Chem1b Problem Set One

Name Section TA Ch1b, Problem Set One Due Friday, Jan. 16, 2015 at 4 PM in the Ch1b Box Chem1b Problem Set One Problems five and six are designated ♬ as no collaboration problems. These problems will be considered as quiz-‐like problems. There are a total of five pages to this problem set. Problem One (30 points) The following is a table depicting the equilibrium constants (K) measured for the decomposition of sulfite to sulfur dioxide at a range of different temperatures. Temperature (K) K 800 0.0383 825 0.0494 900 0.150 953 0.309 1000 0.553 a. (6 points) Without performing any calculations, use the data above to determine whether this reaction is endothermic or exothermic. Explain your reasoning. b. (8 points) In class we learned that there is a linear relationship between lnK and 1/T. Use Excel or other software to demonstrate this relationship using the data above. Fit the plot with a trend line. Display the trend line and equation on the chart. Include axis labels with appropriate units. c. (8 points) Estimate ∆H° and ∆S° at 900 K using the equation for the trend line. What assumptions do you have to make? d. (3 points) Use your results from part c. to estimate ∆G° at 900 K. e. (5 points) What must be true for the reaction to occur spontaneously? Determine the temperature above which this reaction is spontaneous. 1 Name Ch1b, Problem Set One Section Due Friday, Jan. 16, 2015 TA at 4 PM in the Ch1b Box Problem Two (20 points) In 2011, the world’s nations produced about 38 billion tons of CO2. The rise of atmospheric carbon dioxide has significant effects on not only global warming, but also on the world’s oceans and their inhabitants. While some people have proposed that dissolution of carbon dioxide in the oceans may help curb global warming by removing it from the atmosphere, it is also known that increased aqueous CO2 concentrations results in acidification. a) (5 points) Write out a three-‐step reaction sequence in which steps 1 and 2 show how carbon dioxide can react with water to lower the pH and step 3 shows the production of carbonate ions (CO32-‐). All reactions should be written as equilibria. b) (5 points) Many marine organisms rely on carbonate (CO32-‐) ions to produce calcium carbonate (CaCO3), which is an important component of shell material. Write an equation and use Le Chatelier’s principle to explain what will happen to the calcium carbonate present in shells if the oceans become more acidic. c) (10 points) If 1.0 ton of carbon dioxide was dissolved in 1.0x106 gallons of ocean water, what would be the pH of this sample of ocean water? Use two ICE tables. Assume that the sample of water does not interact with nearby water and assume that other chemical components of the sea water which might change the pH can be ignored. Since the change in moles of water is minute, you can ignore it. The equilibrium constant for the reaction of carbon dioxide with seawater is 1.2 x 10-‐3 and the initial concentration of H+ ions can be taken as 0. The acid dissociation constant (Ka) for H2CO3 is 4.3 x 10-‐7. 2 Name Ch1b, Problem Set One Section Due Friday, Jan. 16, 2015 TA at 4 PM in the Ch1b Box Problem Three (30 points) In the manufacture of ammonia, the chief source of hydrogen gas is the following reaction for the reforming of methane at high temperatures: CH! 𝑔 + 2H! O 𝑔  CO! 𝑔 + 4H! (𝑔) (eqn 1) The following data are also given: a) CO(g)+H2O(g)  CO2(g)+H2(g) Δ𝐻° = −40𝑘𝐽, 𝐾 = 1.4 𝑎𝑡 1000 𝐾 b) CO(g)+3H2(g)  H2O(g)+CH4(g) Δ𝐻° = −230𝑘𝐽, 𝐾 = 190 𝑎𝑡 1000 𝐾 AT 1000 K, 1.00 mol each of CH4 and H2O are allowed to come to equilibrium in a 10.0 L vessel. a. (10 points) Obtain ΔH° and K for the overall reaction in eqn 1. b. (10 points) Fill in the following ICE table to obtain the equilibrium amounts of each species present, using x to denote the magnitude of change: The reaction: CH4(g) + H2O(g)  CO2(g) + 4H2(g) Initial amount: Changes: Equilibrium amounts: c. (5 points) Set up an expression for K and solve for x. Solve for x using your expression for K. Can you make any assumptions to simplify your equation? Why or why not? d. (5 points) Calculate the number of moles of H2 present at equilibrium. 3 Name Ch1b, Problem Set One Section Due Friday, Jan. 16, 2015 TA at 4 PM in the Ch1b Box Problem Four (20 points) AgNO3(aq) is slowly added to a solution that has CrO! !! = 0.010 𝑀 and Br ! =
0.010 𝑀 . There are two equations for solubility equilibria that must be considered, as follows: (1) Ag ! CrO! 𝑠 2Ag ! 𝑎𝑞 + CrO! !! 𝑎𝑞 𝐾!" = 1.1×10!!" (2) AgBr 𝑠 Ag ! 𝑎𝑞 + Br ! 𝑎𝑞 𝐾!" = 5.0×10!!" a. (10 points) Would you expect AgBr(s) or Ag2CrO4(s) to precipitate first? Explain your answer using the solubility products given above. (Hint: What are the required values of [Ag+] for precipitation of each product to start?) b. (5 points) When Ag2CrO4(s) begins to precipitate, what is [Br–] in solution? c. (5 points) Is complete separation of Br–(aq) and CrO42–(aq) by fractional precipitation feasible? Explain your answer in two sentences or less. 4 Name Section TA Problem Five (20 points) Consider the following reaction: Ch1b, Problem Set One Due Friday, Jan. 16, 2015 at 4 PM in the Ch1b Box CO2 + H2 CO + H2O a. (2 points) Write an expression for the equilibrium constant (K) for the reaction. b. (2 points) If equilibrium concentrations are [CO2] = 0.0853 M, [H2] = 0.0322 M, [CO] = 0.00501 M and [H2O] = 0.00465 M at 298 K, calculate K. c. (8 points) If a 5.00 L reaction vessel contains 0.941 mol CO2, 0.510 mol H2, 0.0120 mol CO, and 0.000835 mol H2O, which way will the reaction proceed? d. (5 points) Calculate ∆G˚ at 298 K. e. (3 point) Is the reaction spontaneous at 298 K? Explain. Problem Six (30 points) Phosphoric acid is a triprotic acid (one which can give off up to three protons) whose salts can be used as buffers. It has equilibrium constants Ka1 = 7.1 x 10-‐3, Ka2 = 6.3 x 10-‐8, and Ka3 = 4.2 x 10-‐13. a. (6 points) Write out three equations for the dissociation of H3PO4 (i.e. show how it gives up each H+). b. (4 points) Combine all three equations to provide the overall equation for this reaction. c. (5 points) Write an expression for the overall equilibrium constant, Ktotal, for this reaction in terms of concentration of the reactants and products. Calculate Ktotal using this equation. d. (15 points) Phosphate salts can be used to buffer solutions at various pH levels. In order to calculate the pH of a buffer, the Henderson-‐Hasselbalch equation is needed. For a given chemical equilibrium in the form of HA H+ + A–, the Henderson-‐Hasselbalch equation is pH = pKa + log ([A–]/[HA]) where the pH represents the pH of the buffer solution and the pKa is that of the buffering acid. Using this equation, determine how you would you prepare 10mL of a 0.01M phosphate buffer, pH 7.40, from stock solutions of 0.10M KH2PO4 and 0.25M K2HPO4. Give your answer in terms of mL of each solution and water necessary to bring the solution to 10 mL. 5

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