Consider three identical flasks filled with different gases. Flask A: \(\mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask B: \(\mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask C: \(\mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?

The flasks are all at \(0^{\circ} \mathrm{C}\). Since temperature is the same for all three flasks, the molecules are sharing the same average kinetic energy. To find the difference in velocity, let's look at molecular mass.

The molecular masses for the gases in each flask are as follows: Flask A: Carbon monoxide (CO) has a molecular mass of 12 + 16 = 28 g/mol. Flask B: Nitrogen (N2) has a molecular mass of 28 g/mol (14 x 2 = 28 g/mol). Flask C: Hydrogen (H2) has a molecular mass of 2 g/mol (1 x 2 = 2 g/mol).

Since temperature is the same for all three flasks, the molecules in each flask have the same average kinetic energy. Therefore, the answer for part (a) is that all flasks A, B, and C have equal average kinetic energy.

The relationship between molecular mass and molecular velocity is given by the equation: \(v_{rms} = \sqrt{\dfrac{3RT}{M}}\) where \(v_{rms}\) is the root mean square velocity, R is the gas constant (8.314 J/mol K), T is the temperature (0°C = 273.15 K), and M is the molar mass in kg/mol. For Flask A, the average velocity is: \[ v_{A} = \sqrt{\dfrac{3(8.314)(273.15)}{0.028}}\] For Flask B, the average velocity is: \[ v_{B} = \sqrt{\dfrac{3(8.314)(273.15)}{0.028}}\] For Flask C, the average velocity is: \[ v_{C} = \sqrt{\dfrac{3(8.314)(273.15)}{0.002}}\] Now, comparing the average velocities: Since 0.028 > 0.002, \(v_{C} > v_{A} = v_{B}\). Therefore, the answer for part (b) is that Flask C (Hydrogen gas) has the greatest average velocity among the molecules of all flasks.