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QJEEAdv19Ch5c85: JEE Advanced 2019 Chemistry - Class 11 JEEAdv19Ch5c85 Solution: Which of the following statement(s) is(are) correct regarding…

Which of the following statement(s) is(are) correct regarding the root mean square speed (Urms) and average translational kinetic energy (Eav) of a molecule in a gas at equilibrium?

Multiple Choice Options

  • A Urms is inversely proportional to the square root of its molecular mass.
  • B Urms is doubled when its temperature is increased four times.
  • C Eavg is doubled when its temperature is increased four times.
  • D Eavg at a given temperature does not depend on its molecular mass.

Step-by-Step Verified Solution

The explanation of given statements are as follows :

(a) Urms is inversely proportional to the square root of its molecular mass.

Urms=3RTM{U_{rms}} = \sqrt {{{3RT} \over M}}

Hence, option (a) is correct.

(b) When temperature is increased four times then Urms become doubled.

Urms=3RM×4T{U_{rms}} = \sqrt {{{3R} \over M} \times 4T}

Urms=2×3RTM{U_{rms}} = 2 \times \sqrt {{{3RT} \over M}}

Hence, option (b) is correct.

(c) and (d) Eav is directly proportional to temperature but does not depends on its molecular mass at a given temperature as Eav=32KT{E_{av}} = {3 \over 2}KT . If temperature raised four times than Eav becomes four time multiple.

Thus, option (c) is incorrect and option (d) is correct.

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