Final answer:
To find the temperature that corresponds to a given average velocity of carbon dioxide molecules, the root-mean-square velocity equation is used by rearranging it to solve for temperature. Substituting the given values for average velocity and molecular mass into the equation allows us to calculate the temperature.
Step-by-step explanation:
The question asks to determine the temperature corresponding to the observed average velocity of carbon dioxide molecules. The relationship between the root-mean-square velocity (Vrms or Urms), molecular mass, and temperature for an ideal gas is given by the equation:
\(Vrms = \sqrt{(3RT/M)}\)
Where:
- Vrms is the root-mean-square velocity of the gas molecules,
- R is the gas constant (8.314 J/mol·K),
- T is the absolute temperature in Kelvin,
- M is the molar mass of the gas in kilograms per mole (kg/mol).
Given the molecular mass of CO2 is 44.0 g/mol (0.044 kg/mol) and the average velocity Vrms is 420 m/s, we can rearrange the equation to solve for the temperature (T):
\(T = \frac{Vrms^2 \times M}{3R}\)
Plugging in the given values:
\(T = \frac{420^2 \times 0.044}{3 \times 8.314}\)
By calculating, we can find the correct temperature which can then be matched to the provided multiple-choice options.