Molecular speeds: A 5.0-liter gas tank holds 1.4 moles of helium (He) and 0.70 moles of oxygen (O₂), at a temperature of 260 K. The atomic masses of helium and oxygen are 4.0 g/mol and 16.0 g/mol, respectively. Avogadro's number is 6.022 × 10²³ molecules/mol and the Boltzmann constant is 1.38 × 10^-23 J/K. The total random translational kinetic energy of the gas in the tank is closest to

Question

Quizplus · Accepted Answer

The total random translational kinetic energy of the gas in the tank is given by:$$E_k = (3/2)nRT$$where:* $n$ is the total number of moles of gas in the tank* $R$ is the ideal gas constant* $T$ is the temperature in KelvinIn this problem, we have:* $n = 1.4 	ext{ mol} + 0.70 	ext{ mol} = 2.1 	ext{ mol}$* $R = 8.31 	ext{ J/mol K}$* $T = 260 	ext{ K}$Plugging these values into the equation, we get:$$E_k = (3/2)(2.1 	ext{ mol})(8.31 	ext{ J/mol K})(260 	ext{ K}) = 6.8 	ext{ kJ}$$Therefore, the total random translational kinetic energy of the gas in the tank is closest to 6.8 kJ.

Molecular Speeds: a 5