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 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.The average translational kinetic energy of a nitrogen molecule is closest to A)4.0 × 10^-21 J. B)6.0 × 10^-21 J. C)8.0 × 10^-21 J. D)10 × 10^-21 J. E)12 × 10^-21 J.

Question

Quizplus · Accepted Answer

The average translational kinetic energy ($E_{k}$) of a molecule in an ideal gas is given by the equation $E_{k} = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature in Kelvin. Substituting the given values, $E_{k} = \frac{3}{2} \times 1.38 \times 10^{-23} \, \text{J/K} \times 290 \, \text{K} = 6.0 \times 10^{-21} \, \text{J}$.

A Sealed Container Holds 0