Question
What is the temperature at which all the gas molecule become immobile?

Answer

According to the molecular kinetic theory of gas, the average kinetic energy per molecule of gas is directly proportional to the absolute temperature, that mean
$\frac{1}{2} mC _{ rms }^2 \propto T$
The mean square velocity $\left( C _{ rms }\right)$ of the gas will be zero if absolute temeprature $T =0$.
Therefore, at absolute zero temperature all the molecules become motionless.

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