Behavior of Gases

Airbags fill with N 2 gas in an accident. Gas is generated by the decomposition of sodium azide Gas molecules save your life! 2 NaN 3 ---> 2 Na + 3 N 2 Example of Importance of Gases

Kinetic Molecular Theory (KMT) Particles in an ideal gas… Particles in an ideal gas… have no volume. have no volume. have elastic collisions. have elastic collisions. are in constant, random, straight-line motion. are in constant, random, straight-line motion. don’t attract or repel each other. don’t attract or repel each other. have an avg. KE directly related to Kelvin temperature. have an avg. KE directly related to Kelvin temperature.

Real Gases Particles in a REAL gas… Particles in a REAL gas… have their own volume have their own volume attract each other attract each other Gas behavior is most ideal… Gas behavior is most ideal… at low pressures at low pressures at high temperatures at high temperatures when very small in size when very small in size when nonpolar when nonpolarPLIGHT

Characteristics of Gases Gases expand to fill any container uniformly. Gases expand to fill any container uniformly. Are in random motion, have no attraction Are in random motion, have no attraction Gases have very low densities. Gases have very low densities. Particles have no volume = lots of empty space Particles have no volume = lots of empty space

Characteristics of Gases There is a lot of “free” space in a gas. There is a lot of “free” space in a gas. Gases can be compressed. Gases can be compressed. no volume = lots of empty space no volume = lots of empty space

Gases undergo diffusion & effusion. Gases undergo diffusion & effusion. Are always in random motion Are always in random motion Smaller and lighter gas particles do this faster Smaller and lighter gas particles do this faster

Gas Pressure Which shoes create the most pressure?

What Causes Pressure? What Causes Pressure? oleculartheory/Pressure.html oleculartheory/Pressure.html oleculartheory/Pressure.html oleculartheory/Pressure.html

Factors Affecting Gas Pressure Number of Moles (Amount of gas) Number of Moles (Amount of gas) As # of particles increase, the number of collisions with the container wall increases. As # of particles increase, the number of collisions with the container wall increases. Volume Volume Smaller the volume, the greater the pressure exerted on the container. Smaller the volume, the greater the pressure exerted on the container. Temperature Temperature As temp. increases, KE increases, this increases frequency of collisions making pressure increase. As temp. increases, KE increases, this increases frequency of collisions making pressure increase.

Measuring Gas Pressure Barometer Barometer measures atmospheric pressure measures atmospheric pressure (developed by Torricelli in 1643) (developed by Torricelli in 1643) Mercury Barometer Aneroid Barometer

Standard Pressure (Sea Level) Standard Pressure (Sea Level) kPa (kilopascal) 1 atm 760 mm Hg (also called torr) You may be asked to convert between units of pressure!

Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in soft drink) Column height measures pressure of atmosphere 1 standard atmosphere (atm) = 760 mm Hg (or torr)

Measuring Gas Pressure Manometer Manometer measures contained gas pressure measures contained gas pressure U-tube Manometer

Working with Formulas The Gas Laws

Temperature ºC K K = ºC Always use absolute temperature (Kelvin) when working with gases. Always use absolute temperature (Kelvin) when working with gases.

Gas properties can be modeled using math. Model depends on: V = volume of the gas (L) V = volume of the gas (L) T = temperature (K) T = temperature (K) ALL temperatures MUST be in Kelvin!!! ALL temperatures MUST be in Kelvin!!! n = amount (moles) n = amount (moles) P = pressure (atmospheres or kPa) P = pressure (atmospheres or kPa)

Standard Temperature & Pressure 0°C 1 atm 273 K kPa 760 mmHg -OR- STP

Boyle’s Law The pressure and volume of a gas are inversely related The pressure and volume of a gas are inversely related at constant mass & temp at constant mass & temp P V PV = k Robert Boyle ( ). Son of Earl of Cork, Ireland.

Boyle’s Law Since P x V is always a constant: P 1 x V 1 = P 2 x V 2

Pressure and Volume Relationship son.edu/vce/kineticm oleculartheory/PV.htm l

If Mass and Temp are Constant

Boyle’s Law Balloon in a Vacuum

V T Charles’ Law The volume and absolute temperature (K) of a gas are directly related The volume and absolute temperature (K) of a gas are directly related at constant mass & pressure at constant mass & pressure Jacques Charles ( ). Isolated boron and studied gases. Balloonist.

Charles’ Law Since V/T is always a constant: V 1 = V 2 T 1 T 2

If Mass and Pressure are Constant

Charles’ Law hfiles/gaslaw/charles_law.html Pour Liquid Nitrogen on Balloon!!

P T Gay-Lussac’s Law The pressure and absolute temperature (K) of a gas are directly related The pressure and absolute temperature (K) of a gas are directly related at constant mass & volume at constant mass & volume

Gay – Lussac’s Law Since P/T is always a constant: P 1 = P 2 T 1 T 2

Pressure and Temperature Relationship Pressure and Temperature Relationship /PT.html /PT.html /PT.html /PT.html

Review of 3 Gas Laws Summary of Changing Variables Summary of Changing Variables sentialchemistry/flash/gasesv6.swf sentialchemistry/flash/gasesv6.swf

P1V1T1P1V1T1 = P2V2T2P2V2T2 P 1 V 1 T 2 = P 2 V 2 T 1 The good news is that you don’t have to remember all three gas laws! We can combine them into a single equation. If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! Combined Gas Law (on Ref Table)

Example Set up Data Table P 1 = atm V 1 =.180 L T 1 = 302 K P 2 = 3.20 atm V 2 =.090 L T 2 = ?? A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. What is the new temperature (°C) of the gas at a volume of.090 L and a pressure of 3.20 atm?

GIVEN: V 1 = 473 ml T 1 = 36°C = 309K V 2 = ? T 2 = 94°C = 367K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Gas Law Problems A gas occupies 473 ml at 36°C. Find its volume at 94°C. A gas occupies 473 ml at 36°C. Find its volume at 94°C. CHARLES’ LAW TT VV (473 ml )(367 K)=V 2 (309 K) V 2 = 562 ml

GIVEN: V 1 = 100. mL P 1 = 150. kPa V 2 = ? P 2 = 200. kPa WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Gas Law Problems A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa. BOYLE’S LAW PP VV (150.kPa)(100.mL)=(200.kPa)V 2 V 2 = 75.0 mL

GIVEN: V 1 = 7.84 ml P 1 = 71.8 kPa T 1 = 25°C = 298 K V2 = ?V2 = ? P 2 = kPa T 2 = 273 K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (71.8 kPa)(7.84 ml)(273 K) =( kPa) V 2 (298 K) V 2 = 5.09 ml Gas Law Problems A gas occupies 7.84 ml at 71.8 kPa & 25°C. Find its volume at STP. A gas occupies 7.84 ml at 71.8 kPa & 25°C. Find its volume at STP. P  T  VV COMBINED GAS LAW

GIVEN: P 1 = 765 torr T 1 = 23°C = 296K P 2 = 560. torr T 2 = ? WORK: P 1 V 1 T 2 = P 2 V 2 T 1 Gas Law Problems A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GAY-LUSSAC’S LAW PP TT (765 torr)T 2 = (560. torr)(309K) T 2 = 226 K = -47°C

Dalton’s Law of Partial Pressures P total =P 1 +P 2 +…. P total =P 1 +P 2 +…. Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone. Total pressure of a mixture of gases in a container is the sum of the individual pressures (partial pressures) of each gas, as if each took up the total space alone. This is often useful when gases are collected “over water” This is often useful when gases are collected “over water”

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P P atm = P H2 + P H2O

GIVEN: P H2 = ? P total = 94.4 kPa P H2O = 2.72 kPa WORK: P total = P H2 + P H2O 94.4 kPa = P H kPa P H2 = 91.7 kPa Dalton’s Law Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. Hydrogen gas is collected over water at 22.5°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa. Look up water-vapor pressure on for 22.5°C. Sig Figs: Round to least number of decimal places. The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.

GIVEN: P gas = ? P total = torr P H2O = 42.2 torr WORK: P total = P gas + P H2O torr = P H torr P gas = torr A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? DALTON’S LAW Look up water-vapor pressure for 35.0°C. Sig Figs: Round to least number of decimal places. Dalton’s Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

Graham’s Law Diffusion Diffusion Spreading of gas molecules throughout a container until evenly distributed. Spreading of gas molecules throughout a container until evenly distributed. Effusion Effusion Passing of gas molecules through a tiny opening in a container Passing of gas molecules through a tiny opening in a container

Graham’s Law Speed of diffusion/effusion Speed of diffusion/effusion Kinetic energy is determined by the temperature of the gas. Kinetic energy is determined by the temperature of the gas. At the same temp & KE, heavier molecules move more slowly. At the same temp & KE, heavier molecules move more slowly.

V n Avogadro’s Principle Equal volumes of gases contain equal numbers of moles at constant temp & pressure true for any gas Equal volumes of gases at the same T and P have the same number of molecules.