Final answer:
The total translational kinetic energy of 1.0 mole of diatomic oxygen at 50°C is directly related to its absolute temperature. The kinetic energy depends on the temperature as shown in the ideal gas law with kinetic energy being ¾NkT, where T is the temperature in Kelvin. The correct answer is b) Independent of its temperature.
Step-by-step explanation:
The student's question pertains to the total translational kinetic energy of 1.0 mole of diatomic oxygen at 50°C. From the principles of thermodynamics and ideal gas behavior, we understand that the average kinetic energy of a molecule in a gas is directly proportional to its absolute temperature (measured in Kelvin).
Since this is true for any ideal gas, and the question simplifies to an ideal scenario, the translational kinetic energy of a mole of any gas, including diatomic oxygen, is dependent on temperature.
The correct answer to the question is that the total translational kinetic energy of 1.0 mole of diatomic oxygen at 50°C is directly related to its absolute temperature.
This relationship is formalized in the equation derived from the ideal gas law: KE = ½mv² = ¾NkT, where KE is the total translational kinetic energy, m is the mass of a molecule, v is the velocity, N is the Avogadro's number for one mole of particles, k is Boltzmann's constant, and T is the absolute temperature.
The temperature must be converted to Kelvin, which is done by adding 273.15 to the Celsius temperature. Given the temperature of 50°C, the equivalent in Kelvin is 323.15 K. The ideal gas law further supports this, as it relates pressure, volume, and temperature to the kinetic energy of a gas.