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. A)0.251 K B)2090 K C)6270 K D)1.52 × 10²³ K

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Quizplus · Accepted Answer

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

At What Temperature Would the Root Mean Square Speed of Oxygen