Final answer:
The thermal energy of 1 mole of atomic hydrogen at 0 degrees Celsius is calculated using the average kinetic energy formula for monatomic ideal gas, resulting in an internal energy of 3.77 x 10^3 J/mol.
Step-by-step explanation:
To calculate the thermal energy of 1 mole of atomic hydrogen at 0 degrees Celsius, we can use the formula for the average kinetic energy of the particles in an ideal monatomic gas, which is given by ½ kT per particle, or ¾ kT per mole, where k is Boltzmann's constant and T is the temperature in Kelvin.
At 0 degrees Celsius, the temperature in Kelvin is 273.15 K. Therefore, one mole of a monatomic ideal gas has a thermal energy calculated as:
E = ¾ kT
Remembering that 1 mole of a substance contains Avogadro's number (NA) of particles, and using the value for Boltzmann's constant (k = 1.38 × 10-23 J/K) and Avogadro's number (NA = 6.022 × 1023 particles/mol), the calculation is:
E = (3/2) × (1.38 × 10-23 J/K × 273.15 K) × NA
E = (3/2) × (1.38 × 10-23 J/K × 273.15 K) × 6.022 × 1023 mol-1
E = 3.77 × 103 J/mol
This is the internal energy of 1 mole of hydrogen gas at 0 degrees Celsius.