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A gas sample in a container has a volume of 0.2 \mathrm{~m}^{3} and contains 0.3 \mathrm{~mol} of helium gas (\mathrm{He}) at a temperature of 25^{\circ} \mathrm{C}.

(a) Calculate the total translational kinetic energy of the helium molecules.

(b) Determine the average kinetic energy per molecule.

Given: Number of moles (n)=0.3 mol Temperature (T)=25^{\circ} \mathrm{C}=25+$ $273.15 \mathrm{~K} Volume (V)=0.2 \mathrm{~m}^{3} Universal gas constant (R)=8.31 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} (approximately) Boltzmann constant (k)=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K} (approximately)

Option: 1

1.64 \times 10^{-21} \mathrm{~J}


Option: 2

2.5 \times 10^{-21} \mathrm{~J}


Option: 3

8.84 \times 10^{-21} \mathrm{~J}


Option: 4

9.4 \times 10^{-21} \mathrm{~J}


Answers (1)

best_answer

(a) The total translational kinetic energy of a gas can be calculated using the formula:

\text { Total } \mathrm{KE}=\frac{3}{2} n R T

Plugging in the values:

\text { Total KE }=\frac{3}{2} \times 0.3 \times 8.31 \times(25+273.15) \text { J }

Total KE \approx 139.86 \mathrm{~J}

(b) The average kinetic energy per molecule can be calculated using the formula:

 

Plugging in the values:

Average KE per molecule =\frac{3}{2} \times 1.38 \times 10^{-23} \times(25+273.15) JAverage KE per molecule \approx 1.64 \times 10^{-21} \mathrm{~J}

So, the answers are: (a) The total translational kinetic energy of the helium molecules is approximately 139.86 \mathrm{~J}. (b) The average kinetic energy per molecule is approximately 1.64 \times 10^{-21} \mathrm{~J}.

Posted by

HARSH KANKARIA

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