Final answer:
The average kinetic energy of molecules can be calculated using the equation KE = 1/2mv². At a given temperature, the average kinetic energy of different molecules is the same. To calculate the average kinetic energy at specific temperatures, you need to know the masses of the molecules and use the equation KE = 1/2mv².
Step-by-step explanation:
The average kinetic energy of a molecule can be calculated using the equation KE = 1/2mv², where KE is the average kinetic energy, m is the mass of the molecule, and v is the root mean square (rms) speed of the molecule. At a given temperature, the average kinetic energy of different molecules is the same. To calculate the average kinetic energy at 273 K and 546 K, you need to know the masses of CH₄ and N₂ molecules. The molar mass of CH₄ is 16.04 g/mol, and the molar mass of N₂ is 28.01 g/mol.
Using the equation KE = 1/2mv², you can calculate the average kinetic energy of CH₄ and N₂ at 273 K and 546 K. First, calculate the rms speed by using the equation v = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass. Then, substitute the values into the equation KE = 1/2mv² to get the average kinetic energies.
For example, at 273 K:
RMS speed of CH₄ = √(3(8.314 J/(mol·K))(273 K)/(16.04 g/mol))
AVG kinetic energy of CH₄ = 1/2(16.04 g/mol)(RMS speed of CH₄)²