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  • A container holds  of carbon dioxide gas <img alt="\left(\mathrm{CO}_{2}\right)

A container holds 0.1 \mathrm{~mol} of carbon dioxide gas \left(\mathrm{CO}_{2}\right) at a temperature of 400 \mathrm{~K}.

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

(b) Determine the average kinetic energy per molecule.

Given: Number of moles (n)=0.1 \mathrm{~mol} Temperature (T)=400 \mathrm{~K} 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

8.28 \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 } \mathrm{KE}=\frac{3}{2} \times 0.1 \times 8.31 \times 400 \mathrm{J}

Total\mathrm{KE}=996.6 \mathrm{~J}

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

\text { Average KE per molecule }=\frac{3}{2} k T

Plugging in the values:

Average KE per molecule =\frac{3}{2} \times 1.38 \times 10^{-23} \times 400 \mathrm{~J} 

Average KE per molecule =8.28 \times 10^{-21} \mathrm{~J}

So, the answers are: (a) The total translational kinetic energy of the carbon dioxide molecules is 996.6 \mathrm{~J}. (b) The average kinetic energy per molecule is 8.28 \times 10^{-21} \mathrm{~J}.

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Gunjita

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