Question

At what temperature will the root-mean-square speed of oxygen molecules have the value of 640 m/s? 1 kilomole of oxygen has a mass of 32kg.

Answer 1

Answer on Question #45271, Physics, Molecular Physics | Thermodynamics

Question:

At what temperature will the root-mean-square speed of oxygen molecules have the value of $640~\mathrm{m/s}$? 1 kilomole of oxygen has a mass of $32\mathrm{kg}$.

Answer:

The root mean square velocity can be expressed as:

$$v = \sqrt{\frac{3RT}{M}}$$

where $R$ is ideal gas constant $R = 8.3145 \frac{J}{K \cdot mol}$, $T$ is absolute temperature in Kelvin, $M$ is mass of a mole of the gas in kilograms.

Therefore, temperature equals:

$$T = \frac{v^2 M}{3R} = \frac{640^2 \cdot 0.32}{3 \cdot 8.31} = 5258~K \approx 5300~K$$

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