[Solved] Find The Rms Speed Of Nitrogen Molecules In A Gas At 300 K

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CONCEPT

  • Root Mean Square Speed is defined as the square root of the mean of squares of the speed of different molecules.
    • The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
    • The rms speed of any homogeneous gas sample is given by:

\(V_{rms}= \sqrt {\frac{{3RT}}{M}} \)

Where R = universal gas constant, T = temperature and M = molar mass

CALCULATION:

Given - Temperature (T) = 300 K, molar mass of Nitrogen (M) =28 gm./mol = 28 × 10-3 kg/mol

    • The rms speed of nitrogen molecules in a gas is given by:

\(\Rightarrow V_{rms}= \sqrt {\frac{{3RT}}{M}} \)

\(\Rightarrow {V_{rms}} = \sqrt {\frac{{3\; × \;8.3\; × \;300}}{{28\; × \;{{10}^{ - 3}}}}} = 516.5\frac{m}{s}\)

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