What is the average translational kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is $17 ^ { \circ } \mathrm { C } ?$ The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$
A) $6.01 \times 10 ^ { - 21 } \mathrm {~J}$
B) $7.00 \times 10 ^ { - 21 } \mathrm {~J}$
C) $5.00 \times 10 ^ { - 21 } \mathrm {~J}$
D) $9.00 \times 10 ^ { - 21 } \mathrm {~J}$
E) $4.00 \times 10 ^ { - 21 } \mathrm {~J}$

Question

Quizplus · Accepted Answer

The average translational kinetic energy of a molecule can be calculated using the formula $\frac{3}{2} kT$, where $k$ is the Boltzmann constant and $T$ is the temperature in Kelvin. To convert $17^\circ C$ to Kelvin, add 273, giving $290 K$. Thus, the average kinetic energy is $\frac{3}{2} \times 1.38 \times 10^{-23} \times 290 = 6.01 \times 10^{-21} J$.

What Is the Average Translational Kinetic Energy of a Nitrogen 17∘C?17 ^ { \circ } \mathrm { C } ?17∘C?

What Is the Average Translational Kinetic Energy of a Nitrogen $17 ^ { \circ } \mathrm { C } ?$