Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains helium (monoatomic), the second contains fluorine (diatomic) and the third contains sulfur hexafluoride (polyatomic). The correct statement, among the following is :

The root mean square speed of helium is the largest

The root mean square speed of sulfur hexafluoride is the largest

All vessels contain unequal number of respective molecules

The root mean square speed of molecules is same in all three cases

Heat and Thermodynamics PYQ — NEET 2022 · Q181 with Solution

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Correct answer: D

All three vessels have equal volume and same temperature and pressure.

From ideal gas equation

$PV = nRT$

$nR = {{PV} \over T}$

$$n = {{PV} \over {RT}} = $$ constant

So, here all three vessels contains equal number of moles and number of gas molecules.

Now, $${v_{rms}} = \sqrt {{{3RT} \over M}} \Rightarrow {v_{rms}} \propto {1 \over {\sqrt M }}$$

Here, rms speed of helium is the largest.