Question
Two samples of ideal gas in separate containers have the same number of molecules and the same temperature, but the molecular mass of gas X is greater than that of gas Y. Which of the following correctly compares the average speed of the molecules of the gases and the average force the gases exert on their respective containers?
| Average Speed of Molecules | Average Force on Container | |
|---|---|---|
| (a) | Greater for gas X | Greater for gas X |
| (b) | Greater for gas X | The forces cannot be compared without knowing the volumes of the gases. |
| (c) | Greater for gas Y | Greater for gas Y |
| (d) | Greater for gas Y | The forces cannot be compared without knowing the volumes of the gases. |
Final Answer
(d)
Solution video
OpenStax College Physics for AP® Courses, Chapter 13, Problem 3 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. So we have two samples of ideal gases which means these ideal gas law formulas apply. In two containers, there's the same number of molecules so that means n is the same, same number of moles. Now, the same temperature but the molecular mass of gas X is greater than that of gas Y. So that means the mass of a single molecule of X is greater than a single molecule of gas Y. And so with a greater mass for X, it will have a smaller Vrms because as you increase this denominator you're going to decrease the quotient. And so gas Y will have the higher Vrms because it has a lower molar molecular mass. So, that narrows our options down to c or d. And the next part of the question is how is the average force of the gas exert in the respective container is compare. So average force in the container is another way of saying pressure. And so we've solve for pressure here by dividing both sides by V in our pV equals nRT formula. And so we have same number of moles, same number of molecule, same gas constant obviously, same temperature and we don't know what the volumes of the containers are, though. We're not told that the containers are the same volume. And so we're not able to compare the pressures. And so the answer is d. The forces cannot be compared without knowing the volumes of the gases.