Question

Calculate the root mean square velocity and average velocity for oxygen molecules at 0 degrees c

Answer 1

Given:

Temperature = 0°C

Mass of oxygen molecule = 32 gmol⁻¹

To find:

Root mean square velocity and average velocity.

Solution:

Kinetic energy of molecule are dependent on temperature and molecular mass of molecule. Just like that root mean square velocity also depends on temperature and molecular mass of molecule.

Root mean square velocity can be calculated as -

    $v_r_m_s = \sqrt{\frac{3 RT}{M} }$

here, $v_r_m_s$ = root mean square velocity

         R = gas constant

         T = temperature(0⁰C = 273K)

         M = molecular mass

by, substituting all the values, we get

       $v_{rms} = \sqrt{\frac{3 \times 8.314 Jmol^-^1K^-^1 \times 273K}{0.032Kgmol^-^1} }$

       $v_{rms} = \sqrt{\frac{6809.166}{0.032} }$

       $v_{rms} = \sqrt{212786.43}$

      $v _{rms} = 461.28 ms^-^1$

The root mean square velocity for oxygen molecule is 461.28 ms⁻¹.

The average velocity of a gas molecule is directly proportional to temperature and inversely proportional to molecular mass of gas molecule.

Formula used to calculate average velocity is -

         $v_{avg} = \sqrt{\frac{8RT}{\pi M} }$

here, $v_{avg}$ = average speed velocity

         M = molecular mass

         R = gas constant

         T = temperature

therefore, putting all the values, we get

        $v_{avg} = \sqrt{\frac{8 \times 8.314 \times 273}{3.14 \times 0.032} }$

        $v_{avg} = \sqrt{\frac{18157.776}{0.10048} }$

        $v_{avg} = \sqrt{180710.35}$

        $v_{avg} = 425.10 ms^-^1$

The average velocity of oxygen molecule is 425.1 ms⁻¹.