Four gas molecules have the speed 8.0 ms-1, 6.0 ms-1, 6.0 ms-1 and √120 ms-1 . What is their root-mean-square speed?
Correct answer: A. 8.0 ms-1
- A. 8.0 ms-1
- B. 6.0 ms-1
- C. 5.0 ms-1
- D. 7.0 ms-1
Explanation
To find the root-mean-square (RMS) speed of the gas molecules, use the formula:Vrms = √((v1^2 + v2^2 + v3^2 + v4^2) / total number of molecules)Substituting the given speeds, we calculate: Vrms = √((8.0^2 + 6.0^2 + 6.0^2 + (√120)^2) / 4) = √((64 + 36 + 36 + 120) / 4) = √(256 / 4) = √64 = 8.0 ms-1.However, the correct calculation is actually: Vrms = √((64 + 36 + 36 + 120) / 4) = √(64 + 36 + 36 + 120) / 4 = √64 = 8.0 ms-1, demonstrating the initial explanation was incorrect.Option A is correct because when calculated accurately, the RMS speed comes out to be 8.0 ms-1.
This question appeared on the ETEA MDCAT 2013 paper, which you can sit online with every answer explained.
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Kinetic molecular theory explains gases as rapidly moving particles separated by large distances, with negligible volume and negligible intermolecular attraction in the ideal model. It relates temperature to average kinetic energy and explains gas pressure, Boyle's and Charles's laws, diffusion, effusion and the conditions under which real gases deviate from ideal behavior.
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