Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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:

All vessels contain an unequal number of respective molecules.

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

The root mean square speed of helium is the largest.

The root mean square speed of sulfur hexafluoride is the largest.

Step-by-Step Solution

Number of Molecules: According to Avogadro's Law, equal volumes of all gases under the same conditions of temperature and pressure contain an equal number of molecules. Since capacity (volume), temperature, and pressure are the same, all vessels contain the same number of molecules. Thus, option 1 is incorrect.
RMS Speed ( $v_{rms}$ ): The root mean square speed is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$ , where $M$ is the molar mass. Since $T$ is constant, $v_{rms} \propto \frac{1}{\sqrt{M}}$ .
Comparison:

Molar mass of Helium ( $He$ ) $\approx 4$ g/mol.
Molar mass of Fluorine ( $F_2$ ) $\approx 38$ g/mol.
Molar mass of Sulfur Hexafluoride ( $SF_6$ ) $\approx 146$ g/mol. Since Helium has the smallest molar mass, it possesses the largest RMS speed. Sulfur hexafluoride has the largest mass and thus the smallest RMS speed.

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