Question

The coldest temperature recorded at ground level on Earth was −89.2 °C at the Vostok Station in Antarctica. What is the speed of a nitrogen molecule at this temperature?

Group of answer choices

a. 12.8 m/s

b. 40.2 m/s

c. 404 m/s

d. 933 m/s

Answer 1

The conversion of temperature from \(-89.2^{\circ} \mathrm{C}\) to Kelvin:

\(\begin{aligned} \mathrm{T}(\mathrm{K}) &=\mathrm{T}\left({ }^{\circ} \mathrm{C}\right)+273 \mathrm{~K} \\ &=-89.2+273 \mathrm{~K} \\ &=183.8 \mathrm{~K} \end{aligned}\)

The relation between temperature and velocity is:

\(\mathrm{v}_{\mathrm{ms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}\)

The velocity of nitrogen molecule at \(-89.2^{\circ} \mathrm{C}\) at the Vostok Station in Antarctica is:

\(\begin{aligned} \mathrm{v}_{\mathrm{ms}} &=\sqrt{\frac{3 \times 8.314 \mathrm{~kg} \cdot \mathrm{m}^{2} \cdot \mathrm{s}^{-2} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1} \times 183.8 \mathrm{~K}}{28 \mathrm{~g} \cdot \mathrm{mol}^{-1} \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}}}} \\ &=404 \mathrm{~m} / \mathrm{s} \end{aligned}\)

The correct option is c) \(404 \mathrm{~m} / \mathrm{s}\).