Question

Calculate the total translational kinetic energy (in J) of $CH_4$ gas molecules, present in its 0.8 gm sample, at $27^\circ C)$

Answer 1

187.065 J

Answer 2

The translational kinetic energy of $n$ moles of a gas at temperature $T$ is given by $E_{trans} = \frac{3}{2} nRT$.

First, convert temperature to Kelvin: $T = 27^\circ C + 273 = 300$ K.

Calculate the number of moles of $CH_4$: Molar mass of $CH_4$ is $16$ g/mol. $n = \frac{0.8 \text{ g}}{16 \text{ g/mol}} = 0.05$ mol.

Using $R = 8.314$ J/mol.K, the total translational kinetic energy is: $E_{trans} = \frac{3}{2} \times 0.05 \text{ mol} \times 8.314 \text{ J/mol.K} \times 300 \text{ K}$ $E_{trans} = 187.065$ J.