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, $ T = \frac{(5.312 \times 10^{-26} \, \text{kg})(14.0 \, \text{m/s})^2}{3(1.38 \times 10^{-23} \, \text{J/K})} \approx 0.251 \, \text{K} $.

At What Temperature Would the Root Mean Square Speed of Oxygen