Three vessel of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). Do the vessels contains equal number of respectice molecules ? Is the root mean square speed of molecules the same in the three cases ? If not, which case is `v_(rms)` the largest?

Explanation

To solve the problem step by step, let's break it down into two main parts: determining if the vessels contain equal numbers of molecules and comparing the root mean square (rms) speeds of the molecules in each vessel.

### Step 1: Determine if the vessels contain equal numbers of molecules

1. **Understanding Avogadro's Law**: Avogadro's law states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.
2. **Given Conditions**: We have three vessels of equal capacity (volume) containing gases at the same temperature and pressure.
3. **Conclusion**: Since all three vessels have the same volume, temperature, and pressure, according to Avogadro's law, the number of molecules in each vessel must be equal.

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