Gases http://www.mhhe.com/physsci/chemistry/animations/chang_7e_esp/gam2s2_6.swf

Section 1 – The Gas Laws 1. Use the kinetic-molecular theory to explain the behavior of gases 2. State, apply, & calculate the 3 following gas laws: a. Boyle’s Law b. Charles’s Law c. Gay-Lussac’s Law

A. The Kinetic-Molecular Theory 1. Gas particles do NOT attract or repel 2. Gas particles are small; virtually no volume 3. Gas particles are in constant, random motion 4. Kinetic energy is transferred during the elastic collisions All gases have same average kinetic energy at given temp

1. Actual gases do not always obey the kinetic-molecular theory B. The Nature of Gases 1. Actual gases do not always obey the kinetic-molecular theory 2. The KMT is based on 4 factors: a. Temperature (measured in Kelvin) [oC + 273 = K] b. Pressure (measured in atm, kPa, etc.) [1atm = 101.3kPa = 760 mmHg or torr] c. Volume (measured in liters or mL) d. Amount of Gas (measured in moles)

1. Temperature held CONSTANT http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/gaslaw/boyles_law_graph.html C. Boyle’s Law 1. Temperature held CONSTANT 2. Found inverse relationship between pressure & volume 3. P1 V1 = P2 V2

Volume –vs- Pressure of a Gas

Complete Practice Problems: #1 - #5 P1 V1 = P2 V2 Sample Problem 1: If the pressure of helium gas in a balloon has a volume of 4.0 L at 210 kPa, what will the pressure be at 2.5 L? 340 kPa Complete Practice Problems: #1 - #5 SHOW YOUR WORK!!!

1. Pressure held CONSTANT http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/gaslaw/charles_law.html http://www.marymount.k12.ny.us/marynet/06stwbwrk/06gas/2slyscharles/2slysflash.html D. Charles’s Law 1. Pressure held CONSTANT 2. Found direct relationship between temperature & volume 3. V1 = V2 T1 T2 http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/gaslaw/charles_law.html

Temperature –vs- Volume of a Gas

Complete Practice Problems: #6 - #8 V1 = V2 T1 T2 Sample Problem 2: A gas sample at 40 oC occupies a volume of 2.32 L. If the temperature is increased to 75 oC, what will be the final volume? 2.58 L Complete Practice Problems: #6 - #8 SHOW YOUR WORK!!!

What would a graph look like for Gay-Lussac’s Law? http://www.marymount.k12.ny.us/marynet/06stwbwrk/06gas/1amcslussac/amcsgaylussac.html E. Gay-Lussac’s Law 1. Volume held CONSTANT 2. Found direct relationship between temperature & pressure 3. P1 = P2 T1 T2 What would a graph look like for Gay-Lussac’s Law?

Complete Practice Problems: #9 - #11 P1 = P2 T1 T2 Sample Problem 3: The pressure of a gas in a tank is 3.2 atm at 22 oC. If the temperature rises to 60oC, what will be the pressure in the tank? 3.6 atm Complete Practice Problems: #9 - #11 SHOW YOUR WORK!!!

Section 2 – The Combined Gas Law & Avogadro’s Principle 1. State, apply, & calculate the combined gas law 2. Relate number of particles and volumes using Avogadro’s Principle

A. The Combined Gas Law 1. Amount of Gas held CONSTANT 2. P1 V1 = P2 V2 T1 T2 3. This law combines which 3 laws? http://kids.earth.nasa.gov/archive/air_pressure/balloon.html

Complete Practice Problems: #12 - #14 Sample Problem 4: A gas at 110 kPa and 30 oC fills a container at 2.0 L. If the temperature rises to 80oC and the pressure increases to 440 kPa, what is the new volume? 0.58 L Complete Practice Problems: #12 - #14 SHOW YOUR WORK!!!

B. Avogadro’s Principle 1. Equal volumes of gases at the same temperature and pressure contains equal number of particles 2. Molar volume = 22.4 L/mol at STP 3. STP (Standard Temp & Pressure) Temperature = 0 oC or 273 K Pressure = 1 atm

Complete Practice Problems: #15 - #17 Sample Problem 5: Calculate the volume that 0.881 mol of a gas at STP will occupy. 19.7 L Complete Practice Problems: #15 - #17 SHOW YOUR WORK!!!

Section 3 – The Ideal Gas Law 1. State, apply, & calculate the ideal gas law 2. State, apply, & calculate Dalton’s Law of Partial Pressure 3. State, apply, & calculate Graham’s Law of Effusion http://www.chemistry.ohio-state.edu/betha/nealGasLaw/fr2.1.html

A. The Ideal Gas Law 1. Contains ALL variables 2. P V = n R T Where P = pressure (depends on R) V = volume (liters) n = amount of gas (moles) R = ideal gas constant (depends on pressure) T = temperature (Kelvin)

R = ideal gas constant (depends on pressure) Pressure R value atm 0.0821 kPa 8.314 mm Hg torr 62.4

Sample Problem 6: Calculate the volume of a gas at STP with 2.80 moles. Sample Problem 7: Calculate the moles of a gas at STP with a volume of 238 L. 10.6 mol

Complete Practice Problems: #18 - #20 Sample Problem 8: Calculate the number of moles of gas contained in a 3.0 L vessel at 27 oC with a pressure of 1.50 atm. 0.18 mol Complete Practice Problems: #18 - #20 SHOW YOUR WORK!!!

B. Dalton’s Law of Partial Pressure 1. Contains only pressure 2. Where pressure must be in the same units 3. Ptotal = P1 + P2 + P3 + . . .

Complete Practice Problems: #21 - #22 4. Sample Problem 9: If the total pressure of a mixture of oxygen & nitrogen gases was 820 mmHg, how much pressure would nitrogen exert if oxygen had 580 mmHg? 240 mmHg Complete Practice Problems: #21 - #22 SHOW YOUR WORK!!!

C. Graham’s Law of Effusion 1. Contains rates & masses of gases 2. Rate A = Mass B Rate B Mass A Where Rate is measured in m/s Mass is measured in grams

Sample Problem 8: If neon travels at 400 Sample Problem 8: If neon travels at 400. m/s, estimate the average speed of butane (C4H10) at the same temperature. 235 m/s Sample Problem 9: Chlorine has a velocity of 0.0380 m/s. What is the average velocity of sulfur dioxide under the same conditions? 0.0400 m/s

Complete Practice Problems: #23 - #24 SHOW YOUR WORK!!!