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Molecular Speeds - Vrms, Vavg, Vmps

The RMS speed...

Question

The RMS speed at NTP of alas can be calculated from the expression:

\sqrt{3 P / d}

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\sqrt{3 P V / M}

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\sqrt{3 R T / M}

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\sqrt{3 d / P}

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Solution

The correct option is D $\sqrt{3 P / d}$
RMS speed at NTP is calculated by $\sqrt{3 P / d}$
Where d is density and P is pressure.

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Similar questions

The rms velocity at NTP of the species can be calculated from the expression

\sqrt{\frac{3 P V}{M}}

P V = \frac{1}{3} (m N_{A}) u^{2} = \frac{1}{3} M u^{2}

m N_{A} = M

N_{A} = Avogadro's number

u = root mean square velocity

Translational kinetic energy of n mole \frac{1}{2} M u^{2} = \frac{3}{2} (P V) = \frac{3}{2} (n R T)

Average translational kinetic energy per molecule = \frac{3}{2} (\frac{R T}{N_{A}}) = \frac{3}{2} (K T)

u_{r m s} = \sqrt{\frac{3 P V}{M}} = \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 P}{d}}

u_{a v} = \sqrt{\frac{8 R T}{π M}}

10^{- 12}

27^{\circ} C

(Given R = 8 J K^{- 1} m o l^{- 1}, N_{A} = 6 \times 10^{23})

P V = \frac{1}{3} (m N_{A}) u^{2} = \frac{1}{3} M u^{2}

m N_{A} = M

N_{A} = Avogadro's number

u = root mean square velocity

Translational kinetic energy of n mole \frac{1}{2} M u^{2} = \frac{3}{2} (P V) = \frac{3}{2} (n R T)

Average translational kinetic energy per molecule = \frac{3}{2} (\frac{R T}{N_{A}}) = \frac{3}{2} (K T)

u_{r m s} = \sqrt{\frac{3 P V}{M}} = \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 P}{d}}

u_{a v} = \sqrt{\frac{8 R T}{π M}}

R M S

N T P

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