Chem 452 – HW 6Winter 2012CHEM 452 – Homework 6•••••Due by 11:00 PM on Friday February 10 2012 in the CHEM 452 catalystmailbox. Please scan you HW into a single PDF file and then submit it online.The link to the dropbox is: https://catalyst.uw.edu/collectit/dropbox/mkhalil/19205No late homework will be accepted on this or future homework sets.This homework is worth a total of 10 points.Please box your answers.Please give all answers in SI units.Refer to the article below and answer the following questions (same article as homework 2)Article: Lewis Nathan S. and Daniel G. Nocera. “Powering the planet: Chemicalchallenges in solar energy utilization.” PNAS 103: (Oct. 2006) 15729-35.1.For each of the following statements indicate if they are True or False.a. The challenge with solar energy is to dramatically decrease the cost per Watt forelectricity production.b. Three carbon-neutral fuel options according to this article are nuclear fission carbon capture and storage and clean coal.c. Multi-layer quantum dots could be used to overcome the Shockley-Queisser limit(the maximum efficiency of most solar cells).d. Based on the statistics in the article the resource base of fossil energy resourcescould support the world’s energy needs for several centuries to come.e. Without cost-effective storage solar energy could be the primary source ofelectrical power.2.Answer the following questions. Your answers do not need to be in full sentences.a. Why will higher levels of carbon-neutral power be required by 2050 if theirintroduction does not start immediately with a constant ramp-up?b. Why is it important to have low material costs in order to make a solar-basedprocess economical?c. What would the result be of having multiple-bandgap absorbers in a cascadedjunction configuration?d. In the water splitting process what needs to happen in order to close the catalyticcycle?e. What are the only established molecular electro-catalysts for generating O2 fromH2O?3.Assume that we can harness the energy stored in the bonds of H2 and O2. Using theenergy consumption rates tabulated in table 1 answer the following questions for2001 2050 and 2100. Looking back at the calculation from homework 2 will behelpful.a. How many moles of water do you need to store all the energy consumed in oneyear in the form of hydrogen and oxygen bonds? Assume standard conditions.(Answers: 1.49×1015 3.044×1015 and 4.76×1015 molH2O/year)1 Chem 452 – HW 6Winter 2012b. For comparison how many gallons is that? (Remember density of water 1g =1mL and 1gal = 3.785 L). (Answers: 7.09×1012 1.45×1013 and 2.26x1013gal/year)The following questions do not pertain to the article.4. Find ?S for the following processes:a. The isothermal reversible expansion at room temperature of one mole of an ideal gasfrom 2L to 3L. (Answer: 3.4 J/K)b. One mole of ice at 265K is melted under usual lab conditions to form water at 329K.(Answer: about 37 J/K)5. Two blocks of the same metal and mass are at different initial temperatures T1 and T2. Theblocks are brought into contact and come to a final temperature Tf. Assume the system istotally isolated from the surroundings and that the surroundings are at equilibrium.a. Your intuition probably tells you that for 2 identical blocks Tf is the average of theinitial temperatures so that Tf = 1/2 (T1 T2). Show that for a system of two blockstotally isolated from the surroundings that this is true.b. Show that the change in entropy is? S = CP ln(T1 T2 )24 T1 T2c. How does this expression show that this process is spontaneous?Hints: (1) Since the blocks are of the same material they will have the same Cp. (2)Remember that the system is isolated. (3) For part c you can show this in various waysincluding assuming numerical values for T1 and T2 in different cases.6. Steam is condensed at 100 °C and the water is cooled to 0 °C and frozen to ice. Whatis the molar entropy change of the water? Consider that the average specific heat ofliquid water at constant pressure to be 4.2 J K-1 g-1 ?Hvap is 2258.1 J g-1 and ?Hmelt is333.5 J g-1. (Ans: -154.6 J K-1 mole-1)7. In class we said that the entropy of mixing for two ideal gases is:?Smixing = – R ( nA ln( x A ) nB ln( xB ) )Say we have nA moles of gas A initially at 1 atm pressure mix with nB moles of gas Balso at 1 atm pressure to form 1 mole of a mixture of A and B at a final pressure of 1 atm.The entire process occurs at a constant temperature T.a. Show that the entropy change is given by :?S mixing = – Rx A ln( x A ) – RxB ln( xB )b. What can you say about the sign of ?S? Is it in keeping with the second law?c. Gibbs Free Energy can be written as dG = dH – d(TS). Given that temperature isconstant in this problem what is the sign of dG? Based upon this is the mixingprocess spontaneous?2 Chem 452 – HW 6Winter 2012d. Given that xA xB = 1 what values of xA and xB give the largest entropy ofmixing? (Prove it). Hint: Recall how to prove that a function is at its maximum.8. Text 5.26A 25.0-g mass of ice at 273 K is added to 150.0 g of H2O(l) at 360. K at constantpressure. Is the final state of the system ice or liquid water? Calculate ?S for the process.Is the process spontaneous?9.a.b.c.d.e.f.Describe in one short phrase whether ?S will generally increase or decrease inthe following:Neutralization of charges in an aqueous solutionA polar molecule is placed in a nonpolar solvent (or the opposite)DNA mixed with cationic lipids in an aqueous solution (drawing a picture ishelpful)A phase change from a gas to a liquidIncreasing the number of molecules in the system (i.e. doubling the system)Increasing the temperature of the systemStretching a rubberband.3