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Ch.21 - Nuclear Chemistry
All textbooksBrown 14th EditionCh.21 - Nuclear ChemistryProblem 92b
Chapter 21, Problem 92b

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. (b) Calculate the Ksp for the precipitate under the conditions of the experiment.

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Identify the chemical reaction: When barium nitrate (Ba(NO₃)₂) is mixed with sodium sulfate (Na₂SO₄), barium sulfate (BaSO₄) precipitates. The balanced chemical equation is: Ba(NO₃)₂ (aq) + Na₂SO₄ (aq) → BaSO₄ (s) + 2 NaNO₃ (aq).
Determine the initial moles of barium ions and sulfate ions: Calculate the moles of Ba²⁺ and SO₄²⁻ using the molarity and volume of the solutions. For Ba²⁺: moles = 0.050 M × 0.025 L. For SO₄²⁻: moles = 0.050 M × 0.025 L.
Calculate the change in activity: The initial activity of the sodium sulfate solution is given as 1.22 × 10⁶ Bq/mL. Calculate the total initial activity by multiplying by the volume. The final activity of the filtrate is 250 Bq/mL, so calculate the total final activity by multiplying by the total volume of the filtrate.
Determine the amount of sulfate ions remaining in solution: Use the change in activity to find the moles of sulfate ions that remain in the solution. Subtract this from the initial moles of sulfate ions to find the moles of sulfate ions that precipitated as BaSO₄.
Calculate the Ksp of BaSO₄: Use the moles of Ba²⁺ and SO₄²⁻ that remain in solution to find their concentrations in the final solution. The Ksp expression for BaSO₄ is Ksp = [Ba²⁺][SO₄²⁻]. Substitute the concentrations into this expression to calculate the Ksp.

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Related Practice
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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Textbook Question
The two most common isotopes of uranium are 235U and 238U. (d) 238U undergoes radioactive decay to 234Th. How many protons, electrons, and neutrons are gained or lost by the 238U atom during this process?
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