Recitation Worksheet Seven

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Apr 3, 2024

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Recitation Worksheet Seven (Ch. 5.5-5.9, 6.1-6.2 (heat capacity)) Name: UGA ID: Instructions: § Please enter your first and last name as it appears on the eLC roster (do not use a nickname that is not reflected in eLC). § Your UGA myID is a combination of letters and numbers (example: mine is jmj81738). Do not enter your 81x number. § Download this worksheet and print it if you have a printer. Write the answers in the answer boxes and show your work when appropriate. Using the instructions in the Welcome module on eLC, convert your worksheet to a PDF and then upload it to Gradescope. If you have an iPhone or Android device, you can scan and upload directly through the Gradescope app. The pages must be in the correct order or Gradescope will not be able to read it. § If you do not have a printer, download the worksheet and type your answers in the answer boxes and upload it to Gradescope. Write your work on separate sheets of paper, convert these pages to a PDF using the instructions in the Welcome module on eLC, then upload them to the dropbox on eLC for this worksheet. § If you are using an app to annotate the worksheet, make sure the pages are in the correct order and have the same layout as the original or Gradescope will not be able to read it. § Answers must be written in the corresponding answer box or no credit will be awarded. § This worksheet is due no later than 9:00 AM on the Saturday of the recitation week. § The instructions for uploading worksheets to Gradescope can be found in the Content area of eLC in the Welcome Module. § You must show your work to receive credit. § A periodic table and formula sheet are attached to the end of this worksheet. Please keep these attached to your worksheet in the correct order when submitting to Gradescope. 1. Which of the following would be false according to kinetic molecular theory? A. All gases behave identically regardless of identity B. Gases do not exchange energy when they collide with other gases or their container C. The volume of a gas particle is negligible D. Gases exert small attractive forces on other gases, but no repulsive forces E. The average kinetic energy of a gas rises with rising temperature

2. A small piece of zinc reacts with an excess of hydrochloric acid according to the balanced reaction below. Zn (s) + 2 HCl (aq) → ZnCl 2 (aq) + H 2 (g) A total of 87.5 mL of gas was collected over water at 25.0 °C while monitoring the reaction. The gas pressure was recorded at 757 mm Hg. What was the initial mass of zinc metal (in grams) assuming all of the H 2 gas was captured? A table listing the vapor pressure of water at various temperatures is provided below. Temperature (°C) Vapor Pressure (torr) 15.0 12.79 17.0 14.54 19.0 16.49 21.0 18.66 23.0 21.08 25.0 23.78 30.0 31.86 g

3. The velocity of different samples of gases are graphed below. Which of the following statements are true according to the graph? Select any that apply . A. If all of the gases are at the same temperature, the gas with the lowest molar mass is graphed on line A B. If all of the gases are at the same temperature, the gas with the lowest molar mass is graphed on line D C. If all of the gases are the same molar mass, the gas with the highest temperature is graphed on line A D. If all of the gases are the same molar mass, the gas with the lowest temperature is graphed on line A 4. Calculate the root-mean-square speed (m/s) for bromine gas at 45 ° C. m/s

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5. The effusion rate of carbon dioxide was measured at 70 ° C. Afterwards, the effusion rate of a number of gases were collected at the same temperature. Which of the following gases provided below had the closest rate of effusion to carbon dioxide? 6. An experiment was conducted in which the ratio of the rates of effusion of nitrogen gas to another diatomic gas was 2.3881. What is the identity of the unknown gas? Write the chemical formula in the box below. 7. Many reactions done in the laboratory are air-sensitive and require inert gases such as N 2 or Ar to prevent unwanted reactivity. Although only one gas is typically chosen in any given scenario, consider a situation in which a scientist introduces 3.50 mol of N 2 and 3.50 mol of Ar into a closed container. If a pinhole leak is introduced at a constant temperature, which of the following statements are true after a period of time? Select any that apply. A. The partial pressure of both gases will increase B. The partial pressure of both gases will decrease C. The partial pressure of both gases will remain the same D. The partial pressure of N 2 will be higher than the partial pressure of Ar E. The partial pressure of Ar will be higher than the partial pressure of N 2 A. Ar B. Xe C. C 3 H 8 D. O 2 E. He F. Ne

8. Answer the following questions using the table below of five different hypothetical gases and their van der Waals correction factors Gas a ((L 2 × atm)/mol 2 ) b (L/mol) Gas A 12.391 0.819 Gas B 13.711 0.901 Gas C 1.341 0.100 Gas D 4.981 0.244 (a) Which gas will behave the most nonideally? (b) Which gas would have the most similar volume to an ideal gas? (c) Which gas would have the least similar pressure to an ideal gas? 9. Consider an unknown gas that is placed in various temperature and pressure conditions provided below. Under which set of conditions will the unknown gas behave most ideally? A. Gas A B. Gas B C. Gas C D. Gas D A. Gas A B. Gas B C. Gas C D. Gas D A. Gas A B. Gas B C. Gas C D. Gas D A. Pressure: 0.1 atm; temperature: 273 K B. Pressure: 0.1 atm; temperature: 350 K C. Pressure: 1 atm; temperature: 273 K (STP) D. Pressure: 1 atm; temperature: 350 K E. The identity of the gas is required to determine what conditions will affect ideal behavior

10. A silver rod is heated to 150 °C and placed in a beaker of water at room temperature. After some time, both the water and silver rod are at the same temperature. Assuming no heat is lost to the surroundings, which of the following is/are true ? A. The beaker of water and silver rod together are considered an open system B. Thermal equilibrium is met in this process C. Heat transferred from the silver rod to the water D. All of the above are true E. None of the above are true 11. Which of the following are endothermic processes? Select any that apply . A. When solid KBr is dissolved in water, the solution gets colder. B. When concentrated H 2 SO 4 is added to water, the solution gets very hot. C. Water is boiled in a tea kettle. D. Water condenses on a cold pipe. 12. Which of the following is a state function? 13. The change in internal energy of a system is -123 J. If 85 J of work was done on the system by the surroundings, how much was heat exchanged (in J)? Report your answer in standard notation . J A. q B. w C. q + w D. q – w E. More than one of the options above are state functions F. None of the above are state functions

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14. Consider a system that absorbs 225 kJ of heat and performs 96 kJ of work on the surroundings at constant pressure. What is the ΔE (or ΔU) in this process? What is ΔH? Report your answers in standard notation . ΔE = kJ ΔH = kJ 15. In which of the following reactions would PV work occur? Select any that apply . A. N 2 (g) + O 2 (g) ® 2 NO (g) B. N 2 (g) + 3 H 2 (g) ® 2 NH 3 (g) C. 3 Mg (s) + N 2 (g) ® Mg 3 N 2 (s) D. C (s) + O 2 (g) ® CO 2 (g) E. Ba(OH) 2 (aq) + H 2 SO 4 (aq) ® BaSO 4 (aq) + 2 H 2 O (l) 16. In which of the following reactions would PV work not occur? A. 2 C 2 H 6 (g) + 7 O 2 (g) ® 4 CO 2 (g) + 6 H 2 O (l) B. CO (g) + H 2 O (g) ® CO 2 (g) + H 2 (g) C. 8 N 2 O 5 (g) ® 16 NO 2 (g) + 4 O 2 (g) D. Ba (s) + CO 2 (g) + ½ O 2 (g) ® BaCO 3 (s) E. 2 Na (s) + 2 H 2 O (l) ® 2 NaOH (aq) + H 2 (g) F. More than one of the options above G. None of the options above

17. Samples of copper, silver, and gold are all subjected to equal amounts of heat. Which metal will undergo the smallest change in temperature if they all have equal masses? The molar heat capacities of each metal are given in the table below. A. Copper B. Silver C. Gold D. The change of temperature will be the same since equal amounts of heat are being applied. 18. Liquid bromine has a specific heat of 0.226 J g -1 K -1 . What is liquid bromine’s molar heat capacity (in J/mol·°C)? Report your answer in standard notation . J/mol·°C 19. Consider an experiment in which it is determined that 2.66 kJ of heat is required to raise the temperature of 80.0 g of an unknown organic compound by 15.0 K. Based on this information, what is the specific heat of the organic compound (in J/g·K)? A. 0.115 J/g·K B. 2.22 × 10 -3 J/g·K C. 2.22 J/g·K D. -1.29 × 10 -4 J/g·K E. 1.29 × 10 -4 J/g·K Metal Molar Heat Capacity (J mol -1 K -1 ) Copper 24.4 Silver 24.9 Gold 25.6

20. A 28.0 g iron sample is heated to a target temperature and then is allowed to cool over a given period of time in which it loses 80.0 J of heat. After losing this amount of heat, the temperature of the iron sample is determined to be 72.5 °C. If iron has a specific heat of 0.450 J/g·K, what was the initial (target) temperature of the iron sample (in °C)? Report your answer in standard notation . °C 21. What is true when heat goes from the surroundings to the system? Select any that apply. A. The sign of the heat change in the surroundings is positive B. Work is done on the system C. The internal energy of the system increases D. The potential energy of the surroundings increases E. The sign of the heat change in the system is positive 22. Which statement is true if ΔH = - 85 J? A. The system is gaining 85 J; the surroundings are losing 85 J. The process is exothermic. B. The system is gaining 85 J; the surroundings are losing 85 J. The process is endothermic. C. The system is losing 85 J; the surroundings are gaining 85 J. The process is exothermic. D. The system is losing 85 J; the surroundings are gaining 85 J. The process is endothermic. E. Both the system and surroundings are losing 85 J. The process is exothermic.

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Extra Practice Questions: these questions will not be graded. 1. An unknown gas effuses from a container 1.66 times more rapidly than CO 2 . Which of the following is the most reasonable guess of the identity of the unknown gas? A. CH 4 B. Sb C. O 2 D. CCl 2 F 2 2. A real gas will behave most like an ideal gas under which of the following conditions? A. 1 atm and 73 K B. 1 atm and 550 K C. 10 atm and 73 K D. 10 atm and 550 K 3. What is the change in internal energy of a system (in kJ) when the system releases 158.5 kJ of heat and the surroundings perform 105.0 kJ of work on the system? Report your answer in standard notation . kJ

4. Which of the following is an exothermic process? 5. A 187 g sample of an organic compound requires 18.56 kJ amount of heat to raise the temperature from 25.4 °C to 83.1 °C. What is the specific heat of the compound (in J/g·K)? Report your answer in standard notation . J/g·°C 6. A 50.0 g aluminum sample originally at 26.5 °C absorbs 5.25 kJ of heat. If aluminum has a specific heat of 0.385 J/g·K, what will be the new temperature of the aluminum sample (in °C)? Report your answer in standard notation . °C A. Baking an apple pie B. A sample of liquid gold solidifying C. Hydrogen peroxide evaporating from your skin D. Ice melting in your hand

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Formula Sheet Length 1 kilometer = 0.62137 mile 1 inch = 2.54 centimeters (exactly) 1 Å ngstrom = 1 × 10 −10 meter Energy 1 joule = 1 kg·m 2 /s 2 1 calorie = 4.184 joules 1 Calorie = 1 kilocalorie = 1000 calories 1 L·atm = 101.325 joules Pressure 1 pascal = 1 N/m 3 = 1 kg/m·s 2 1 atmosphere = 101.325 kilopascals = 760 mm Hg = 760 torr = 14.70 lb/in 2 1 bar = 1 × 10 5 Pa (exactly) Temperature 0 K = −273.15°C K = °C + 273.15 °C = (5/9)(°F − 32) Mass 1 kg = 2.205 lbs Volume 1 mL = 1 cm 3 = 1 cc Constants c = 2.998 × 10 8 m/sec h = 6.626 × 10 −34 J·sec R = 0.08206 L·atm/mol·K = 8.314 J/mol·K Specific heat of water = 4.184 J/g∙K Mass of an electron: 9.109 x 10 −31 kg Mass of a proton: 1.673 x 10 -27 kg RH = 2.18 x 10 −18 J Specific heat of water = 4.184 J/g∙K STP = 273.15 K and 1 atm Avogadro's number: 6.022 × 10 23 Equations d (density) = m/V P 1 V 1 =P 2 V 2 V 1 /T 1 =V 2 /T 2 P 1 V 1 /n 1 T 1 =P 2 V 2 /n 2 T 2 PV=nRT (P + a(n 2 /V 2 ))·(V − nb) = nRT molar mass (M) = mRT/PV density (d) = MP/RT x A = n A /n tot = P A /P tot = V A /V tot

P tot = P A + P B + … n tot = n A + n B + … 𝜇𝜇 𝑟𝑟𝑟𝑟𝑟𝑟 = � 3 𝑅𝑅𝑅𝑅 𝑀𝑀 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑜𝑜𝑜𝑜 𝑅𝑅𝑜𝑜𝑜𝑜𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑒𝑒 𝐴𝐴 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑜𝑜𝑜𝑜 𝑅𝑅𝑜𝑜𝑜𝑜𝑒𝑒𝑒𝑒𝑒𝑒𝑜𝑜𝑒𝑒 𝐵𝐵 = � 𝑀𝑀𝑀𝑀 𝐵𝐵 𝑀𝑀𝑀𝑀 𝐴𝐴 Q = C × ΔT = c specific × m × ΔT Q = n × ΔH (kJ/mol) = m × ΔH (kJ/g) w = −PΔV ΔE = q + w ΔH° = ΣnΔHf°(products) − ΣnΔHf°(reactants) ΔH° = ΣnΔH°(bonds broken) − ΣnΔH°(bonds formed) E=hν c=λν λ = h/mv ∆𝐸𝐸 = − 2.18 × 10 −18 𝐽𝐽 ( 1 𝑒𝑒 𝑓𝑓 2 − 1 𝑒𝑒 𝑖𝑖 2 ) C g = kP g P solution =P solvent X solvent P solution =∑P j =∑P j X j ΔT b = K b m i ΔT f = K f m i π = MRT i Thermodynamic and Electrochemistry S = k b × ln( W ) k b = 1.381 × 10 −23 J/K ΔS = q rev /T ΔS surr = q surr /T = −q rev /T ΔS univ = ΔS sys + ΔS surr ΔS° rxn = Σ ν S° products − Σ ν S° reactants ΔH° rxn = Σ ν H° products − Σ ν H° reactants ΔG° rxn = Σ ν G° products − Σ ν G° reactants ΔG = ΔH – TΔS ∆ G = ∆ G° + RT∙lnQ R=8.314 J/mol.K ∆ G° = −RT∙lnK ∆ G= −nFE cell F = 96485 J/(V∙mol e − ) E° cell = RT/nF lnK E° cell = (0.0257/n) lnK = (0.0592/n) logK E cell = E° cell − (RT/nF) lnQ E cell =E° cell − (0.0257/n) lnQ Electrolysis: Q (total charge) = I × t = n × F

Integrated Rate Laws & half-life Equilibrium and Acid / Base K P = K c × (RT) Δn pH = −log[H 3 O + ] K w = 1.0 × 10 −14 at 25 °C K w = [H 3 O + ] × [OH − ] K w = K a × K b pK a = −log[K a ] Buffer: pH = pK a + log ln 𝐾𝐾 2 𝐾𝐾 1 = ∆ 𝐻𝐻 𝑟𝑟𝑟𝑟𝑟𝑟 ° 𝑅𝑅 ( 1 𝑇𝑇 1 − 1 𝑇𝑇 2 )

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