Chemistry: If the absolute temperature of a gas is tripled, what happens to the root‑mean‑square speed of the molecules? a. nothing happens to the rms speed. b. the new rms speed is 9 times the original rms speed. c. the new rms speed is 3 times the original rms speed. d. the new rms speed is 1.732 times the original rms speed. e. the new rms speed is 1/3 the original rms speed.

If the absolute temperature of a gas is tripled,

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10.01.2022

D. The new rms speed is 1.732 times the original rms speed.

Explanation:

The expression for the root mean square speed is:

$C_{rms}=\sqrt {\dfrac {3RT}{M}}$

R is Gas constant having value = 8.314 J / K mol

M is the molar mass of gas

T is the absolute temperature

As seen from the formula, root mean square speed is directly proportional to the square root of the absolute temperature.

So,

$C_{rms}\propto \sqrt {T}$

Given, absolute temperature of a gas is tripled, so, the new rms speed will be √3 (1.732) of the original.

Hence, the correct option is:- D. The new rms speed is 1.732 times the original rms speed.

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