Final answer:
The temperature of a flame can be determined from the root-mean-square velocity of carbon dioxide molecules using kinetic theory and the ideal gas law. The molecular mass of carbon dioxide is used in the calculation, which needs to be in kilograms per molecule. Additional details such as the flame's pressure, density, and concentration of carbon dioxide require more information.
Step-by-step explanation:
The average velocity of carbon dioxide molecules in a flame can be used to calculate the temperature of the flame using the root-mean-square (rms) speed relation for an ideal gas. According to the equation for kinetic energy, KE = ½ mβ, and the definition of rms speed related to the temperature, v_{rms} = √(βk_BT/m), where k_B is the Boltzmann constant (1.38 × 10-23 J/K), T is the temperature in kelvins, m is the mass of one molecule, and β is the number of molecules. The molar mass of carbon dioxide (CO2) is 44.0 g/mol, which needs to be converted to kilograms per molecule for use in this equation. To find the temperature, we will rearrange the formula to T = m(v_{rms})2/(3k_B). With the given root-mean-square velocity of 1.05 × 103 m/s, we can plug in the values and calculate the temperature.
The calculation of pressure, density, and concentration of carbon dioxide in the flame would require additional information, such as the volume of the gas and the number of moles present.