There is a "Marathon Problem" that pertains to almost every chapter in our book. Throughout the year, these problems represent an opportunity to earn bonus points. They are challenging and, as their name implies, they are long. You are welcome to work together on these problems, but each individual must write an answer. If you choose to submit an answer for a Marathon Problem, you can have it graded one of two ways:
· 5 points, all-or-nothin'. If you get all parts of the problem correct, you will earn 5 bonus points added to your semester total of about 500 points. (Yes, that's a percentage point increase to your semester average!) However, it's a bit of gamble: if you get any part wrong, then you receive no points at all.
· 3 points, partial credit. If you get the entire problem correct, you receive a maximum of 3 points. However, good work earns partial credit. If you make a solid attempt at the problem, you are guaranteed some credit.
Each Marathon Problem is due the day you are assessed on that chapter. For example, the Chapter 1 Marathon Problem is due the day you take the quiz on Chapter 1.
Click on one of the numbers below to scroll down to the Marathon Problem of that chapter #:
A cylindrical bar of gold that is 1.5 in high and 0.25 in in diameter has a mass of 23.1984 g, as determined on an analytical balance. An empty graduated cylinder is weighed on a triple-beam balance and has a mass of 73.47 g. After pouring a small amount of a liquid into the graduated cylinder, the mass is 79.16 g. When the gold cylinder is placed in the graduated cylinder (the liquid covers the top of the gold cylinder), the volume indicated on the graduated cylinder 8.5 mL. Assume that the temperatures of the gold bar and the liquid are 86°F. If the density of the liquid decreases by 1.0% for each 10°C rise in temperature (over the range 0 to 50°C), determine
a) the density of the gold at 86°F.
b) The density of the liquid at 40°F.
Note: Parts (a) and (b) can be answered independently.
From the information below, determine the mass of substance C that will be formed if 45.0 grams of substance A reacts with 23.0 grams of substance B. (Assume that the reaction between A and B goes to completion.)
a) Substance A is a gray solid that consists of an alkaline earth metal and carbon (37.5% by mass). It reacts with substance B to produce substances C and D. Forty million trillion formula units of A have a mass of 4.26 milligrams.
b) 47.9 grams of substance B contains 5.36 grams of hydrogen and 42.5 grams of oxygen.
c) When 10.0 grams of C is burned in excess oxygen, 33.8 grams of carbon dioxide and 6.92 grams of water are produced. A mass spectrum of substance C shows a parent molecular ion with a mass-to-charge ratio of 26.
d) Substance D is the hydroxide of the metal in substance A.
Three students were asked to find the identity of the metal in a particular sulfate salt. They dissolved a 0.1472-g sample of the salt in water and treated it with excess barium chloride, resulting in the precipitation of barium sulfate. After the precipitate had been filtered and dried, it weighed 0.2327 g.
Each student analyzed the data independently and came to different conclusions. Pat decided that the metal was titanium. Chris thought it was sodium. Randy reported that it was gallium. What formula did each student assign to the sulfate salt?
Look for information on the sulfates of gallium, sodium, and titanium in your text and in reference books such as the CRC Handbook of Chemistry and Physics. What further tests would you suggest to determine which student is most likely correct?
From the information below, identify element X.
a) The wavelength of the radio waves sent by an FM Station broadcasting at 97.1 Mhz is 30 million (3.00 x 107) times greater than the wavelength corresponding to the energy difference between a particular excited state of the hydrogen atom and the ground state.
b) Let V represent the principal quantum number for the valence shell of element X. If an electron in the hydrogen atom falls from shell V to the inner shell corresponding to the excited stated mentioned above in part (a), the wavelength of light emitted is the same as the wavelength of the an electron moving at the speed of 570. m/s.
c) The number of unpaired electron for element X is the same as the maximum number of electrons in an atom that can have the quantum number designations n = 2, ml = -1, and ms = -1/2.
d) Let A equal the charge of the stable ion that would form when the undiscovered element 120 forms ionic compounds. This value of A also represents the angular momentum quantum number for the subshell containing the unpaired electron(s) for element X.
Identify the five compounds of H, N, and O described below. For each compound, write a Lewis structure that is consistent with the information given.
a) All the compounds are electrolytes, although not all of them are strong electrolytes. Compounds C and D are ionic and compound B is covalent.
b) Nitrogen occurs in its highest possible oxidation state in compounds A and C; nitrogen occurs in its lowest possible oxidation state in compounds C, D, and E. The formal charge on both nitrogens in compound C is +1; the formal charge on the only nitrogen in compound B is 0.
c) Compounds A and E exist only in solution. Both solutions give off gases. Commercially available concentrated solutions of compound A are normally 16 M. The commercial, concentrated solution of compound E is 15 M.
d) Commercial solutions of compound E are labeled with a misnomer that implies that a binary, gaseous compound of nitrogen and hydrogen has reacted with water to produce ammonium ions and hydroxide ions. Actually, this reaction occurs to only a slight extent.
e) Compound D is 43.7% N and 50.0% O by mass. If compound D was a gas at STP, it would have a density of 2.86 g/L.
f) A formula unit of compound C has one more oxygen than a formula unit of compound D. Compounds C and A have one ion in common.
g) Solutions of compound C are weakly acidic; solutions of compound A are strongly acidic; solutions of compounds B and E are basic. The titration of 0.726 g of compound B requires 21.98 mL of 1.00 M HCl for complete neutralization.
A sample consisting of 22.7 g of a nongaseous, unstable compound X is placed inside a metal cylinder with a radius of 8.0 cm, and a piston is carefully placed on the surface of the compound so that, for all practical purposes, the distance between the bottom of the cylinder and the piston is zero. (A hole in the piston allows trapped air to escape as the piston is placed on the compound; then this hole is plugged so that nothing inside the cylinder can escape.) The piston-and-cylinder apparatus in carefully placed in 10.00 L of water at 25.00°C. The barometric pressure is 778 torr.
When the compound spontaneously decomposes, the piston moves up, the temperature of the water reaches a maximum of 29.52°C, and then it gradually decreases as the water loses heat to the surrounding air. The distance between the piston and the bottom of the cylinder, at the maximum temperature, is 59.8 cm. Chemical analysis shows that the cylinder contains 0.30 mol carbon dioxide, 0.25 mol liquid water, 0.025 mol oxygen gas, and an undetermined amount of a gaseous element A.
It is known that the enthalpy change for the decomposition of X, according to the reaction described above, is 1893 kJ/mol X. The standard enthalpies of formation for gaseous carbon dioxide and liquid water are 393.5 kJ/ mol and 286 kJ/mol, respectively. The heat capacity for water is 4.184 J/g°C. The conversion factor between (L x atm) and J can be determined from two values for the gas constant R, namely, 0.08206 (L)(atm)/(mol)(K) and 8.3145 J/(mol)(K). The vapor pressure of water at 29.5°C is 31 torr. Assume that the heat capacity of the piston-and-cylinder apparatus is negligible and that the piston has negligible mass.
Given the preceding information, determine
a) The formula for X.
b) The pressure-volume work (in kJ) for the decomposition of the 22.7-g sample of X.
c) The molar change in internal energy for the decomposition of X and the approximate standard enthalpy of formation for X.
Impure nickel, refined by smelting sulfide ores in a blast furnace, can be converted into metal from 99.90% to 99.99% purity by the Mond process. The primary reaction involved in the Mond process is
Ni(s) + 4 CO(g) Û Ni(CO)4(g)
a) Without referring to Appendix 4, predict the sign of DS° for the above reaction. Explain.
b) The spontaneity of the above reaction is temperature dependent. Predict the sign of DSsurr for this reaction. Explain.
c) For Ni(CO)4(g), DHf° = 607 kJ/mol and S° = 417 J/K×mol at 298 K. Using these values and data in your textbook, calculate DH° and DS° for the above reaction.
d) Calculate the temperature at which DG° = 0 (K = 1) for the above reaction, assuming that DH° and DS° do not depend on temperature.
e) The first step of the Mond process involves equilibrating impure nickel with CO(g) and Ni(CO)4(g) at about 50°C. The purpose of this step is to convert as much nickel as possible into the gas phase. Calculate the equilibrium constant for the above reaction at 50.°C.
f) In the second step of the Mond process, the gaseous Ni(CO)4 is isolated and heated to 227°C. The purpose of this step is to deposit as much nickel as possible as pure solid (the reverse of the above reaction). Calculate the equilibrium constant for the above reaction at 227°C.
g) Why is temperature increased for the second step of the Mond process?
h) The Mond process relies on
the volatility of Ni(CO)4 for its success. Only pressures and temperatures at which Ni(CO)4
is a gas are useful. A recently
developed variation of the Mond process caries out the first step at higher
pressures and a temperature of 152°C. Estimate the maximum pressure of Ni(CO)4(g) that can be attained before the gas will liquefy at
152°C. The boiling point for Ni(CO)4
and the enthalpy of vaporization is 29.0 kJ/mol. [Hint: The phase change reaction and the
corresponding equilibrium expression are
Ni(CO)4(l) Û Ni(CO)4(g) Kp = PNi(CO)4
Ni(CO)4(g) will liquefy when the pressure of Ni(CO)4 is great than the Kp value.]
An empty glass container has a mass of 658.57 g. It has a mass of 659.45 g after it has been filled with nitrogen gas at a pressure of 790. torr and a temperature of 15°C. When the container is evacuated and refilled with a certain element (A) at a pressure of 745 torr and a temperature of 26°C, it has a mass of 660.6 g.
Compound B, a gaseous organic compound that consists of 85.6% carbon and 14.4% hydrogen by mass, is placed in a stainless steel vessel (10.68 L) with excess oxygen gas. The vessel is placed in a constant-temperature bath at 22°C. The pressure in the vessel is 11.98 atm. In the bottom of the vessel is a container that is packed with Ascarite and a desiccant. Ascarite is asbestos impregnated with sodium hydroxide; it quantitatively absorbs carbon dioxide:
2 NaOH(s) + CO2(g) ® Na2CO3(s) + H2O(l)
The desiccant is anhydrous magnesium perchlorate, which quantitatively absorbs the water produced by the combustion reaction as well as the water produced by the above reaction. Neither the Ascarite nor the desiccant reacts with compound B or oxygen. The total mass of the container with the Ascarite and desiccant is 765.3 g.
The reaction is initiated by a spark. The pressure immediately rises, then begins to decrease, and finally reaches a steady value of 6.02 atm. The stainless steel vessel is carefully opened, and the mass of the container inside the vessel is found to be 846.7 g. A and B react quantitatively in a 1:1 mole ratio to form one mole of the single product, gas C.
a) How many grams of C will be produced if 10.0 L of A and 8.6 L of B (each at STP) are reacted by opening a stopcock connecting the two samples?
b) What will be the total pressure in the system?
General Zod has sold Lex Luther what Zod claims to be a new copper-colored form of kryptonite, the only substance that can harm Superman. Lex, not believing in honor among thieves, decided to carry out some tests on the supposed kryptonite. From previous tests, Lex knew that kryptonite is a metal having a specific heat capacity of 0.082 J/g*¡C and a density of 9.2 g/mL.
a) Lex Luther’s first experiment was an attempt to find the specific heat capacity of kryptonite. He dropped a 10 g +/Ð 3 g sample of the metal into a boiling water bath at a temperature of 100.0 ¡C +/Ð 0.2 ¡C. He waited until the metal had reached the bath temperature and then quickly transferred it to 100 g +/Ð 3 g of water that was contained in a calorimeter at an initial temperature of 25.0¡C +/Ð 0.2 ¡C. The final temperature of the metal and water was 25.2 ¡C. Based on these results, is it possible to distinguish between copper and kryptonite? Explain.
b) When Lex found that his results from the first experiment were inconclusive, he decided to determine the density of the sample. He managed to steal a better balance and determined the mass of another portion of the purported kryptonite to be 4 g +/Ð 1 g. He dropped this sample into water contained in a 25-mL graduated cylinder and found that it displaced a volume of 0.42 mL +/ 0.02 mL. Is the metal copper or kryptonite? Explain.
c) Lex was finally forced to determine the crystal structure of the metal General Zod had given him. He found that the cubic unit cell contained 4 atoms and had an edge length of 600. pm. Explain how this information enabled Lex to identify the metal as copper of kryptonite.
d) Will Les be going after Superman with the kryptonite or seeking revenge on General Zod? What improvements could he have made in his experimental techniques to avoid performing the crystal structure determination?
Using on the periodic table, a calculator, and the information below, identify the strong electrolyte whose general formula is
Mx(A)y * Z H2O
Ignore the effect of interionic attractions in the solution.
a) A^nÐ is a common oxyanion. When 30.0 mg of the anhydrous sodium salt containing the oxyanion (NanA, where n = 1, 2, or 3) is reduced in a reaction that involves the gain of 2 moles of electrons per mole of oxyanion, 15.26 mL of 0.02313 M reducing agent is required to react completely with the NanA present. (NanA reactions with the reducing agent in a 1:1 ratio.)
b) The cation is derived from a silvery white metal that is relatively expensive. The metal itself crystallizes in a body-centered cubic unit cell and has an atomic radius of 198.4 pm. The solid, pure metal has a density of 5.243 g/cm^3. The oxidation number of M in the strong electrolyte in question is +3.
c) When 33.4 mg of the compound is present (dissolved) in 10.0 mL of aqueous solution at 25¡C, the solution has an osmotic pressure of 558 torr.
Consider the reaction
A(g) + B(g) <==> C(g)for which K = 1.30 * 10^2. Assume that 0.406 mol C(g) is placed in a cylinder that is capable of expanding. The temperature is 300.0 K, and the barometric pressure on the outside of the cylinder is constant at 1.00 atm. The original volume [before the 0.406 mole C(g) begins to decompose] is 10.00 L. What is the volume in the cylinder at equilibrium?