The average kinetic energy of a molecule in air at room temperature of 20^ C

Step-by-step solution

The average kinetic energy of a molecule is given by the formula K_ avg = 3 2 k_ B T , where k_ B is the Boltzmann constant and T is the absolute temperature in Kelvin. Given temperature T = 20^ C = 20 + 273.15 = 293.15 ~K . The Boltzmann constant k_ B 1.38 10⁻²³ ~J/K . Substituting the values into the formula: K_ avg = 3 2 (1.38 10⁻²³ ~J/K ) 293.15 ~K K_ avg = 1.5 1.38 293.15 10⁻²³ ~J K_ avg = 2.07 293.15 10⁻²³ ~J K_ avg 606.82 10⁻²³ ~J K_ avg 6.0682 10⁻²¹ ~J Rounding to three significant figures, we get 6.07 10⁻²