JEE Advance - Chemistry (2019 - Paper 1 Offline - No. 8)
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?
Urms is inversely proportional to the square root of its molecular mass.
Urms is doubled when its temperature is increased four times.
Eavg is doubled when its temperature is increased four times.
Eavg at a given temperature does not depend on its molecular mass.
Explanation
The explanation of given statements are as follows :
(a) Urms is inversely proportional to the square root of its molecular mass.
$${U_{rms}} = \sqrt {{{3RT} \over M}} $$
Hence, option (a) is correct.
(b) When temperature is increased four times then Urms become doubled.
$${U_{rms}} = \sqrt {{{3R} \over M} \times 4T} $$
$${U_{rms}} = 2 \times \sqrt {{{3RT} \over M}} $$
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 $${E_{av}} = {3 \over 2}KT$$. If temperature raised four times than Eav becomes four time multiple.
Thus, option (c) is incorrect and option (d) is correct.
(a) Urms is inversely proportional to the square root of its molecular mass.
$${U_{rms}} = \sqrt {{{3RT} \over M}} $$
Hence, option (a) is correct.
(b) When temperature is increased four times then Urms become doubled.
$${U_{rms}} = \sqrt {{{3R} \over M} \times 4T} $$
$${U_{rms}} = 2 \times \sqrt {{{3RT} \over M}} $$
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 $${E_{av}} = {3 \over 2}KT$$. 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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