A sealed container holds 0.020 moles of ideal nitrogen $\left( \mathrm { N } _ { 2 } \right)$ gas, at a pressure of 1.5 atm and a temperature of 290 K. The atomic mass of nitrogen is 14.0 g/mol. What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$
A) $4.0 \times 10 ^ { 21 } \mathrm {~J}$
B) $8.0 \times 10 ^ { 21 } \mathrm {~J}$
C) $12 \times 10^{21} \mathrm {~J}$
D) $6.0 \times 10^{21} \mathrm {~J}$
E) $10 \times 10^{21} \mathrm {~J}$

Question

A sealed container holds  0.020  moles of ideal nitrogen $\left( \mathrm { N } _ { 2 } \right)$ gas, at a pressure of  1.5 atm and a temperature of  290 K. The atomic mass of nitrogen is  14.0 g/mol. What is the average translational kinetic energy of a nitrogen molecule? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$
A) $4.0 \times 10 ^ { 21 } \mathrm {~J}$
B) $8.0 \times 10 ^ { 21 } \mathrm {~J}$
C) $12 \times 10^{21} \mathrm {~J}$
D) $6.0 \times 10^{21} \mathrm {~J}$
E) $10 \times 10^{21} \mathrm {~J}$

Quizplus · Accepted Answer

The average translational kinetic energy ($E_{\text{kin}}$) of a molecule in an ideal gas is given by the equation $E_{\text{kin}} = \frac{3}{2} kT$, where $k$ is the Boltzmann constant and $T$ is the temperature in Kelvin. Substituting the given values, $E_{\text{kin}} = \frac{3}{2} \times 1.38 \times 10^{-23} \mathrm{J/K} \times 290 \mathrm{K} = 6.0 \times 10^{-21} \mathrm{J}$.

A Sealed Container Holds 0 (N2)\left( \mathrm { N } _ { 2 } \right)(N2​)

A Sealed Container Holds 0 $\left( \mathrm { N } _ { 2 } \right)$