At what temperature would the root mean square speed of oxygen molecules,O₂,be $14.0 \mathrm {~m} / \mathrm { s }$ if oxygen behaves like an ideal gas? The mass of one O₂ molecule is 5.312 × 10^-26 kg,and the Boltzmann constant is 1.38 × 10^-23 J/K.

Question

Quizplus · Accepted Answer

The root mean square speed $v_{rms}$ is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$. Solving for $T$, we get $T = \frac{mv_{rms}^2}{3k}$. Substituting the given values, $m = 5.312 \times 10^{-26} \, \text{kg}$, $v_{rms} = 14.0 \, \text{m/s}$, and $k = 1.38 \times 10^{-23} \, \text{J/K}$, we find $T \approx 0.251 \, \text{K}$.

At What Temperature Would the Root Mean Square Speed of Oxygen