Final answer:
The root-mean-square speed of a molecule in Mars's atmosphere can be calculated using the formula v_rms = sqrt(3RT/M), with the gas constant R, the temperature in Kelvin T, and the molar mass of CO2 M. After unit conversions and calculations, the rms speed can be determined.
Step-by-step explanation:
The student has inquired about calculating the root-mean-square (rms) speed of a molecule in Mars's atmosphere, which is known to be largely composed of carbon dioxide, with temperatures averaging around -63 °C. Assuming the value of the gas constant R is 8.315 J/mol·K, and given that the rms speed (vrms) is derived from the formula vrms = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of carbon dioxide (CO2). The calculation requires firstly converting the temperature to Kelvin: -63 °C + 273.15 = 210.15 K. Then, the molar mass of CO2, which is about 44.01 g/mol, needs to be converted to kg/mol by dividing by 1000, resulting in 0.04401 kg/mol. Now we can plug these values into the equation: vrms = √(3 * 8.315 J/mol·K * 210.15 K / 0.04401 kg/mol), which yields the rms speed of a CO2 molecule in the Martian atmosphere.