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Gas Laws

Gas Laws. Chapter 13. Warm Up!. If you have a balloon filled with air and the temperature increased what would you observe? what happens to the gas particles inside the balloon? What would happen if the temperature was decreased?. Today’s Agenda.

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Gas Laws

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  1. Gas Laws Chapter 13

  2. Warm Up! • If you have a balloon filled with air and the temperature increased what would you observe? • what happens to the gas particles inside the balloon? • What would happen if the temperature was decreased?

  3. Today’s Agenda • QOTD: What are the variables involved in the behavior of gases and what are the laws that govern gas behavior? • Boyle’s Law • Charles’ Law • Gay-Lusacc’s Law

  4. Gas Laws • We are considering 4 variables: • V = n = • T = P = • Simulation: http://phet.colorado.edu/en/simulation/gas-properties • We want to know if you change one variable, how does that affect the other measurements? volume moles pressure temperature

  5. Relationships of P,V,T,n F A • Remember that: P = • Volume is related to area, so as volume gets larger the area will increase and P will • Volume and pressure are related. • Temperature and moles are related to because as T increases it will result in more – meaning larger forces. Also, moremeans more “stuff” to collide and larger . The larger the the higher the . • Temperature/moles are related to pressure. decrease INVERSELY force collisions moles forces pressure forces DIRECTLY

  6. Gas Law’s • The individual gas laws assume that you hold all other variables that are NOT used ! • Boyles Law– Describes the inverse relationship between volume and pressure • As volume decreases, pressure increases. P1V1=P2V2 constant

  7. Using Boyle’s Law When conditions change, you solve for a new volume or pressure. Example! A balloon filled with gas at a pressure of 1.3 atm has a volume of 2.2 L. When the volume is increased to 4.1 L what is the new pressure?

  8. Boyle’s Law • Your turn! • What is the volume of a gas if 0.76 L of a gas is in a piston at 820 mmHg of pressure if the pressure is reduced to 610 mmHg?

  9. Gas Laws • Charles’ Law- Describes the direct relationship between volume and temperature. • As volume increases, temp increases! • V1 = V2is the same as T1 = T2 T1 T2 V1 V2

  10. Using Charles’ Law When conditions change, you solve for a new temperature or volume. Example! A balloon filled with gas has a volume of 2.2 L at 298K . When the balloon is heated to 355 K what is the new volume?

  11. Charles’ Law • Your turn! • A gas mixture at 400K occupies a volume of 2.76 L. If the volume is decreased to 1.32 L what is the temperature?

  12. Gas Laws • Gay-Lussac’s Law – Describes the direct relationship between temperature and pressure. • As temperature increases, pressure increases. • P1 = P2is the same as T1 = T2 T1 T2 P1 P2

  13. Using Gay-Lussac’s Law When conditions change, you solve for a new temperature or pressure. Example! • Gas particles are at standard pressure and temperature in a rigid container. When the container is heated at 373 K, what is the new pressure?

  14. Gay-Lussac’s Law • Your turn! • What is the temperature of a gas in a sealed rigid container at 268 kPa, if initially it was at a temperature of 200 K and a pressure of 85 kPa.

  15. Gas Laws • Combined Gas Law – relates pressure, temperature and volume and assumes moles is held constant. • All the relationships in one tidy law! • P1V1 = P2V2is the same as T1 = T2 T1 T2 P1V1 P2V2

  16. Combined Gas Law • When conditions change, you solve for a new pressure, temperature, or volume! • Example • A 350 mL sample of helium gas is collected at 22.0 oC and 99.3 kPa.  What volume would this gas occupy at STP?

  17. Combined Gas Law • Your turn! • Initially a gas is at a pressure of 12 atm, a volume of 23 liters, and a temperature of 200 K. The pressure is raised to 14 atm and temperature increased to 300 K, what is the new volume of the gas?

  18. Warm Up! • A gas has a final volume of 22.4 L at STP. What was the initial volume measured at 810 mmHg and 200 K? • What is the missing variable in the combined gas law? • Considering P= F/A, where would this last variable belong if added to the combined gas law?

  19. Todays Agenda • QOTD: What is the ideal gas constant and how is it calculated? • Avogadros Principle • Ideal gas constant and law • Calculating density and molar masses • Lab Books Due Thurs pm (Baking Soda Lab)! • All bookwork and Gas Law Packet due Friday

  20. Combined Gas Law • Combined Gas Law – relates pressure, temperature and volume and assumes moles is held constant. • P = F F related to T Where does moles fit? • A A related to V • P1V1 = P2V2is the same as T1 = T2 T1 T2 P1V1 P2V2

  21. The missing variable – n! Avogadro’s Principle - Equal volumes of gases contain the SAME number of particles • Molar volume of a gas – volume that 1 mol occupies at STP (273K and 1 atm) • What is that volume??? 22.4 L

  22. Ideal Gas Constant • Combined Gas law, plug in values from warm up and see if both sides are equal… P1V1 = P2V2  T1 T2 • For a specific sample of gas – relationship between pressure, volume, and temp is ALWAYS the same PV T 0.0821 = 0.0821 = R = .0821 L atm/mol K

  23. Deriving the Ideal Gas Law • Use the combined gas law and R, add in moles and….. PV = R rearranges to PV = nRT nT In class practice: Calculate the number of moles of ammonia gas (NH3) contained in a 3.0 L vessel at 300 K and 1.50 atm of pressure.

  24. Your turn! • Determine the temperature (in °C) of 2.49 mol of a gas contained in a 1.0 L vessel at 143 kPa. (Remember that because of R, your calculations have to be in Kelvin and atm!) Make an inventory and remember your conversions!

  25. Warm Up! • Find the pressure at which 2.05 moles of gas occupy 1.5 L at 298K. • How many moles of oxygen gas occupy a 3 L tank at STP?

  26. Today’s Agenda • QOTD: How can you calculate density of gases using the ideal gas law and when are gases non-ideal? • Density and mass derivations • REAL gases • Practice Problems

  27. Finding Molar Mass • You can use the ideal gas law to find the molar mass of an unknown gas! • Remember: moles (n) = mass (g) molar mass (g/mol) So we replace n with m/MM in PV = nRT PV = mRT which rearranges to MM = mRT MM PV

  28. Substituting with Density • Since MM = mRT , and we know that PV D = how can we use density to find MM? m/v MM = DRT P In summary, PV = nRT and since n = m/MM then MM = mRT/PV AND since d = m/v now MM = DRT/P!

  29. Practice Problem • What is the molar mass of gerinol (a compound found in perfumes) if its vapor has a density of 0.480 g/L at a temperature of 260 °C and a pressure of 0.140 atm?

  30. Your Turn! • Rearrange MM= DRT/P to solve for D. • Determine the density of chlorine gas at 295K and 1 atm.

  31. Warm Up! • Find the pressure at which 2.05 moles of gas occupy 1.5 L at 298K. • How many grams of oxygen gas are contained in 3.25 L at STP? • Find the density of Kr gas at STP.

  32. Today’s Agenda • QOTD: How do real gases behave? • Non-ideal behavior • Practice Problems

  33. Deviations of REAL gases • Remember that the IDEAL gas law assumes that all gases behave ideally as described by kinetic molecular theory. • Gas particles are tiny - take up negligible volume • Gases experience no intermolecular attractions • Collisions of gas particles are perfectly elastic and do not lose energy.

  34. Gases aren’t really IDEAL • Gas particles are small but do take up volume. • Gases do experience some intermolecular attractions • Collisions are not perfectly elastic and some energy is lost. BUT • Most gases behave similarly to ideal so we can still use the ideal gas law to approximate them!

  35. Factors Contributing to Non-Ideal Behavior • Gases can not be approximated accurately by the ideal gas law at really HIGH PRESSURE and reallyLOW TEMPERATURE Why? Consider IMF’s and phases

  36. Factors Contributing to Non-Ideal Behavior • Gases are less ideal when: A gas is HIGHLY POLAR or has LARGE PARTICLES Why?

  37. Warm Up! • A 250 mL flask is filled with helium gas at a pressure of 1.2 atm and a 130 K. What is the mass of helium in the flask? • If the same sample of helium was stored at STP, what is the final volume? • How do you determine if the units of P, V, and T are the RIGHT units??

  38. Today’s Agenda • QOTD: None, review! • Combined/Ideal worksheet – classwork only • Quiz tomorrow: Combined gas law, ideal gas, law, ideal gas with mass and density. You will be given PV=nRT, R = 0.0821 Latm/molK, and P1V1/T1 = P2V2/T2 • Lab books due TODAY (baking soda lab) • HW: CompletedGas Law, Ideal gas law packets and Combined Gas Law Sheet due tomorrow!

  39. Warm Up! • Write the balanced equation for the reaction of nitrogen and hydrogen gases reacting to form ammonia (NH3). • What is the mole ratio of nitrogen and hydrogen gases? • What is the mole ratio of hydrogen gas to ammonia?

  40. Today’s Agenda • QOTD: How can you use the ideal gas law with the chemical reaction to calculate stoichiometry of a gas reaction. • Stoichiometry with gas reactions • Volume – Volume Problems • Mass – Volume Problems • Classwork Problems • Homework (Due Wed) – Ch 13: 80 to 98 evens

  41. Stoichiometry with Ideal Gas Law • Remember the key to stoichiometry is a balanced chemical eqn. • Review formula writing/naming, types of reactions, and balancing reactions if you need help!! • When gases react the coefficients in the balanced equation represent both molar amounts and relative volumes!

  42. Volume-Volume Stoich of Gases • What volume of oxygen gas is needed for the combustion of 4.0 L of propane gas (C3H8)? • C3H8 + 5O2 3CO2 + 4H2O • Given : V = 4.0 L C3H8Want : V = ? L O2 • 4.0 L C3H8 x 5 volume units O2 = 1 volume unit C3H8 20.0 L O2

  43. Your Turn! • How many liters of propane gas (C3H8) will undergo complete combustion with 34.0 L of O2 gas? • Determine the volume of hydrogen gas needed to react completely with 5.0 L of oxygen gas to form water.

  44. Volume-Mass Stoich of Gases • Ammonia (NH3) is synthesized from nitrogen and hydrogen. If 5.0 L of nitrogen reacts completely with hydrogen at a pressure of 3.0 atm and a temperature of 298 K, how much ammonia, in grams, is produced? • Write the balanced equation!

  45. N2 + 3H2 2NH3 • Given: V = 5.0 L Want: m = ? g NH3 P = 3.00 atm T = 298 K 2. Convert from liters of N2 to liters of NH3 5.0 L N2 x 2 volume units NH3 = 1 volume unit N2 10.0 L NH3

  46. N2 + 3H2 2NH3 3. Use the ideal gas law to calculate moles of NH3 PV = n RT 3 atm x 10.0 L NH3 = 1.23 mol NH3 0.0821Latm/molKx 298 K 4. Convert moles of NH3 to grams 1.23 mol NH3 x 17 g NH3 = 21 g NH3 1 mol NH3

  47. Set up Eqn and Solve! Your Turn! • Ammonium nitrate decomposes into dinitrogen monoxide and water. Calculate the mass of solid ammonium nitrate that must be used to obtain 0.1 L of dinitrogen monoxide gas at STP.

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