Calculate the average translational kinetic energy (kJ/molecule) for a molecule of NH3 at 431 K, assuming it is behaving as an ideal gas.
I understand how to figure out the kJ/mole, but I don't understand how to get the kJ/molecule that this question is asking for. Can someone please help me out here?
kJ/mol x (1 mol/6.022 x 10^23 molecules) = kJ/molecule.
1+2+3+4
To calculate the average translational kinetic energy in kJ/molecule, you need to consider Avogadro's number (6.022 x 10^23 molecules/mol) and convert the kJ/mol value to kJ/molecule.
Here's how you can do it:
1. Calculate the average translational kinetic energy per mole (kJ/mol) using the formula:
E = (3/2) * R * T
where:
- E is the average translational kinetic energy per mole
- R is the ideal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin (431 K)
E = (3/2) * 8.314 J/mol·K * 431 K = 16235.761 J/mol
2. Convert the average translational kinetic energy from Joules to kilojoules (kJ):
16235.761 J/mol ÷ 1000 = 16.235761 kJ/mol
3. Finally, divide the kJ/mol value by Avogadro's number to get the average translational kinetic energy per molecule:
16.235761 kJ/mol ÷ (6.022 x 10^23 molecules/mol) = 2.6999 x 10^-23 kJ/molecule
Therefore, the average translational kinetic energy per molecule of NH3 at 431 K is approximately 2.6999 x 10^-23 kJ/molecule.