1 Answers Lecture Exercises 31 and 32 This is a summary of the most important things regarding gases. Please also read Chapter 9 in your textbook. Boyle’s Law: correlation between volume and pressure V∝1/P P1 circle4 V1 = P2 circle4 V2 (T and n are constant) Problems involving Boyle’s Law: 1. 1.0 L of a gas at STP is compressed to 473 mL. What is the new pressure of the gas? (answer on page 3) 2. Synthetic diamonds can be manufactured at pressures of 6.00 x 104 atm. If you took 2.00 L of gas at 1.00 atm and compressed it to a pressure of 6.00 x 104 atm, what would the volume of the gas be? (answer on page 3) Charles’s Law: correlation between volume and absolute temperature (K) V∝T V1 circle4 T2 = T1 circle4 V2 (P and n are constant) Problems involving Charles’s Law: 3. The temperature inside a refrigerator is about 4°C. If you place a balloon that has a temperature of 22°C and a volume of 0.5 L in that refrigerator, what will the volume of the balloon be if its temperature is fully cooled by the refrigerator? (answer on page 3) 4. A soda bottle is flexible enough that the volume of the bottle can change even without opening. If you have an empty soda bottle (volume = 2 L) at room temperature (25°C), what will the new volume be if you put it in your freezer (-4°C)? (answer on page 3) Avogadro’s hypothesis: V∝n V1 circle4 n2 = n1 circle4 V2 (P and T are constant) Avogadro also stated that at STP (Standard Temperature and Pressure: 0°C and 1 atm) 1 mol of any ideal gas occupies a volume of 22.414 L. Combined Gas Law: correlation between volume, pressure and temperature 2 Problems involving the combined gas law: 5. If you initially have a gas at a pressure of 12 atm, a volume of 23 L, and a temperature of 200 K, and then you raise the pressure to 14 atm and increase the temperature to 300 K, what is the new volume of the gas? (answer on page 3) Note: This question would be a little more difficult if you were given the pressure in mm Hg and the temperature given in °C. Then you need the following important conversions: 1 atm = 760 torr = 760 mm Hg and TK = T°C + 273 6. You have an unknown volume of gas at a pressure of 380 mm Hg and a temperature of 52 °C. If you raise the pressure to 912 mm Hg, decrease the temperature to 47°C, and measure the final volume to be 48.0 L, what was the initial volume of the gas? (answer on page 3) Ideal Gas Law: correlation between moles, volume, pressure, and temperature Pcircle4V = ncircle4Rcircle4T R (ideal gas constant) = 0.08206 Lcircle4atm/molcircle4K) When is a gas ideal? -point masses (molecules occupy no volume) -molecules are in constant motion -no intermolecular forces between particles -collisions involving gas molecules are totally elastic Problems involving the ideal gas law: 7. How many molecules of N2 could fit in a 2.00 L soda bottle at 23°C an 755 mm Hg? (answer on page 3) 8. How much pressure would 4.85 moles of He gas exert in a 4.50 L tank at 55°C ? (answer on page 3) 9. What is the density of Helium at STP? (answer on page 3) 10. 2.58 g of a gas has a volume of 31.8 L at 745 mm Hg and 21°C. Determine the molecular weight of the gas. What gas might that be? (answer on page 3) The gas law and the stoichiometric coefficients Avogadro stated that “at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas present”. According to this law, when two gases react with each other, their reacting volumes have a simple ratio to each other (coefficients in the balanced chemical equation) and also the volume of the gaseous product is related to the reactants by a simple ratio. 3 Example: 3 H2(g) + N2(g)→ 2 NH3(g) T,P = constant 0.45 L H2(g) reacting with excess N2(g) yields 0.3 L NH3 [0.45 L (2 mol NH3/3 molH2)]. If the temperature and the volume are constant the mole ratio between reactants and products can be used to directly relate the pressures. Answers to questions 1-10. 1. 2.11 atm 2. 3.33x10-5 L 3. 0.47 L 4. 1.81 L 5. 29.6 L 6. 117 L 7. 4.9x1022 8. 29.0 atm 9. 0.179 g/L 10. 2.00 g/mol H2 Answers to selected problems from the Lecture Exercises. Lesson 31 3. T,P,V,n 4. T in K P in tam V in L n in mol 5. A.273.15 K B.373.15 K C.298.15 K 6. A.0.98 tam B.1.12 atm C.0.98 tam 7. see pg.2 8. relatively low pressure and temperature 28. 40.97 g 29. greater, 64.42 g 30. 1 atm pressure, 0°C (273 K) 31. 0.758 g/L 32. less δ(O2) = 1.43 g/L 33. 42.00 g/mol 34. C3H6 (cyclopropane) Lesson 32 1. P1circle4V1 = n1circle4Rcircle4T1 2. P2circle4V2 = n2circle4Rcircle4T2 4 3. n = constant 4. P1circle4V1 / T1 = n1circle4R 5. P2circle4 V2 / T2 = n2circle4R 6. P1circle4V1 / T1 = P2circle4V2 / T2 7. n and V 8. n 9. P1circle4V1circle4T2 / T1circle4P2 = V2 10. P1circle4V1circle4T2 / P2circle4V2 = T1 11. 1.34 g/L 12. Increase 1.64 g/L 13. no change 14. 149.18 L 15. 149.08 K 16. 578.24 K 17. n 18. yes 19. V and n 20. P and n 21. 370.1 L 22. 8628.15 L 23. 3.88 L 24. 855.8 L air 26. 9.0 L 28. 1.7 atm ABLECKING Microsoft Word - Answers LE Lesson 32 and 33