Question

A sealed container holds 0.020 moles of nitrogen (n2) gas, at a pressure of 1.5 atmospheres and a temperature of 290 k. the atomic mass of nitrogen is 14.0 g/mol. the boltzmann constant is 1.38 × 10-23 j/k and the ideal gas constant is r = 8.314 j/ mol · k = 0.0821 l · atm/mol · k. What is the average kinetic energy of the translational motion of a nitrogen molecule?

Answer 1

At 290 K, a nitrogen molecule exhibits an average translational kinetic energy of approximately 6.3 × 10^-21 J, illustrating the temperature-dependent nature of kinetic energy in accordance with the kinetic theory of gases.

The average kinetic energy of a nitrogen molecule in translational motion can be determined using the equation:

K = (3/2) * k_b * T

where K is the average kinetic energy, k_b is the Boltzmann constant (1.38 × 10^-23 J/K), and T is the temperature in Kelvin. Substituting the given values into the equation for a temperature of 290 K:

K = (3/2) * (1.38 × 10^-23 J/K) * (290 K)

K = 6.3 × 10^-21 J

The average kinetic energy of a nitrogen molecule's translational motion at 290 K is approximately 6.3 × 10^-21 J. This calculation exemplifies the relationship between temperature and kinetic energy as described by the kinetic theory of gases and underscores the microscopic nature of thermal motion in gases.