Question

. 04. The RMS velocity of Nitrogen molecules at N.T.P. is?​

Answer 1

Answer:

• The R.M.S velocity of Nitrogen molecules at N.T.P. is 493 m/s

Given:

Here, N.T.P specifies Standard conditions.

1. Therefore, Temperature will be 273 K.
2. Molar mass of Nitrogen = 28 grams.

Explanation:

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From the Formula,

$\large \bigstar\;{\boxed{\tt V_{RMS} = \sqrt{\dfrac{3\;R\;T\;}{M}}}}$

$\bold{Here}\begin{cases}\text{R Denotes Universal gas constant} \\ \text{T Denotes Temperature} \\ \text{M Denotes Molar mass (Kg)} \end{cases}$

Now,

$\large{\boxed{\tt V_{RMS} = \sqrt{\dfrac{3\;R\;T}{M}}}}$

Substituting the Values,

$\longmapsto\large{\tt V_{RMS} = \sqrt{\dfrac{3 \times 8.314 \times 273}{0.028}}}$

As,

• R = 8.314 J/mol.K
• Mass of Nitrogen = 28 grams = 0.028 Kg.

$\longmapsto\large{\tt V_{RMS} = \sqrt{\dfrac{24.942 \times 273}{0.028}}}$

$\longmapsto\large{\tt V_{RMS} = \sqrt{\dfrac{6809.166}{0.028}}}$

$\longmapsto\large{\tt V_{RMS} = \sqrt{243184.5}}$

$\longmapsto\large{\underline{\boxed{\red{\tt V_{RMS} = 493.137 \; m/s}}}}$

∴ The R.M.S velocity of Nitrogen molecules at N.T.P. is 493 m/s (approx).

$\boxed{\begin{minipage}{7.5cm} \bigstar \underline{\text{Extra Formulas}} \\\\ \tt \star \;V_{(average)} = \sqrt{\dfrac{8 \; R \; T}{\pi \; M}} \\\\ \tt \star \;V_{(mp)} = \sqrt{\dfrac{2 \; R \; T}{ M}} \\\\ \star \; \text{Ratio of Three velocities,} \\ \longmapsto V_{(RMS)} : V_{(mp)} : V_{(Average)} = \sqrt{3} : \sqrt{2} : \sqrt{\dfrac{8}{\pi}} \\\\ \rule{200}{1} \\ \text{Note} \\ \bullet\; V_{(mp)} = \text{Most probable Speed} \\ \bullet\;V_{(average)} = \text{Average Speed} \end{minipage}}$

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Answer 2

Question

The RMS velocity of Nitrogen molecules at N.T.P. is

Solution

Given,

The nitrogen molecules are NTP

• Temperature is 293 K

• Pressure is 1 atm

To finD

RMS Velocity of the Nitrogen Molecules

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RMS Velocity is given as

$\boxed{\boxed{\sf V_RMS = \sqrt{\dfrac{3RT}{M}}}}$

$\sf{Here}\begin{cases}\sf{T \longrightarrow Temperature }\\\sf{R \longrightarrow Gas Constant}\\ \sf{M \longrightarrow Molar Mass}\end{cases}$

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Nitrogen molecules occupy 28g at NTP

• Nitrogen molecules occupy 28 × 10^-3 Kg at NTP

• The gas constant is 8.2 NTP conditions

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Substituting the values,we get :

$\longmapsto \: \tt \: v = \sqrt{ \dfrac{3 \times 8.2 \times 293}{28 \times {10}^{ - 3} } } \\ \\ \: \longmapsto \: \tt \: v = \sqrt{ \dfrac{7207.8 \times {10}^{3} }{28} } \\ \\ \longmapsto \ \boxed{\boxed{\tt{v = 160.60 ms^{-1}}}}}$

The RMS Velocity of the nitrogen molecules is 160.60 m/s

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