Textbook Question
A typical nuclear reactor produces about 1.0 MW of power per day. What is the minimum rate of mass loss required to produce this much energy?
Ch.21 - Radioactivity & Nuclear Chemistry
Chapter 21, Problem 84
In one of the neutron-induced fission reactions of U-235 (atomic mass = 235.043922 amu), the products are Ba-140 and Kr-93 (a radioactive gas). What volume of Kr-93 (at 25.0 °C and 1.0 atm) is produced when 1.00 g of U-235 undergoes this fission reaction?
Verified step by step guidance1
Calculate the number of moles of U-235 using its atomic mass: \( \text{moles of U-235} = \frac{\text{mass of U-235}}{\text{atomic mass of U-235}} \).
Use the stoichiometry of the fission reaction to determine the moles of Kr-93 produced. Assume a 1:1 molar ratio between U-235 and Kr-93 for simplicity.
Apply the ideal gas law to find the volume of Kr-93 produced: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
Convert the temperature from Celsius to Kelvin: \( T(K) = T(°C) + 273.15 \).
Solve the ideal gas law equation for \( V \) to find the volume of Kr-93: \( V = \frac{nRT}{P} \).
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Nuclear Fission
Nuclear fission is a process in which a heavy nucleus, such as U-235, splits into two smaller nuclei, along with the release of energy and neutrons. This reaction can be initiated by the absorption of a neutron, leading to the formation of fission products like Ba-140 and Kr-93. Understanding this process is crucial for calculating the amounts of products formed in a fission reaction.
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Stoichiometry
Stoichiometry involves the calculation of reactants and products in chemical reactions based on the conservation of mass. In the context of fission, it allows us to determine the moles of U-235 consumed and the corresponding moles of fission products produced. This is essential for converting the mass of U-235 into the volume of Kr-93 produced.
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Ideal Gas Law
The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. It is used to calculate the volume of gases under specific conditions. In this question, it will help determine the volume of Kr-93 produced from the moles calculated from the fission reaction, given the temperature and pressure conditions.
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