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

We can use the formula for the total translational kinetic energy of a gas:
KE = (3/2) nRT
Where n is the number of moles, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.

First, we need to find the total number of moles in the tank:
n_total = n_He + n_O2
n_total = 1.4 mol + 0.7 mol
n_total = 2.1 mol

Now we can calculate the total random translational kinetic energy of the gas:
KE = (3/2) n_total RT
KE = (3/2) (2.1 mol) (8.314 J/mol·K) (260 K)
KE ≈ 6.8 kJ

Therefore, the best choice is A, with an explanation as shown above.

A 50-Liter Gas Tank Holds 1