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Ch.21 - Nuclear Chemistry
All textbooksBrown 14th EditionCh.21 - Nuclear ChemistryProblem 88
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Chapter 21, Problem 88

Calculate the mass of octane, C8H18, that must be burned in air to evolve the same quantity of energy as produced by the fusion of 1.0 g of hydrogen in the following fusion reaction: 4 1^1H → 4 2He + 2 0^1e. Assume that all the products of the combustion of octane are in their gas phases. Use data from Exercise 21.50, Appendix C, and the inside covers of the text. The standard enthalpy of formation of octane is -250.1 kJ/mol.

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Step 1: Calculate the energy released by the fusion of 1.0 g of hydrogen. Use the given fusion reaction: 4 1^1H → 4 2He + 2 0^1e. Determine the energy released per mole of hydrogen atoms and then convert this to the energy released per gram of hydrogen.
Step 2: Determine the energy released per mole of octane (C8H18) during combustion. Use the standard enthalpy of formation of octane (-250.1 kJ/mol) and the balanced chemical equation for the combustion of octane: 2 C8H18 + 25 O2 → 16 CO2 + 18 H2O.
Step 3: Calculate the total energy released by burning one mole of octane. This involves using the enthalpy change of the combustion reaction, which can be found by using the standard enthalpies of formation for CO2 and H2O from Appendix C.
Step 4: Compare the energy released by the fusion of hydrogen to the energy released by the combustion of octane. Set up a proportion to find the mass of octane needed to release the same amount of energy as the fusion of 1.0 g of hydrogen.
Step 5: Solve the proportion to find the mass of octane required. Use the molar mass of octane (C8H18) to convert from moles to grams, ensuring that the energy released by the combustion of this mass of octane matches the energy released by the fusion of hydrogen.
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Related Practice
Open Question
The average energy released in the fission of a single uranium-235 nucleus is about 3 * 10^-11 J. If the conversion of this energy to electricity in a nuclear power plant is 40% efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces 1000 megawatts? Recall that a watt is 1 J/s.
Open Question
Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits 8 * 10^-13 J of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.
Open Question
A 53.8-mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half-life of chlorine-36 is 3.0 * 105 yr.
Open Question
Naturally found uranium consists of 99.274% 238U, 0.720% 235U, and 0.006% 234U. As we have seen, 235U is the isotope that can undergo a nuclear chain reaction. Most of the 235U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF6(g). (a) What is the mass of UF6 in a 30.0-L vessel of UF6 at a pressure of 695 torr at 350 K? (b) What is the mass of 235U in the sample described in part (a)? (c) Now suppose that the UF6 is diffused through a porous barrier and that the change in the ratio of 238U and 235U in the diffused gas can be described by Equation 10.23. What is the mass of 235U in a sample of the diffused gas analogous to that in part (a)? (d) After one more cycle of gaseous diffusion, what is the percentage of 235UF6 in the sample?
Open Question
Charcoal samples from Stonehenge in England were burned in O2, and the resultant CO2 gas bubbled into a solution of Ca(OH)2 (limewater), resulting in the precipitation of CaCO3. The CaCO3 was removed by filtration and dried. A 788-mg sample of the CaCO3 had a radioactivity of 1.5 × 10^-2 Bq due to carbon-14. By comparison, living organisms undergo 15.3 disintegrations per minute per gram of carbon. Using the half-life of carbon-14, 5700 years, calculate the age of the charcoal sample.
Textbook Question

A 25.0-mL sample of 0.050 M barium nitrate solution was mixed with 25.0 mL of 0.050 M sodium sulfate solution labeled with radioactive sulfur-35. The activity of the initial sodium sulfate solution was 1.22⨉106 Bq/mL. After the resultant precipitate was removed by filtration, the remaining filtrate was found to have an activity of 250 Bq/mL. (a) Write a balanced chemical equation for the reaction that occurred.

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