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Chapter 5: Problem 67

What does the Maxwell speed distribution curve tell us? Does Maxwell's theory work for a sample of 200 molecules? Explain.

Short Answer

Expert verified
The Maxwell speed distribution curve reveals that at any given temperature, gas molecules possess a wide range of speeds, with a particular speed at which the maximum number of molecules move. While Maxwell's theory gives accurate predictions for large numbers of molecules, it may not perfectly apply to a small sample due to statistical fluctuations.

Step by step solution

01

Understanding the Maxwell speed distribution curve

In Kinetic Theory, the Maxwell speed distribution curve is a statistical means of representing the speeds of gas molecules in a given sample at a specific temperature. The speed distribution is presented in a graph where the x-axis signifies the speed (or velocity) and the y-axis represents the number of molecules. The curve tells us that at any given temperature, gas molecules have a wide range of speeds, from quite slow to extremely fast. It also indicates that there's a particular speed (most probable speed) at which the maximum number of molecules moves.
02

Application of Maxwell's theory to a small sample

Maxwell's theory is a statistical theory which means it applies to larger samples of molecules. The statistical approach considers the average behavior of a large number of particles. Thus, for a sample of only 200 molecules, the distribution may not be perfect and the most probable speed that Maxwell's theory predicts might not be the most common speed in such a small sample. This is due to statistical fluctuations, where the smaller the sample, the larger the relative fluctuations. In statistical mechanics, it is assumed that a macroscopic system consists of a very large number of particles. That is not the case for a sample of 200 molecules.

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Most popular questions from this chapter

A mixture of gases contains \(\mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{6},\) and \(\mathrm{C}_{3} \mathrm{H}_{8}\). If the total pressure is 1.50 atm and the numbers of moles of the gases present are 0.31 mole for \(\mathrm{CH}_{4}\) 0.25 mole for \(\mathrm{C}_{2} \mathrm{H}_{6},\) and 0.29 mole for \(\mathrm{C}_{3} \mathrm{H}_{8},\) calculate the partial pressures of the gases.

A \(2.5-\mathrm{L}\) flask at \(15^{\circ} \mathrm{C}\) contains a mixture of three gases, \(\mathrm{N}_{2},\) He, and \(\mathrm{Ne},\) at partial pressures of \(0.32 \mathrm{~atm}\) for \(\mathrm{N}_{2}, 0.15 \mathrm{~atm}\) for \(\mathrm{He},\) and \(0.42 \mathrm{~atm}\) for Ne. (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the \(\mathrm{N}_{2}\) is removed selectively.

Assuming that air contains 78 percent \(\mathrm{N}_{2}, 21\) percent \(\mathrm{O}_{2},\) and 1 percent \(\mathrm{Ar},\) all by volume, how many \(\mathrm{mol}-\) ecules of each type of gas are present in \(1.0 \mathrm{~L}\) of air at STP?

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