular forces with VAN DER WAALS’s EQUATION. J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910. Measured V = V(ideal) Measured P nRT V - nb V 2 n a P + ----- ) ( vol. correction intermol. forces

Deviations from Ideal Gas Law Cl2 gas has a = 6.49, b = 0.0562 For 8.0 mol Cl2 in a 4.0 L tank at 27 oC. P (ideal) = nRT/V = 49.3 atm P (van der Waals) = 29.5 atm