Final answer:
The question involves using the rms speed of carbon dioxide molecules to calculate the gas temperature. The Kinetic Theory of Gases provides a relationship between rms speed, the mass of a molecule, and temperature, allowing us to solve for temperature once we have the rms speed and molar mass.
Step-by-step explanation:
The student is asking about the relationship between the rms speed of carbon dioxide molecules and the temperature of a gas. In the context of an ideal gas, the rms speed (Urms) is related to temperature using the formula derived from the kinetic theory of gases:
Urms = sqrt(3kBT/m)
where Urms is the root-mean-square speed, kB is Boltzmann's constant (1.38 x 10-23 J/K), T is the temperature in kelvins, and m is the mass of one molecule. m can be calculated by dividing the molar mass by Avogadro's number. However, in this case, since we are provided with the rms speed and molar mass of carbon dioxide, we are rearranging to solve for T:
T = m(Urms)2 / (3kB)
First, we need to convert the molar mass to kilograms per mole (kg/mol) by dividing it by 1000, since it is given in grams per mole (g/mol). Then, we substitute the values into the equation to find the temperature.