Questions: Calculate the average translational kinetic energy, Ek, for one mole of gas at 801 K. Translational kinetic energy is sometimes called average kinetic energy. Ek= J / mol Calculate the average translational kinetic energy for a single gas molecule at 801 K. Ek= J / molecule

Solution Steps

The average translational kinetic energy per mole of gas is given by: \[ E_{\mathrm{k}} = \frac{3}{2} RT \] where \( R \) is the universal gas constant (\(8.314 \, \mathrm{J/(mol \cdot K)}\)) and \( T \) is the temperature in Kelvin.

Given \( T = 801 \, \mathrm{K} \), we substitute this value into the formula: \[ E_{\mathrm{k}} = \frac{3}{2} \times 8.314 \, \mathrm{J/(mol \cdot K)} \times 801 \, \mathrm{K} \]

Perform the multiplication: \[ E_{\mathrm{k}} = \frac{3}{2} \times 8.314 \times 801 \] \[ E_{\mathrm{k}} = 3 \times 4.157 \times 801 \] \[ E_{\mathrm{k}} = 3 \times 3330.657 \] \[ E_{\mathrm{k}} = 9991.971 \, \mathrm{J/mol} \]

The average translational kinetic energy per molecule is given by: \[ E_{\mathrm{k}} = \frac{3}{2} k T \] where \( k \) is the Boltzmann constant (\(1.38 \times 10^{-23} \, \mathrm{J/K}\)) and \( T \) is the temperature in Kelvin.

Given \( T = 801 \, \mathrm{K} \), we substitute this value into the formula: \[ E_{\mathrm{k}} = \frac{3}{2} \times 1.38 \times 10^{-23} \, \mathrm{J/K} \times 801 \, \mathrm{K} \]

Perform the multiplication: \[ E_{\mathrm{k}} = \frac{3}{2} \times 1.38 \times 10^{-23} \times 801 \] \[ E_{\mathrm{k}} = 2.07 \times 10^{-23} \times 801 \] \[ E_{\mathrm{k}} = 1.65807 \times 10^{-20} \, \mathrm{J/molecule} \]

Final Answer