What is the average kinetic energy per particle in 1.00 mole of an ideal gas at a pressure of 1.50 atmospheres and a temperature of $20^{\circ} \mathrm{C}$ ?
A) $6.03 \times 10-21 \mathrm{~J}$
B) $5.05 \times 10-21 \mathrm{~J}$
C) $4.75 \times 10-21 \mathrm{~J}$
D) $6.67 \times 10^{-21} \mathrm{~J}$
E) $6.07 \times 10^{-21} \mathrm{~J}$

Question

Quizplus · Accepted Answer

The average kinetic energy per particle in an ideal gas is given by the equation $\frac{3}{2}kT$, where $k$ is the Boltzmann constant ($1.38 \times 10^{-23} \mathrm{~J/K}$) and $T$ is the temperature in Kelvin. To convert $20^{\circ} \mathrm{C}$ to Kelvin, add 273.15, giving $293.15 \mathrm{~K}$. Plugging these values into the equation gives $\frac{3}{2} \times 1.38 \times 10^{-23} \mathrm{~J/K} \times 293.15 \mathrm{~K} = 6.07 \times 10^{-21} \mathrm{~J}$. Pressure is not directly used in calculating the average kinetic energy per particle for an ideal gas.

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