We separate U-235 from U-238 by fluorinating a sample of uranium to form UF6 (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio of effusion rates for 238UF6 and 235UF6. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.
Ch.5 - Gases
Chapter 5, Problem 88
A sample of N2O effuses from a container in 42 seconds. How long will it take the same amount of gaseous I2 to effuse from the same container under identical conditions?
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Graham's Law of Effusion
Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases effuse faster than heavier gases. In this question, we can use this principle to compare the effusion rates of N2O and I2, allowing us to calculate the time it takes for I2 to effuse based on the known time for N2O.
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Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in Graham's Law, as the molar masses of the gases involved determine their rates of effusion. For N2O, the molar mass is approximately 44 g/mol, while for I2, it is about 254 g/mol, indicating that I2 is significantly heavier and will effuse more slowly.
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Effusion
Effusion is the process by which gas molecules escape from a container through a small opening into a vacuum or another space. The rate of effusion is influenced by factors such as temperature and the size of the gas molecules. Understanding effusion is essential for solving the problem, as it allows us to apply Graham's Law to determine the time required for I2 to effuse based on the effusion time of N2O.
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