QuestionApril 25, 2025

014 100 points Find the total translational kinetic energy of 3 L of oxygen gas held at a temperature of 9^circ C and a pressure of 0.5 atm.

014 100 points Find the total translational kinetic energy of 3 L of oxygen gas held at a temperature of 9^circ C and a pressure of 0.5 atm.
014 100 points Find the total translational kinetic energy of 3 L of oxygen gas held at a temperature of 9^circ C and a pressure of 0.5 atm.

Solution
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Answer

E_k \approx 52.7 \, J Explanation 1. Convert temperature to Kelvin T = 9^\circ C + 273.15 = 282.15 \, K 2. Use Ideal Gas Law to find moles PV = nRT, where P = 0.5 \, atm = 0.5 \times 101325 \, Pa, V = 3 \, L = 0.003 \, m^3, R = 8.314 \, J/(mol \cdot K). n = \frac{PV}{RT} = \frac{(0.5 \times 101325) \times 0.003}{8.314 \times 282.15} 3. Calculate translational kinetic energy **Translational Kinetic Energy** E_k = \frac{3}{2} nRT Substitute n from Step2 and calculate E_k.

Explanation

1. Convert temperature to Kelvin<br /> $T = 9^\circ C + 273.15 = 282.15 \, K$<br />2. Use Ideal Gas Law to find moles<br /> $PV = nRT$, where $P = 0.5 \, atm = 0.5 \times 101325 \, Pa$, $V = 3 \, L = 0.003 \, m^3$, $R = 8.314 \, J/(mol \cdot K)$.<br /> $n = \frac{PV}{RT} = \frac{(0.5 \times 101325) \times 0.003}{8.314 \times 282.15}$<br />3. Calculate translational kinetic energy<br /> **Translational Kinetic Energy** $E_k = \frac{3}{2} nRT$<br /> Substitute $n$ from Step2 and calculate $E_k$.
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