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Ch.21 - Nuclear Chemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Brown 14th EditionCh.21 - Nuclear Chemistry문제 89
21장, 문제 89

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?

검증된 단계별 안내
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Step 1: To find the mass of UF6 in a 30.0-L vessel at 695 torr and 350 K, use the ideal gas law: PV = nRT. Convert the pressure from torr to atm by dividing by 760. Use R = 0.0821 L·atm/mol·K for the gas constant.
Step 2: Solve the ideal gas law equation for n (number of moles): n = PV / RT. Substitute the values for P (in atm), V (30.0 L), R, and T (350 K) to find n.
Step 3: Calculate the molar mass of UF6. The molar mass of uranium (U) is approximately 238 g/mol, and the molar mass of fluorine (F) is approximately 19 g/mol. Since there are six fluorine atoms, the molar mass of UF6 is 238 + 6(19).
Step 4: Multiply the number of moles of UF6 (n) by the molar mass of UF6 to find the mass of UF6 in the vessel.
Step 5: To find the mass of 235U in the UF6 sample, calculate the fraction of 235U in natural uranium (0.720%) and apply it to the mass of UF6. Consider the molar mass of 235U when calculating its mass in the sample.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the mass of UF6 in the given vessel, as it allows us to determine the number of moles of gas present under specific conditions of pressure and temperature.
추천 영상:
가이드 코스
01:15
Ideal Gas Law Formula

Isotopes and Atomic Mass

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. Understanding the composition of naturally occurring uranium, particularly the proportions of 238U and 235U, is crucial for calculating the mass of 235U in the UF6 sample.
추천 영상:
가이드 코스
02:19
Atomic Mass

Gaseous Diffusion

Gaseous diffusion is the process by which gas molecules move from an area of higher concentration to an area of lower concentration through a porous barrier. This concept is important for understanding how the ratio of isotopes changes during the diffusion of UF6, which affects the mass of 235U in the diffused gas and subsequent calculations.
추천 영상:
가이드 코스
02:33
Effusion vs Diffusion
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교과서 질문

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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교과서 질문

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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