Hydrogen molecules at 300 K have a certain rms speed…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Hydrogen molecules at K have a certain rms speed. To what temperature must oxygen be heated so that its molecules have the same rms speed? Hydrogen is g/mol and oxygen is g/mol.
Need a reminder? The key ideaShow
with in kg/mol. The ratio is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. . The speeds are equal when is the same for both gases.
Step 1. .
Step 2. K.
Answer: K. Oxygen is 16 times heavier, so it needs 16 times the temperature, not 4 times.
Watch out. The speeds go as , but here we need equal speeds, so itself must match. The square root does not change the ratio of temperatures.
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