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Referring to Figure $17.1,$ we see that the probability of finding all 100 molecules in the same bulb is $8 \times 10^{-31} .$ Assuming that the age of the universe is 13 billion years, calculate the time in seconds during which this event can be observed.

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$$3 \times 10^{-13} s$$

Chemistry 102

Chapter 17

Entropy, Free Energy, and Equilibrium

Thermodynamics

Rice University

University of Maryland - University College

University of Kentucky

Brown University

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So, uh, we've got, ah, a time centered, minus 31 chance. I guess that would be for finding all 100 molecules in one bowl when they could be otherwise distributed. So ah, we want to take all of the time since the beginning of the universe. 13 billion years. Convert that two seconds and then multiply that by the probability. So, really, all of this is just taking that year, converting today's two hours two minutes two seconds than multiplying by the probability. And we get 3.3 times 10 to the negative 13 second. So if the arrangement was constantly changing and that arrangement dead occurred some point, it would not last very long. Three times 10 to the minus 13 seconds.

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