Average Molar Kinetic Energy Answer Key

Things you should know when you finish the Discussion hand out: 2  M∙𝑢rms 3 2 = √3∙𝑅∙𝑇 Average molar kinetic energy = ̅ E= = R ∙ T; 𝑢rms = √𝑢avg   Rate =  (P𝑜𝑏𝑠 + 𝑎 [ ] ) (V𝑐𝑜𝑛𝑡𝑎𝑖𝑛𝑒𝑟 − 𝑏 ∙ 𝑛) = 𝑛 ∙ R ∙ T V 2 amount ; Time 2 𝑀 rate ∝ velocity Page 438 in the text book “Summary of Intermolecular Forces” Table 11.15. 𝑛 2 𝑛 2 L2 ∙bar 100kPa∙L2 ) mol2 Where 𝑎 [V] accounts for intermolecular forces; units of 𝑎 = ( mol2 ) = ( L ) mol 𝑏 ∙ 𝑛 Accounts for non-zero molecule volume; units of 𝑏 = (  Phase diagram  Triple point  Critical point 1. Two identical containers, one red and one yellow, are inflated with different gases at the same volume and pressure. Both containers have an identically sized hole that allows the gas to leak out. It takes four times as long for the yellow container to leak out compared to the red container. If the red container is twice as hot as the yellow container, what is the ratio of the molar masses of the gases (Myellow / Mred)? 2. A container is filled with He at 18°C and 7.92 bar. It is found that the pressure of the container drops by 50.% in 35 minutes, due to a small hole. If the container had instead been filled with Ne at 18°C and 7.92 bar, what would be the pressure of the Ne after 35 minutes? Express your answer in bar. 3. Which of the following combinations of conditions will a gas behave most ideally? Explain your choice. a. Low P and low T b. Low P and high T c. High P and high T d. High P and low T 1 4. Solve the van der Waals real gas equation for the pressure. a. To investigate how the a coefficient affects the pressure, set the b coefficient to zero. Does a increase or decrease the pressure compared to what you would expect for an ideal gas? b. To investigate how the b coefficient affects the pressure, set the a coefficient to zero. Does b increase or decrease the pressure compared to what you would expect for an ideal gas? c. Below is a plot of the compressibility (PV/RT) as a function of changing pressure for 1 mole of a real gas (dashed line) and an ideal gas (solid line). Using what you learned in parts (a) and (b), at what pressures is the a coefficient dominant and at what pressures is the b coefficient dominant. ). Pressure vs. Compressibility of van der Waals gases PV/RT (note: y-axis is 𝑃𝑉 ) 𝑅𝑇 𝑟𝑒𝑎𝑙 𝑃𝑉 ( ) 𝑅𝑇 𝑖𝑑𝑒𝑎𝑙 ( 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 0 100 200 300 Pressure (atm) 400 5. Put the following molecules in order of increasing Van der Waals constant, b: Cl2, N2, C2H6, C3H8. 2 500 6. For each of the pair of molecules below, which has the highest value of Van der Waals constant, a? Identify the dominant intermolecular forces. H2O vs CO2 Ne vs F2 C6H6 vs CH3OH 7. Which of the following gases will behave least ideally under the same conditions? Explain your choice using the a and b Van der Waals coefficients. CH4 or SO2 Cl2 or N2 8. Match the molecules below with their a and b van der Waals coefficients. 2 L Water (H2O) 0.2476 0.02661 Argon (Ar) 5.536 0.03029 Hydrogen (H2) 1.363 0.03219 Benzene (C6H6) 18.24 0.1154 Molecules L ∙bar 𝑎 ( mol2 ) 𝑏 (mol) 9. The boiling point of cyclohexane, C6H12, is 353.9 K, its molecular weight is 84.16, and its van der Waals coefficients are 𝑎 = 23.11 bar L2/mol2 and 𝑏 = 0.1424 L/mol. At 354.0 K the vapor pressure of cyclohexane is 1.0164 bar and the vapor density is 0.03453 mol/L. Calculate the vapor pressure (in bar) of cyclohexane at 354.0 K if it behaved as an ideal gas. a. Calculate the density of liquid cyclohexane, in g/mL. 10. O2 and H2O have similar values of van der Waals constant, b, but different van der Waals constant, a. Which one will have higher pressure at the same temperature and volume? 3 11. NO2 and Trifluoromethane (CHF3) have similar values of Van der Waals constant, a, but different van der Waals constant, b. Which one will have higher pressure at the same temperature and volume? 12. A 5.0mol sample of NH3 gas is kept at 2.0 L container and 27°C. Calculate the pressure (in bar) of the gas assuming it does not behave ideally. (a =4.0 bar·L2/mol2 and b = 0.040 L/mol) What is the percent error compared to an ideal gas? 13. Consider a container filled with 15N2 gas and placed in larger container filled only with 14N2. If a small hole is made in the smaller container, initially as the gases effuse, will the smaller container gain or lose mass? Assume the pressures inside the containers are the same. Explain your answer. It may help to draw a picture. 14. Two identical containers, one red and one yellow, are filled with different noble gases at the same temperature and pressure. Both containers have an identically sized hole in them allowing the gases to leak out. If it takes the red container 10.0 seconds to empty and the yellow container 57.3 seconds to empty, what are the noble gases contained in each container? Hint: rate is proportional to amount/time. 15. In 2.00 min, 29.7mL of helium effuses through a small hole. Under the same conditions (temperature and pressure), a 10.00 mL of a mixture of CO and CO2 effuse through the same hole in the same amount of time. Calculate the percent composition by volume of the mixture. 16. Two identical containers filled with the same number of moles of gas at the same temperature. Container A contains a gas with a molar mass of 40. g/mol, and container B contains a gas with a molar mass of 160. g/mol. A hole of identical size made in each container. What is the ratio timeA/timeB of the times necessary for the number of moles of gas to drop to half in each container? 4 17. Imagine a substance with the following points on the phase diagram: a triple point at 0.5 atm and -5°C; a normal melting point at 20°C; a normal boiling point at 150°C; and a critical point at 5 atm and 1000°C. For this, complete the following: a. What does it mean to have a normal solid-liquid line? b. Roughly, sketch the phase diagram, using units of pressure (atm) and temperature (°C). Pressure (atm) 5 2 2 1 -80 -5 20 500 150 0 Temperature (°C) 1000 c. Rank the states with respect to increasing density: d. Describe what one would see at pressures and temperatures above 5 atm and 1000°C: e. Describe what will happen to the substance when it begins in a vacuum at -15°C and is slowly pressurized: f. Describe the phase changes from -80°C to 500°C at 2 atm: 5 18. For each of the following questions refer to the phase diagram for mysterious compound. a. What is the critical temperature of compound X? b. If you were to have a bottle containing compound X in your closet, what phase would it most likely be in? c. At what temperature and pressure will all three phases coexist? d. If I have a bottle of compound X at a pressure of 45 atm and temperature of 100°C, what will happen if I raise the temperature to 400°C? e. Why can’t compound X be boiled at a temperature of 200°C? f. If I wanted to, could I drink compound X? 19. At 70.0℃, liquid water is injected into a rigid, evacuated 1.000 L container. After the water has come to equilibrium with its vapor, the volume of the liquid phase is 137 mL. The vapor pressure at 70.0℃ is 31.1760 kPa. Calculate the moles of water vapor present in the space above the liquid. Assume vapor behaves as an ideal gas at 70.0℃. Handout Answers: 1. 2. 3. 8 6.16bar b 4. 𝑛∙𝑅∙𝑇 14. Yellow—Xe; Red—He 15. XCO2 = 45.6%; XCO = 54.4% 16. 0.5 17. a. Positive slope b. c. Gas < liquid < solid d. Only supercritical fluid e. Deposition (opposite of sublimation) gas  solid f. Solid  liquid  gas 18. a. > 750°C b. Gas c. ≈350°C; ≈50 atm d. Sublime; solid  gas e. No liquid phase present f. NO… 19. 9.43*10-3 𝑛 2 𝑃𝑜𝑏𝑠 = −𝑎[ ] 𝑉 ∙ 𝑏 ∙𝑛 𝑉 a. ‘a’ decreases Pobs b. ‘b’ increases Pobs c. ‘a’ dominates at low P; ‘b’ dominates at higher P 5. N2 < Cl2 < C2H6 < C3H8 6. H2O; F2; C6H6 7. SO2; Cl2 8. 9. 1.04 a. 0.5910 10. PO2 > PH2O 11. PCF3H > PNO2 12. Pobs = 44 bar; Pideal = 62 bar; 29% 13. Gain 6 In preparation for next week lecture and discussion sections: 1. Using your own words define lattice enthalpy (ΔlatticeH): 2. Is the lattice enthalpy (ΔlatticeH) (choose one): always positive never positive sometimes positive Write the chemical equation representing lattice enthalpy (ΔlatticeH) of MgCl2: Draw the energy diagram representing lattice enthalpy (ΔlatticeH): 3. Using your own words define enthalpy of aquation (ΔaqH): 4. Is the enthalpy of aquation (ΔaqH) (choose one): always positive never positive sometimes positive Write the chemical equation representing enthalpy of aquation (ΔaqH) of MgCl2: Draw the energy diagram representing enthalpy of aquation (ΔaqH): Draw the picture of hydrated MgCl2 ions by water: 5. What do you need to know to find enthalpy of solution (ΔsolnH): 6. Using your own words define enthalpy of solution (ΔsolnH): 7. Is the enthalpy of solution (ΔsolnH) (choose one): always positive never positive sometimes positive Write the chemical equation representing enthalpy of solution (ΔsolnH) of solid MgCl2: 8. Can enthalpy of solution (ΔsolnH) predict solubility? 7 Useful information:  Units of concentrations mol o Molality, m ( ) = kg   molessolute masssolvent (kg) Colligative property where i is a van’t Hoff factor 𝑚𝑜𝑙 o Osmotic Pressure: Π =MRT·i; where M( 𝐿 ) is Molarity o Freezing Point Lowering: ∆Tfp = −|𝑘fp | ∙ m ∙ 𝑖 ∆Tfp = Tfp𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 − Tfp𝑠𝑜𝑙𝑣𝑒𝑛𝑡 < 0 o Boiling Point Elevation: ∆Tfp = +|𝑘bp | ∙ m ∙ 𝑖 ∆Tbp = Tbp𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 − Tbp𝑠𝑜𝑙𝑣𝑒𝑛𝑡 > 0 o Vapor Pressure Lowering: p𝑠𝑜𝑙𝑣𝑒𝑛𝑡 = χ𝑠𝑜𝑙𝑣𝑒𝑛𝑡 ∙ p°𝑝𝑢𝑟𝑒 𝑠𝑜𝑙𝑣 ∆p𝑠𝑜𝑙𝑣𝑒𝑛𝑡 = χ𝑠𝑜𝑙𝑢𝑡𝑒 ∙ p°𝑝𝑢𝑟𝑒 𝑠𝑜𝑙𝑣 Refer to Page 466-478 in the text book Mahaffy 9. The freezing temperature of the solution is always _____________ compared to the freezing temperature of the pure solvent. greater lower same 10. The boiling temperature of the solution is always ____________ compared to the boiling temperature of the pure solvent. greater lower same 11. The figure to the right is the experimental plot of freezing point temperature, Tf , versus molality, m, for the solution of an unknown solute in cyclohexane. Calculate to two significant figures the freezing point depression constant Kf for cyclohexane, in °C∙kg/mol (use i =1 for this problem). 12. What is the boiling point of a 0.100m sucrose/water solution? (Kb,water = 0.500°C/m) 13. Circle the solution below that has the lowest freezing point and explain your answer. a. 4mol NaCl(s) in 1L of water b. 3mol CaCl2(s) in 1L of water c. 2mol AlCl3(s) in 1L of water d. 4mol C6H12O6(s) in 1L of water 14. The normal freezing point of cyclohexane is 6.6°C. A 0.20 g sample of an unknown solute is dissolved in 50. mL of cyclohexane (d = 0.80 g/mL, Kf = 20.°C/m). If the freezing point of the solution is 3.6°C, what is the molar mass of the solute? 8 15. At 25°C vapor pressure of pure water is 24 mmHg and that of seawater is 23.20 mmHg. Assuming that seawater contains only NaCl estimate its molal concentration. 16. The freezing point of benzene (C6H6) is 6°C at 1 atm. In a laboratory experiment, students synthesized a new compound and found that when 40. grams of the compound were dissolved in 2000 grams of benzene (Kf = 5.12 K·kg/mol), the solution froze at 4°C. The compound found to be nonvolatile and a nonelectrolyte. Calculate the molar mass of the compound. 17. 29.0 g of NaCl(s) is mixed with 200. g of ice. Calculate the boiling point of the mixture. The boiling point elevation constant for water is Kb = 0.5°C/mol (use i =2 for this problem) 18. What mass of CaCl2 (MW = 111 g/mol; i = 3) is required to lower the freezing point of 10.0 mL of water (Kf=1.86°C/m) by 1°C? 19. Benzene freezes at 5.51°C (Kf = 5.12°C/m). A benzene/acetic acid solution freezes at 2.01°C. How many moles of acetic acid were added to 500. g of benzene? Numerical Answers: 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. lower higher 20 100.05 B 30. 0.80 50 102.5 0.199 g 0.342 mol benzene 9