On Mars, the temperature can reach 290 K and the escape speed is 5.0 km/sec. What is the average speed of a carbon dioxide molecule (mass = 7.31 × 10^-26 kg) at this temperature, and what can you say about the retention of carbon dioxide on Mars? A)The average speed is 0.4 km/sec, so Mars should retain its carbon dioxide. B)The average speed is 0.4 km/sec, so Mars should lose its carbon dioxide. C)The average speed is 1.9 km/sec, so Mars should retain its carbon dioxide. D)The average speed is 1.9 km/sec, so Mars should lose its carbon dioxide.

Question

Quizplus · Accepted Answer

The average speed of a carbon dioxide molecule at 290 K can be calculated using the formula for the root-mean-square speed, $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant ($1.38 \times 10^{-23} \, \text{J/K}$), $T$ is the temperature in Kelvin, and $m$ is the mass of a molecule in kilograms. Plugging in the values, we find that the average speed is significantly lower than the escape speed of Mars (5.0 km/sec), indicating that Mars should retain its carbon dioxide.

On Mars, the Temperature Can Reach 290 K and the Escape