A 10.0 L flask contains a mixture of neon and argon gases at a pressure of 2.38 atm. Calculate the total kinetic energy of the gaseous mixture.

• A. 2815 J
• B. 3620 J
• C. 3850 J
• D. 4750 J
• E. 5250 J

Answer: (B)

Verified step by step guidance

1. Start by recalling the formula for the kinetic energy of a gas, which is derived from the kinetic theory of gases. The average kinetic energy per mole of a gas is given by \( KE = \frac{3}{2} RT \), where \( R \) is the ideal gas constant and \( T \) is the temperature in Kelvin.
2. To find the total kinetic energy of the gaseous mixture, you need to determine the number of moles of gas in the flask. Use the ideal gas law \( PV = nRT \) to find \( n \), the number of moles, where \( P \) is the pressure, \( V \) is the volume, \( R \) is the ideal gas constant, and \( T \) is the temperature.
3. Rearrange the ideal gas law to solve for \( n \): \( n = \frac{PV}{RT} \). Substitute the given values for pressure (2.38 atm), volume (10.0 L), and the ideal gas constant \( R \) (0.0821 L atm/mol K). Assume a temperature if not provided, typically room temperature (298 K) is used.
4. Once you have calculated the number of moles \( n \), multiply it by the average kinetic energy per mole \( \frac{3}{2} RT \) to find the total kinetic energy of the gas mixture.
5. Ensure that all units are consistent when performing calculations, particularly when using the ideal gas constant. Convert any necessary units to ensure compatibility, such as converting pressure to atm and volume to liters if needed.