A container of volume 2.00 liters contains 2.00 moles of an ideal gas at a pressure of 1.50 atmospheres. What is the average kinetic energy per particle in the gas? A) 3.96 × 10^-22 J B) 3.78 × 10^-22 J C) 2.83 × 10^-22 J D) 2.52 × 10^-22 J E) 1.98 × 10^-22 J

Question

Quizplus · Accepted Answer

The average kinetic energy per particle in an ideal gas is given by the equation $KE_{avg} = \frac{3}{2}kT$, where $k$ is the Boltzmann constant ($1.38 \times 10^{-23} J/K$) and $T$ is the temperature in Kelvin. To find $T$, we use the ideal gas law $PV = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the ideal gas constant ($0.0821 L\cdot atm/(mol\cdot K)$), and $T$ is the temperature in Kelvin. Rearranging for $T$, we get $T = \frac{PV}{nR}$. Substituting the given values, $T = \frac{(1.50 atm)(2.00 L)}{(2.00 mol)(0.0821 L\cdot atm/(mol\cdot K))}$, we find $T$ and then calculate $KE_{avg}$. The correct calculation leads to the value closest to the option B, considering the units and constants involved.

A Container of Volume 2