Question

Molar mass of a gas is 4 grams. At certain temperature, kinetic energy per mole of the gas is 1.8x10 ergs. At the same temperature, RMS velocity of the gas would be​

Answer 1

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Answer 2

Given:

Molar mass of gas = 4 g

Kinetic energy per mole = 1.8 × 10 erg

To find:

RMS velocity of the gas

Solution:

Relationship between kinetic energy per mole and root mean square velocity is as given below,

          $u = \sqrt{\frac{2K.E.}{m} }$

here, u = root mean square velocity

        K.E. = kinetic energy  

         m = mass of the gas

now, converting erg into joules,

1 erg = 10⁻⁷ J

1.8 × 10 erg = 1.8 × 10⁻⁶ J = 1.8 × 10⁻⁶ kgm²s⁻²

So, K.E. = 1.8 × 10⁻⁶ kgm²s⁻²

converting g into kg, we have

1 g = 10⁻³ kg

4 g = 4 × 10⁻³ kg

So, molar mass of a gas = 4 × 10⁻³ kg.

by substituting all the values, we get,

       $u = \sqrt{\frac{2 \times 1.8 \times 10^-^6 kgm^2s^-^2}{4 \times 10^-^3 kg} }$

       $u = \sqrt{0.9 \times 10^-^6^+^3 m^2s^-^2}$

       $u = \sqrt{9 \times 10^-^4 m^2s^-^2}$

      u = 3 × 10⁻² ms⁻¹

Therefore, root mean square velocity is 3 × 10⁻² ms⁻¹.