A vessel of volume 0.00100 m³ contains 2.00 moles of an ideal gas at a pressure of 1.50 atmospheres. What is the total kinetic energy of the gas in the vessel? A) 175 J B) 228 J C) 267 J D) 303 J E) 367 J

Question

Quizplus · Accepted Answer

The total kinetic energy of an ideal gas is given by the equation $KE = \frac{3}{2} nRT$, where $n$ is the number of moles, $R$ is the ideal gas constant (8.314 J/mol·K), and $T$ is the temperature in Kelvin. To find $T$, we use the ideal gas law $PV = nRT$. Given $P = 1.50$ atm (which we convert to Pa by multiplying by 101325 Pa/atm), $V = 0.00100$ m³, and $n = 2.00$ moles, we can solve for $T$. First, convert pressure to Pascals: $1.50 \times 101325 = 151987.5$ Pa. Then, rearrange the ideal gas law to solve for $T$: $T = \frac{PV}{nR}$. Substituting the given values: $T = \frac{151987.5 \times 0.00100}{2.00 \times 8.314} = \frac{151.9875}{16.628} \approx 91.3$ K.Finally, calculate the kinetic energy: $KE = \frac{3}{2} \times 2.00 \times 8.314 \times 91.3 \approx 227.7$ J, which rounds to 228 J.

A Vessel of Volume 0